Performance Evaluation of OFDM Technique for High Speed Communication Applications

by

Mukul Kabra

A Thesis Submitted in Partial Fulfillment of the Requirements for the Degree of

Master of Technology in Information and Communication Technology to Dhirubhai Ambani Institute of Information and Communication Technology Gandhinagar, India

May, 2005

DA-IICT

Declaration This is to certify that (i) the thesis comprises my original work towards the degree of Master of Technology in Information and Communication Technology at DA-IICT and has not been submitted elsewhere for a degree, (ii) due acknowledgement has been made in the text to all other material used.

Signature of Student (Mukul Kabra)

Certificate

This is to certify that the thesis work entitled “Performance Evaluation of OFDM Technique for High Speed Communication Applications” has been carried out by Mukul Kabra (200311034) for the degree of Master of Technology in Information and Communication Technology at this Institute under my supervision.

Thesis Supervisor (Prof. S.L. Maskara)

i

Acknowledgements

I would like to thank my advisor Prof. S. L. Maskara for his invaluable advice, patience, and support during the work on this thesis. It has been a pleasure as well as a privilege to have had the opportunity to work with him. I would like to thank my committee members Prof. V. P. Sinha, Prof. V. K. Chakka for their expert help and valuable feedback on the thesis. I wish to convey warmest thanks to my parents and my sister Shruti, for providing encouragement and support during work on this thesis. I would like to thank my parents for the inspiration and support they have provided throughout my life. I would like to thank Alok, Sudhir, Gangadhar, Kunal for the many hours of white board discussion, and support. I would also like to thank Dharmendra, Awkash, Krutarth for their support as friends and for sharing my excitement of discoveries made during this thesis. I would particularly like to thank Prof. S.L. Maskara for his motivational discussions about research and publications. Finally, I would like to thank my computer for only crashing seriously once during the writing of this thesis.

ii

Contents Page No.

1

Abstract

v

List of Principal Symbols and Acronyms

vi

List of Figures

viii

List of Tables

xi

Introduction 1.1 1.2 1.3 1.4 1.5

2

3

1 Orthogonal Frequency Division Multiplexing and its Potential……. 1 Motivation………………………………………………………….. 3 Objectives…………………………………………………………... 4 Approach to work…………………………………………………... 5 Thesis Organization………………………………………………… 5

OFDM Principles and Review

6

2.1 2.2 2.3 2.4 2.5 2.6

Orthogonal Frequency Division Multiplexing Basics……………… Theory of OFDM…………………………………………………… Advances in Digital Signal Processing……………………………... Fading channel Characteristics……………………………………... OFDM System……………………………………………………… Major Applications………………………………………………….

6 11 14 15

2.7 Literature Survey and Review of OFDM…………………………...

29

Simulation of OFDM in Wireless LAN application

36

3.1 3.2 3.3 3.4

Wireless Local Area Network Description…………………………. Channel Models for Wireless LAN………………………………… Simulation of OFDM based Wireless LAN………………………... Wireless LAN standards…………………………………………….

36 37 40 47

3.5 Performance Results………………………………………………...

58

iii

21 28

4

Performance of OFDM in Digital Audio Broadcasting 4.1 Digital Audio Broadcasting………………………………………... 4.2 Channel models for DAB………………………………………….. 4.3 Simulation of Digital Audio Broadcasting System………………... 4.4 Performance Results………………………………………………..

66 66 67 68 74

5

Study of OFDM Application in Asymmetric Digital Subscriber Lines 5.1 Digital Subscriber Lines…………………………………………… 5.2 Application of OFDM in Asymmetric Digital Subscriber Lines….. 5.3 Implementation of OFDM based ADSL…………………………... 5.4 Performance Results……………………………………………….

78 78 80 81 90

6

92 Summary and Conclusion Discussion of Results……………………………………………… 92 Conclusion…………………………………………………………. 93 References Appendix A

95 98

iv

Abstract The Internet revolution has created the need for wireless technologies that can deliver data at high speeds in a spectrally efficient manner. However, supporting such high data rates with sufficient robustness to radio channel impairments requires careful selection of modulation techniques. The demand for high-speed mobile wireless communications is rapidly growing. OFDM technology promises to be a key technique for achieving the high data capacity and spectral efficiency requirements for wireless communication systems of the near future. Orthogonal frequency division multiplexing (OFDM) is a special case of multicarrier transmission, where a single data stream is transmitted over a number of lower rate subcarriers. OFDM is currently being used in Europe for digital audio and video broadcasting. The IEEE standardization group decided to select OFDM as the basis for their new 5-GHz standard, targeting a range of data stream from 6 up to 54 Mbps. This standard was the first one to use OFDM in packet-based communications, while the use of OFDM until now was limited to continuous transmission systems. OFDM is also being considered as a serious candidate for fourth generation cellular systems. In this project, transmitter, channel and receiver were simulated with various parameters, to evaluate the performance and different possibilities in the implementation. Also, some considerations about forward error correction coding, interleaving, synchronization and channel estimation are given to improve the system performance.

v

List of Principal Symbols and Acronyms φ(t) ∆f φh(τ) τrms

BC Bd hb(t,τ) KMOD N n(t) Td TS TFFT Xi(t) Xk(f) 2G 3G 4G ADC ADSL ASC AP BER BPSK CCK COFDM CP CSI DA DAB DAC DBLAST DD DDS DFT DSL DVB DVB-T DSSS EGC FEC FEQ FFT FHSS

Subcarrier in time domain Frequency spacing between orthogonal subcarriers Channel correlation function RMS delay spread Coherence bandwidth Doppler spread of the channel Baseband representation of time varying channel Normalization factor for different constellations Number of IFFT point Additive white Gaussian noise in time domain Coherence time OFDM symbol duration FFT duration Transmitted ith OFDM signal in time domain kth subcarrier of OFDM signal in frequency domain 2nd Generation 3rd Generation 4th Generation Analog-to-Digital Converter Asymmetric Digital Subscriber Lines Antenna Selection Combining Access Point Bit Error Rate Binary Phase Shift Keying Complementary Code Keying Coded Orthogonal Frequency Division Multiplexing Cyclic Prefix Channel State Information Data Aided Algorithms Digital Audio Broadcasting Digital-to-Analog Converter Diagonal Bell Labs Layered Space-Time Decision Directed Direct Digital Synthesis Discrete Fourier Transform Digital Subscriber Line Digital Video Broadcasting Digital Video Broadcasting - Terrestrial Direct Sequence Spread Spectrum Equal Gain Combining Forward Error Correction Frequency domain equalizer Fast Fourier Transform Frequency Hopping Spread Spectrum vi

FM HDSL HDTV HiperLAN ICI IDFT IFFT IR ISI LOS LMS LMMSE MAN MARC MIMO MMAC MMSE MRC MSE NDA NLOS OFDM PAPR POTS PRS PBCC PHY QAM QoS QPSK RF RMS SNR SSC STC TEQ VBLAST VDSL WLAN W-OFDM WSS

Frequency Modulation High-bit-rate Digital Subscriber Lines High Definition TeleVision High Performance Radio Local Area Networks Inter Carrier Interference Inverse Discrete Fourier Transform Inverse Fast Fourier Transform Infra Red Inter Symbol Interference Line-Of-Sight Least Mean Square Linear Minimum Mean Squared Error Metropolitan Area Networks Maximum Average (Signal-to-Noise) Ratio Combining Multiple Input Multiple Output Multimedia Mobile Access Communications Systems Minimum Mean Squared Error Maximum Ratio Combining Mean Squared Error Non Data-Aided Algorithms Non Line-Of-Sight Orthogonal Frequency Division Multiplexing Peak-to-Average Power Ratio Plain Old Telephone System Phase reference symbol for DAB Packet Binary Convolutional Coding Physical Layer Quadrature Amplitude Modulation Quality of Service Quadrature Phase Shift Keying Radio Frequency Root-Mean-Square Signal-to-Noise Ratio Subcarrier Selection Combining Space-Time Coding Time domain Equalizer Vertical Bell Labs LAyered Space-Time Very-high-speed Digital Subscriber Lines Wireless Local Area Networks Wideband Orthogonal Frequency Division Multiplexing Wide Sense Stationary

vii

List of Figures Page No. Figure 2.1

Comparison of OFDM with FDM for spectral efficiency

7

Figure 2.2

Time domain construction of an OFDM signal

9

Figure 2.3

Frequency response of the subcarriers in a 5 tone OFDM signal

11

Figure 2.4

Multipath Propagation (Tx- Transmitter, Rx- Receiver)

15

Figure 2.5

Fading channel manifestations

17

Figure 2.6

Complete transmission model of OFDM system

21

Figure 2.7

Constellation diagram for 64 QAM

23

Figure 2.8

Baseband implementation of OFDM scheme

24

Figure 2.9

Effect of Cyclic Prefix in OFDM

25

Figure 2.10

RF up conversion techniques

26

Figure 2.11

Pilot subcarrier arrangement in OFDM symbol

28

Figure 3.1

Impulse response of ETSI channel model A to E

39

Figure 3.2

Data Scrambler

41

Figure 3.3

Convolutional Encoder (Constraint length k = 7)

42

Figure 3.4

Effect of Convolutional Coding and soft Viterbi Decoding

43

Figure 3.5

(a) Transmitted Constellation with QPSK modulation, 128 subcarriers (before normalization), (b) Received Constellation with 6 dB SNR in AWGN channel

Figure 3.6

44

(a) Transmitted Constellation with 16-QAM modulation (before normalization), (b) Received Constellation with 12dB SNR in AWGN channel

44

Figure 3.7

Transmitted waveforms of OFDM signal, 64 QAM Modulation

45

Figure 3.8

PSD of the transmitted OFDM signal 64 subcarrier (48 data, 4 pilot and 12 null subcarriers) with 64QAM Modulation

Figure 3.9

(a) Received Constellation without equalization in 24 Mbps mode, (b) with equalization, in Channel model A with 12dB SNR

Figure 3.10

45 46

(a) Received Constellation without equalization in 24 Mbps mode, (b) with equalization, in Channel model E with 12dB SNR

viii

46

Figure 3.11

(a) Received Constellation without equalization in 54 Mbps mode, (b) with equalization, in Channel model A with 24dB SNR

46

Figure 3.12

PPDU Frame format for the IEEE 802.11a standard

49

Figure 3.13

OFDM training symbol structure (from IEEE 802.11a standard)

50

Figure 3.14

Coding and interleaving performance of 12 Mbps mode (a) in non fading channel and (b) ETSI channel model A

52

Figure 3.15

Subcarrier frequency allocation

53

Figure 3.16

Inputs and Outputs of IFFT

53

Figure 3.17

OFDM frame with cyclic extension and windowing for two receptions of the FFT period

Figure 3.18

54

(a) Auto-Correlation curve and Cross-Correlation peaks for ideal case (No noise, no multipath), (b) Auto-Correlation curve and Cross-Correlation peaks for SNR=10dB and multipath delay spread 60 ns and no frequency offset

Figure 3.19

56

SNR requirements for CP length of 100, 200, 400 and 800 ns in channel model A (max delay spread = 300 ns), v=50 km/hr for different modulation schemes

Figure 3.20

59

Comparison of SNR requirements for number of subcarriers 64, 128 and 256 with 16 QAM Modulation and CP = 800 ns (a) in channel model E, (b) in JTC channel model C, (c) AWGN channel

Figure 3.21

Effect of FEC and Interleaving at different data rates in frequency selective fading channel model A

Figure 3.22

61

The IEEE 802.11a standard for Data rate of (a) 6 Mbps, (b) 12 Mbps and (c) 24 Mbps in ETSI channels A to E

Figure 3.23

60

62

The IEEE 802.11a standard for Data rate of (a) 36 Mbps, (b) 48 Mbps and (c) 54 Mbps in ETSI channels A to E

63

Figure 3.24

Performance in ETSI Channel model A for different data rates

64

Figure 3.25

Performance of modulation schemes in (a) AWGN channel (b) in JTC channel model A without coding and interleaving

Figure 3.26

65

BER performance of OFDM with different modulation schemes in (a) JTC channel model B and C without coding and interleaving

ix

65

Figure 4.1

Impulse response of Urban Area

68

Figure 4.2

Effect of selective channel on the transmitted OFDM signal

68

Figure 4.3

Block diagram of a DAB transmitter

70

Figure 4.4

Structure of the DAB transmission frame

70

Figure 4.5

OFDM signal after D/A converter in time and frequency domain

74

Figure 4.6

OFDM signal after LPF in time and frequency domain

74

Figure 4.7

DAB Transmitted signal (a) in time domain (b) in frequency domain, for mode 1 having 2048 subcarriers

75

Figure 4.8

Rayleigh fading Envelope and phase response at 100 km/hr speed

75

Figure 4.9

BER v/s SNR Curves for Rayleigh fading channels at different speed for transmission mode 1

76

Figure 4.10

Performance for different fading channels for transmission mode-1

77

Figure 4.11

Performance for different fading channels for transmission mode-2

77

Figure 5.1

ADSL Frequency Plan

80

Figure 5.2

Block diagram of a ADSL Transceiver using DMT

82

Figure 5.3

(a) SNR (b) bit allocation for given SNR at each subcarrier for CSA Loop-1

Figure 5.4

83

The fast and interleaved bit streams are merged together and are thereafter transmitted to the tone order

Figure 5.5

84

The constellation points for odd number of bits. (a) 8-QAM and (b) 32-QAM

85

Figure 5.6

Generation of real signal from IFFT

86

Figure 5.7

Channel impulse response for CSA Loop – 1 in time domain before and after channel shortening

88

Figure 5.8

Frequency response of CSA Loop-1

89

Figure 5.9

The adaptive LMS algorithm that is used in FEQ

89

Figure 5.10

Effect of frequency domain equalization on constellations

91

x

List of Tables Page No. Table 2.1

Evaluation of the FFT Complexity

15

Table 2.2

Evaluation of the FFT Complexity

15

Table 2.3

Typical Delay Spread

19

Table 3.1

Channel model for HIPERLAN/2 at 5GHz

38

Table 3.2

Delay profile for channel A to E

38

Table 3.3

JTC Channel Model Parameters for Indoor Office Areas

39

Table 3.4

Physical Layer parameters for WLAN simulation

40

Table 3.5

Modulation-dependent normalization factor KMOD

43

Table 3.6

Rate dependent parameter for the IEEE 802.11a standard

48

Table 3.7

Physical layer parameters for the IEEE 802.11a standard

48

Table 3.8

SNR comparison of different length of cyclic prefix

59

Table 3.9

SNR comparison of different no. of subcarriers for BER of 10-4

59

Table 3.10

SNR comparison for different data rates for the IEEE 802.11a

61

Table 3.11

SNR comparison for various modulation schemes

65

Table 4.1

Delay profile of different channels for DAB

67

Table 4.2

Definition of the parameters for transmission modes I, II and III

71

Table 4.3

SNR requirements for Transmission Mode 1 and 2 for BER 10-4

77

Table 5.1

High speed data communication standards

78

Table 5.2

Physical Layer Parameters for DMT (OFDM) based ADSL

81

Table 5.3.

Simulation results for different CSA Loop channels

91

Table A.1

BPSK encoding table

98

Table A.2

QPSK encoding table

98

Table A.3

16 QAM encoding table

98

Table A.4

64 QAM encoding table

98

xi

Chapter 1

Introduction 1.1

Orthogonal Frequency Division Multiplexing and its Potential

The Orthogonal Frequency Division Multiplexing (OFDM) technique has the potential of enhancing data rates in a band-limited channel in general and under fading condition in particular. In OFDM, multiple subcarriers, each with relatively smaller bandwidth are used to transmit the user’s information requiring relatively higher bandwidth. Instead of transmitting high data rates on a single carrier requiring high bandwidth, in OFDM, the high data rate signal is split into many low data rate streams, which are then transmitted on multiple closely spaced orthogonal carriers. In fact the bandwidth of each subcarrier should be made small compared with the coherence bandwidth of fading channel. In other words, the symbol period of a sub-stream is made large compared to the delay spread of the time dispersive radio channel. Further, the choice of orthogonal subcarriers to each other makes the adjacent subcarriers spacing minimal. Such kind of signal processing results in considerable reduction of the overall bandwidth compared to a single carrier system. OFDM therefore supports higher data rates over channels with limited bandwidth. Implementation of OFDM transmitter and receiver is considerably simplified because of use of Inverse Discrete Fourier Transform (IDFT) using digital signal processing techniques. These features have resulted in wide range applications of OFDM, both in wireline as well as wireless communication systems. Orthogonality of frequencies in OFDM makes it possible to arrange the subcarriers in such a way that the sidebands of the individual carriers overlap and still the signals are received at the receiver without being interfered by ICI. The receiver acts as a bank of demodulators, translating each subcarrier down to DC, with the resulting signal integrated over a symbol period to recover raw data. If the other subcarriers are all down converted to the baseband frequencies, that in the time domain they have a whole number of cycles in a symbol period TS, then the integration process results in zero contribution from all other subcarriers. Thus, the subcarriers are orthogonal (i.e. linearly independent) if the carrier spacing is a multiple of 1/ TS [1].

1

Although OFDM has only recently been gaining interest from telecommunications industry, it has a long history of existence. It is reported that OFDM based systems were in existence during the Second World War. In US military, several high frequency military systems such as KINEPLEX, ANDEFT and KATHRYN had used OFDM. In December 1966, Robert W. Chang [1] outlined a theoretical way to transmit simultaneous data stream through linear band limited channel without Inter Symbol Interference (ISI) and Inter Carrier Interference (ICI). Subsequently, he obtained the first US patent on OFDM in 1970. Around the same time, Saltzberg [2] performed an analysis of the performance of the OFDM system. Until this time, we needed a large number of subcarrier oscillators to perform parallel modulations and demodulations. A major breakthrough in the history of OFDM came in 1971, when Weinstein and Ebert [3] used Discrete Fourier Transform (DFT) to perform baseband modulation and demodulation focusing on efficient processing. This eliminated the need for bank of subcarrier oscillators, thus paving the way for easier, more useful and efficient implementation of the system. All the proposals until this time used guard spaces in frequency domain and a raised cosine windowing in time domain to combat ISI and ICI. Another milestone for OFDM history was when Peled and Ruiz [4] introduced Cyclic Prefix (CP) or cyclic extension in 1980. This solved the problem of maintaining orthogonal characteristics of the transmitted signals at severe transmission conditions. The generic idea that they placed was to use cyclic extension of OFDM symbols instead of using empty guard spaces in frequency domain. This effectively turns the channel as performing cyclic convolution, which provides orthogonality over dispersive channels, when CP is longer than the channel impulse response [5]. It is obvious that introducing CP causes loss of signal energy proportional to length of CP compared to symbol length, but, on the other hand, it facilitates a zero ICI advantage which pays off. By this time, inclusion of FFT and CP in OFDM system and substantial advancements in Digital Signal Processing (DSP) technology made OFDM an important part of telecommunications landscape. In the 1990s, OFDM was exploited for wideband data communications over mobile radio FM channels, High-bit-rate Digital Subscriber Lines (HDSL at 1.6Mbps), Asymmetric Digital Subscriber Lines (ADSL up to 6Mbps) and Very-high-speed Digital Subscriber Lines (VDSL at 100Mbps). Digital Audio Broadcasting (DAB) was the first commercial use of OFDM technology. By 1992, DAB was proposed and the standard was formulated by ETSI in 1994 but this service came to 2

reality in 1995 in UK and Sweden. Digital Video Broadcasting (DVB) along with HighDefinition TeleVision (HDTV) terrestrial broadcasting standard was published in 1995. Several Wireless Local Area Network (WLAN) standards adopted OFDM on their physical layers. Development of European WLAN standard High Performance LAN (HiperLAN) started in 1995. HiperLAN/2 was defined in June 1999 [15], which adopts OFDM in physical layer. Recently IEEE 802.11a [14] in USA has also adopted OFDM in their PHY layer. The primary applications of OFDM are in multimedia push technology, wireless LAN and xDSLs. It has also been suggested for power line communications systems [18] due to its resilience to time dispersive channels and narrow band interferers. Perhaps of even greater importance is the emergence of this technology as a competitor for future 4th Generations (4G) wireless systems. These systems, expected to emerge by the year 2010, promise to at last deliver on the wireless Nirvana of anywhere, anytime, anything communications. Should OFDM gain prominence in this arena, and telecom giants are banking on just this scenario, then OFDM will become the technology of choice in most wireless links worldwide.

1.2

Motivation

Wireless communication has gained momentum in the last decade of 20th century with the success of 2nd Generations (2G) of digital cellular mobile services. With the advent of 3rd Generation (3G) wireless systems, it is expected that higher mobility with reasonable data rate (up to 2Mbps) can be provided to meet the current user needs. But, 3G is not the end of the tunnel; ever increasing user demands have drawn the industry to search for better solutions to support data rates of the range of tens of Mbps. Naturally dealing with ever unpredictable wireless channel at high data rate communications is not an easy task. Hostile wireless channel has always been proved as a bottleneck for high-speed wireless systems. This motivated the researchers towards finding a better solution for combating all the odds of wireless channels; thus, the idea of multi-carrier transmission has surfaced recently to be used for future generations of wireless systems. At high data rates, the channel distortion to the data is very significant, and it is somewhat impossible to recover the transmitted data with a simple receiver. A very complex receiver structure is needed which makes use of computationally extensive equalization and channel estimation algorithms, such that the estimations can be used with the received data to recover the originally transmitted data. OFDM can drastically simplify the equalization problem by 3

turning the frequency selective channel to a flat channel. A simple one-tap equalizer is needed to estimate the channel and recover the data. Future telecommunication systems must be spectrally efficient to support a number of high data rate users. OFDM uses the available spectrum very efficiently, which is very useful for multimedia communications. Orthogonal Frequency Division Multiplexing promises a higher user data rate and great resilience to severe signal fading effects of the wireless channel at a reasonable level of implementation complexity. It has been taken as the primary physical layer technology in high data rate Wireless LAN/MAN standards. IEEE 802.11a and HiperLAN/2 have the capability to operate in a range of a few tens of meters in typical office space environment. In the upcoming standard IEEE 802.20, which is targeted at achieving data rate of greater than 1 Mbps at 250 kmph, OFDM is one of the potential candidates. The industry has not offered any interface yet. Many companies are still researching and developing, over all for the receiver, which is the key part of the system. The standard does not give rules about it and its implementation is up to the designer. Pure OFDM or hybrid OFDM will be most likely the choice for physical layer multiple access technique in the future generation of telecommunication systems. Thus we see that there is a strong possibility that next generation wireless era belongs to OFDM technology.

1.3

Objectives

This thesis investigates the effectiveness of Orthogonal Frequency Division Multiplexing (OFDM) as a modulation technique for wireless and wireline applications. The main aim was to evaluate the performance of OFDM as a modulation technique for high data rate applications. Several of the main factors effecting the performance of a OFDM system, were measured including multipath delay spread, channel noise, modulation scheme, error control coding, interleaving, distortion of the signal (clipping), and time and frequency synchronization requirements. Objective of this thesis is to acquire a sound understanding of OFDM technology and to evaluate the performance of some of the important applications of OFDM like WLAN, DAB and DSL by simulating the transmitter, fading channel, as encountered in practical scenarios and the receiver. This thesis basically finds the performance of OFDM in practical selective channels for various applications.

4

1.4

Approach to Work

Performance of OFDM has been studied for various communication applications through extensive simulation. To compare the performance with different parameter variations, different Matlab scripts have been written and simulation have been done for each block of transmitter, receiver and channel, to access the performance of OFDM system. For practical measurements, data has been taken from a stored text or image or sound file and transmitted using some OFDM application. After applying the channel effect to the transmitted signal, the data is recovered at the receiver and again written into the file for comparison of input to output. Bit error rate versus SNR has been taken as the main performance evaluation criterion in different channel environments for different applications. A file having size of tens of kilobytes has been read so that at least BER of 10-5 can be measured with acceptable simulation time.

1.5

Thesis Organization

The report is structured as follows. Introduction to the OFDM basics and analytical model of OFDM has been discussed in chapter 2. In the same chapter different impairments of radio channel for high data rates have been discussed, a general OFDM system have been explained with basic block diagram, literature survey and review of the OFDM have been given, which includes OFDM implementation issues and recent work done for the same. In chapter 3, basic WLAN description, different channel models for WLAN with general OFDM parameters for physical layer have been considered and results are shown. WLAN standard, IEEE 802.11a and HIPERLAN/2 have been simulated and results have been obtained as specific example of application of OFDM. Next chapter considers Digital Audio Broadcasting as another applications of OFDM. General description, channel models for DAB and simulation of physical layer have been given. Finally, the performance results for different modes have been given and discussed. Chapter 5 includes one wireline application, Asymmetric Digital subscriber Lines, for providing high data rate with twisted pair. This chapter basically provides a study of ADSL as application of OFDM and simulation of ADSL standard. Chapter 6 concludes the report by discussing the result obtained and key research issues related to the development of OFDM wireless system aimed at high data rate.

5

Chapter 2

OFDM and Background and Review 2.1

Orthogonal Frequency Division Multiplexing Basics

OFDM is a modulation scheme that allows digital data to be efficiently and reliably transmitted over a radio channel, even in multipath environments. OFDM transmits data using a large number of narrow bandwidth carriers. These carriers are regularly spaced in frequency, forming a block of spectrum. The frequency spacing and time synchronisation of the carriers is chosen in such a way that the carriers are orthogonal, meaning that they do not cause interference to each other, despite the overlapping of subcarriers with each other in the frequency domain. The name ‘OFDM’ is derived from the fact that the digital data is sent using many carriers, each of a different frequency (Frequency Division Multiplexing) and these carriers are orthogonal to each other, hence Orthogonal Frequency Division Multiplexing. OFDM is a special form of FDM. In conventional broadcasting, each radio station transmits on a different frequency, effectively using FDM to maintain a separation between the stations. There is however no coordination or synchronization between each of these stations. With an OFDM transmission such as DAB, the information signals from multiple stations is combined into a single multiplexed stream of data. This data is then transmitted using an OFDM ensemble that is made up from a dense packing of many subcarriers. All the subcarriers within the OFDM signal are time and frequency synchronised to each other, allowing the interference between subcarriers to be carefully controlled. These multiple subcarriers overlap in the frequency domain, but do not cause Inter-Carrier Interference (ICI) due to the orthogonal nature of the modulation. Typically, with FDM, the transmission signals need to have a large frequency guard-band between channels to prevent interference. This lowers the overall spectral efficiency. However with OFDM, the orthogonal packing of the subcarriers greatly reduces this guard band, improving the spectral efficiency as can be seen from the Figure 2.1.

6

Conventional FDM

Orthogonal FDM

Figure 2.1 Comparison of OFDM with FDM for spectral efficiency Each of the carriers in a FDM transmission can use an analogue or digital modulation scheme. There is no synchronisation between the transmission and so one station could transmit using FM and another in digital using FSK. In a single OFDM transmission all the subcarriers are synchronised to each other, restricting the transmission to digital modulation schemes. OFDM technique is symbol based, and can be treated as a large number of low bit rate carriers transmitting in parallel. All these carriers transmit in unison using synchronised time and frequency, forming a single block of spectrum. This is to ensure that the orthogonal nature of the structure is maintained. Since these multiple carriers form a single OFDM transmission, they are commonly referred to as ‘subcarriers’, with the term of ‘carrier’ reserved for describing the RF carrier mixing the signal from base band. There are several ways of looking at what makes the subcarriers in an OFDM signal orthogonal and why this prevents interference between them. Coded Orthogonal Frequency Division Multiplexing (COFDM) is the same as OFDM except that forward error correction is applied to the signal before transmission. Orthogonality . Orthogonality is a property that allows multiple information signals to be transmitted perfectly over a common channel and detected, without interference because orthogonal signals can be treated as mutually independent of each other. Loss of orthogonality results in blurring between these information signals and degradation in communications. Many 7

common multiplexing schemes are inherently orthogonal. Time Division Multiplexing (TDM) allows transmission of multiple information signals over a single channel by assigning unique time slots to each separate information signal. During each time slot only the signal from a single source is transmitted preventing any interference between the multiple information sources. Because of this TDM is orthogonal in nature. In the frequency domain most FDM systems are orthogonal as each of the separate transmission signals are well spaced out in frequency preventing interference. Although these methods are orthogonal the term OFDM has been reserved for a special form of FDM. The subcarriers in an OFDM signal are spaced as close as is theoretically possible while maintain orthogonality between them (see Figure 2.2). It was Chang [1] and Saltzburg [2] who realized that if the subchannel spacing (∆f) is equal to the reciprocal of symbol period (Ts), then the modulated signals would be orthogonal and could readily be separated by correlation using a conventional matched filter or correlator. Let ∆ f = 1 / TS (where TS is the “useful” symbol period over which the receiver

integrates the demodulated signal). Then k

th

carrier (at baseband) is written as:

e j 2πkΛ f t , 0 <= t <= T Θk (t ) =   0, otherwise

(2.1)

where k∆f is the frequency of the kth subcarrier. and the orthogonality condition that carriers should satisfy is: τ + Ts

∫τ

 0, Θ k ( t ) Θ *p ( t ) dt =  T S ,

for for

k ≠ p k = p

(2.2)

An OFDM signal consists of N such orthogonal subcarriers modulated by N parallel data streams. The baseband frequency of each subcarrier is chosen to be an integer multiple of the inverse of the symbol time, resulting in all subcarriers having an integer number of cycles per symbol. As a consequence the subcarriers are orthogonal to each other. Figure 2.1 shows the construction of an OFDM signal with five subcarriers.

8

(a) (b) (c) (d) (e)

(f)

Figure 2.2 Time domain construction of an OFDM signal

In this example data to be transmitted is of 1 Mbps having 1µs symbol (bit) duration, shown in Figure 2.2 (a). For simplicity this example uses only 5 subcarriers. First bit out of five bits shown, modulates first subcarrier (BPSK) and so on. After modulation symbol duration of each subcarrier becomes five times (5µs) the original symbol (bit) duration. If we transmit all these five subcarriers in parallel then the symbol duration will increased five times the original symbol duration but total data transmitted in given duration is still same i.e. 1 Mbps (each subcarrier transmit only 200 Kbps). This increased symbol duration helps to combat dispersive nature of multipath channel because frequency selective nature of channel depends upon the symbol time. These five subcarriers are orthogonal to each other as the frequency difference between consecutive subcarrier is equal to the inverse of the symbol duration of OFDM symbol (200 KHz in this case as symbol duration is 5µs). Figure 2.2 (b), (c), (d), (e) and (f) show individual subcarriers, with 1, 2, 3,4 and 5 cycles per symbol respectively. The initial phase on all these subcarriers is zero. Note, that each subcarrier has an integer number of cycles per symbol, making them cyclic. Adding a copy of the symbol to the end would result in a smooth join between symbols. Sets of functions are orthogonal to each other if they match the orthogonality conditions in equation (2.2). 9

Equation (2.2) also represents the common procedure of demodulating a subcarrier using multiplication with a carrier of the same frequency (“beating it down to zero frequency”) and then integrating the result. Multiplying the two sine waves together is the same as mixing these subcarriers, which results in sum and difference frequency components. Any different carriers within the set of orthogonal subcarriers will give rise to “beat tones”, which are at integer multiples and have an integer number of cycles during the integration period, thus integrates to zero. Another way of thinking of this is that, if we look at a matched receiver for one of the orthogonal functions, a subcarrier in the case of OFDM, then the receiver will only see the result for that function. The results from all other functions in the set integrate to zero, and thus have no effect. Thus we have established that the frequency components are orthogonal to each other and without any “explicit” filtering and any mutual cross-talk, we can separately demodulate all the carriers, just by our particular choice for the carrier spacing. Furthermore, we have not wasted any spectrum either (in fact we have conserved the bandwidth as compared to simple FDM). Frequency Domain Orthogonality

Another way to view the orthogonality property of OFDM signals is to look at its spectrum. In the frequency domain each OFDM subcarrier has a sinc, sin(x)/x, frequency response, as shown in Figure 2.3. This is a result of the symbol time corresponding to the inverse of the carrier spacing. As far as the receiver is concerned each OFDM symbol transmitted for a fixed time (TS ) with no tapering at the ends of the symbol. This symbol time corresponds to the inverse of the subcarrier spacing of 1 / TS Hz. This rectangular, boxcar, waveform in the time domain results in a sinc (i.e. sin ( x ) / x ) frequency response in the frequency domain. The sinc shape has a narrow main lobe, with many side-lobes that decay slowly with the magnitude of the frequency difference away from the center. Each carrier has a peak at the center frequency and nulls evenly spaced with a frequency gap equal to the carrier spacing. The orthogonal nature of the transmission is because of the peak of each subcarrier corresponds to the nulls of all other subcarriers. When this signal is detected using a Discrete Fourier Transform (DFT) the spectrum is not continuous as shown in Figure 2.3, but has discrete samples. The sampled spectrum are shown as ‘o’s in the figure. If the DFT is time synchronised, the frequency samples of the DFT correspond to just the peaks of the subcarriers, thus the overlapping frequency region between subcarriers does not 10

affect the receiver. The measured peaks correspond to the nulls for all other subcarriers, resulting in orthogonality between the subcarriers.

Figure 2.3 Frequency response of the subcarriers in 5 subcarriers OFDM signal (a) Spectrum of each subcarrier, and the discrete frequency samples seen by an OFDM

receiver, (b) Overall combined response of the 5 subcarriers (thick black line)

2.2

Theory of OFDM

Transmitter

An OFDM signal consists of a sum of subcarriers that are modulated by using any linear modulation method, such as Phase Shift Keying (PSK) or Quadrature Amplitude Modulation (QAM) [5]. Serial to parallel converted low data rate bit streams are first FEC coded, interleaved and then mapped to the signal constellation (in-phase (XI(k)) and quadrature-phase XQ(k) component) using M-QAM or M-PSK modulation. This process will map the given M bits to a symbol X(k) = XI(k)+jXQ(k), where k = 0,1,2 K N − 1 and

N is the number of subcarriers. Angle of the complex quantity X(k) represents phase and th

magnitude of X(k) represents the amplitude of k subcarrier. If k∆f is the k

th

subcarrier

frequency and TS is the symbol period, then the transmitted baseband signal for i OFDM symbol, xi (t ) can be expressed [13] as equation (2.3):

N−1 j 2πk∆ t  xi (t) = Re∑ Xi (k)e f  ; k = 0,1,2KN −1 k =0 

(2.3)

N −1

xi (t ) = ∑ ( X i I (k )cos(2πk∆ f t ) + X i Q (k ) sin(2π∆ f t ) k =0

where ∆ f =

1 ; basic criterion for OFDM Ts

(2.4)

11

th

If Cyclic prefix is used with OFDM symbol then equation becomes

 N−1 xi (t) = Re∑Xi (k)φ(t − iTS ) ; k = 0,1,2KN −1 for 0 < t < TS  k=0 φ(t) in the above equation is the transmitter waveform that can be expressed as:

(2.5)

1  j 2πk∆ f ( t −TCP ) e ; if t ∈ [0, TS ]  (2.6) φ (t ) =  TS − TCP 0 ; otherwise  where N∆f is the total available bandwidth and TCP seconds of TS is used as the Cyclic

Prefix (CP). Note that φ (t ) = φ (t + NTS ) , when t is within the cyclic prefix [0, TCP ] . From equation (2.5) & (2.6), X i (t ) gives the transmitted signal as a Fourier transform of the digital source signal with the useful data part of subcarrier symbol period as TU = TS − TCP

When an infinite sequence of OFDM symbols is transmitted (which is the practical scenario), then the output from the transmitter, which is the combination of signals representing all individual OFDM symbols as presented in equation (2.7): ∞  ∞ N −1  x(t) = ∑ xi (t) = Re ∑ ∑ Xi (k) φ (t − iTS ) i =−∞ i =−∞ k =0 

(2.7)

  ∞ N−1  1 j 2πk∆ (t−T −T )  Xi (k) e f CP S  ; for t ∈[0,TS ] Re∑ ∑ =  i=−∞ k=0 T −T  S CP   0 ; otherwise 

(2.8)

Transmission over Frequency-Selective Wireless Channel

The signal in equation (2.8) is transmitted over the frequency-selective channel, which is comprised of the actual Channel Impulse Response (CIR). The baseband impulse response hb(t,τ) of a multipath channel can be expressed as hb (t ,τ ) =

hb (t , τ ) =

L −1

∑ h (t )δ (τ − τ (t )) i=0

l

(2.9)

i

L −1

∑ a (t ,τ ) exp [ j (2πf τ (t ) + ϕ i =0

i

c

i

i

(t , τ ) )]δ (τ − τ i (t ))

(2.10)

Here L denotes the number of available multipath in the channel and ai(t,τ), ϕi(t,τ) and τi represents attenuation, phase and delay of the ith multipath component, respectively. We will assume that channel taps are uncorrelated with respect to each other and can be modeled as a Wide Sense Stationary (WSS) process where the average energy of the

12

channel energy is normalized to one and the delays τi are taken to be constant for the time of interest. Receiver

The received signal y(t), corresponding to the stream of transmitted OFDM symbols is:

y (t ) = x (t ) ⊗ hb (t ,τ ) + n (t ) =





−∞

x (t − τ ) hb (t ,τ ) d τ + n (t )

(2.11)

where n(t) is the Additive White Gaussian Noise (AWGN) and notation ∗ means linear convolution. Notice that CP is removed after the reception of the signal in equation (2.11). We also have removed the constant term,

1 TS − TCP

for simplicity of calculation.

At the subcarrier level, received signal on the kth subcarrier for ith OFDM symbol is: T

[

]

1 S  N −1  − j 2πp∆ f t j 2πk∆ f t Yi ( p) = ∫ ∑ X i (k )e * hb (t ) + n(t )e dt T TCP  k =0  1 Yi ( p ) = T

TS

 N −1 ∫ ∑ [X i ( k ) * hb (t ) ]e TCP  k = 0

j 2π k∆ f t

 − j 2π p ∆ f t + n (t ) e dt 

(2.12)

Note that the subcarrier index on the transmitter side is denoted with k and on the receiver side with p. They are shown differently to prove the orthogonal behavior of OFDM signals. In practice, there is no difference between k and p. From equation (2.2), it is obvious that the end result of equation (2.1) will be zero if kth transmitted carrier and pth received carrier are not the same carrier. We denote Θ(t, k) and Θ (t, p). So, equation (2.13) can now be written as: T

Yi ( p ) =

1 S  N −1 [X i (k ) * hb (t )]Θ(t , k ) + n(t )Θ ∗ (t , p)dt ∑  ∫ T TCP  k = 0  T

1 S  N −1  Yi ( p ) = ∫ ∑ [X i (k ) * hb (t )]Θ(t , k ) Θ ∗ (t , p ) + n(t )Θ ∗ (t , p ) dt T TCP  k = 0 

(2.13)

Using conditions of equation (2.2) in equation (2.13), it is clear that the output signal will only be noise for p ≠ k . For p = k , the signal can effectively be recovered provided that the channel effect is sufficiently minimized. In this way, by maintaining orthogonality of the subcarrier signals, the received signals from different subcarriers can be separated successfully at the receiver without any Inter Carrier Interference (ICI).

13

Similar to equation (2.3), we can see that equation (2.12) is actually a DFT operation. Thus, OFDM modulation can efficiently be done using Fourier transform.

2.3

Advances in Digital Signal Processing

OFDM was not used prominently for many years because for a large number of subchannels, the arrays of sinusoidal generators and coherent demodulators required in a parallel system become unreasonably expensive and complex. At transmitter, the spectral representation (amplitude and phase) of the data is converted into time domain using an Inverse Discrete Fourier Transform (IDFT). Figure 2.6 shows the block diagram of a typical OFDM transceiver. In practice OFDM systems employs IFFT and FFT algorithms to synthesize the signal at the transmitter and to demodulate the received signal at the receiver respectively. The FFT and IFFT are simply the efficient computational tools for complete digital implementation of DFT and IDFT respectively. Digital filter bank that basically performs DFT may be substituted for when the number of subcarriers are less than 32. For a large number of subcarriers, FFT based systems are computationally more efficient. There is no significant difference [22] in implementation complexity for an FFT with a number of points between 64 and 512. The IFFT and the FFT are complementary function and the most appropriate term depends on whether the signal is being received or generated. In cases where the signal is independent of this distinction then the term FFT and IFFT is used interchangeably. The complexity of performing an FFT is dependent on the number of FFT points. The larger the FFT, the greater the number of calculations required; however since the symbol period is longer, the increased processing required is less then the straight increase in processing to perform a single FFT. Table 2.1 shows the number of calculations required for an FFT (radix-2) of size N, and also the relative processing for various FFT sizes. It can be seen that as the symbol period increases with a larger FFT, the extra processing required is minimal. The processing efficiency of a DSP processor depends on the architecture of the processor; however for most single instruction DSPs the number of cycles required to calculate an FFT is double the total number of calculations shown in Table 2.1. This is due to complex calculations requiring two operations per calculation.

14

Table 2.1 Evaluation of the FFT Complexity FFT size (N)

Total number of complex calculations

32 64 128 256 512 1024 2048 4096

240 576 1344 3072 6912 15360 33792 73728

Relative processing required for OFDM generation (normalized to 1024 points) 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2

Table 2.2 Evaluation of the FFT Complexity FFT size

Clocks required

64 128 256 512 8192

48 96 144 240 4220

Speed in (µs) for 50 MHz clock 0.96 1.92 2.88 4.80 84.48

RAM (Kbits)

Gates Count

2.3 12 20 220

32 30 28 30 50

In fact, the IFFT can be made using an FFT by conjugating input and output of the FFT and dividing the output by the FFT size. This makes it possible to use the same hardware for both the transmitter and the receiver. Of course, this saving in complexity is only possible when the modem does not have to transmit and receive simultaneously, which is the case for the WLAN applications.

2.4

Fading Channel Characteristics

A transmitted signal, which experiences the influence of reflection, refraction and scattering, from objects such as hills, buildings, vehicles, trees or human being, reaches the receiver via many different paths. This phenomenon is called multipath propagation.

Figure 2.4 Multipath Propagation (Tx- Transmitter, Rx- Receiver)

15

Each replica of the signal arriving at the receiver has traveled over a different distance and thus has suffered from different amplitude attenuation, phase shift, and arrives with a different time delay. The receiver collects a superposition of all multipath signals, which can lead either to signal enforcement or to radical signal cancellation giving rise to the term multipath fading. These phenomena are explained below. •

Reflection occurs when an electromagnetic wave encounters a smooth and large (compared to the wavelength of the signal) surface. The wave is then reflected from the surface.



Diffraction occurs when the propagation path between the transmitter and receiver is obstructed by a dense body with dimensions that are large when compared to λ, causing secondary waves to be formed behind the obstructing body. It is often termed shadowing because the diffracted field can reach the receiver even when shadowed by an impenetrable obstruction i.e. non line-of-sight.



Scattering occurs when a radio wave impinges on either a large rough surface or any surface whose dimensions are on the order of λ or less, causing the energy to be spread out (scattered) or reflected in all directions. In an urban environment, typical signal obstructions that yield scattering include lampposts, street signs, and foliage.

Figure 2.5 represents an overview of fading-channel manifestations. It starts with two types of fading effects that characterize mobile communications: large-scale fading and small-scale fading. Large-scale fading represents the average signal power attenuation or the path loss due to motion over large areas. In Figure 2.5, the large-scale fading manifestation is shown in blocks 1, 2, and 3. This phenomenon is affected by prominent terrain contours (hills, forests, billboards, clumps of buildings, and so on) between the transmitter and the receiver. The receiver is often said to be “shadowed” by such prominences. The statistics of large-scale fading provide a way of computing an estimate of path loss as a function of distance. This is described in terms of a mean-path loss (nthpower law) and a log-normally distributed variation about the mean.

16

Figure 2.5 Fading channel manifestations

Small-scale fading refers to the dramatic changes in signal amplitude and phase that can be experienced as a result of small changes (as small as a half wavelength) in the spatial positioning between a receiver and a transmitter. As indicated in Figure 2.5 blocks 4, 5, and 6, small-scale fading manifests itself in two mechanisms: time spreading of the signal (or signal dispersion) and time-variant behavior of the channel. For mobile-radio applications, the channel is time-variant because motion between the transmitter and the receiver results in propagation path changes. The rate of change of these propagation conditions accounts for the fading rapidity (rate of change of the fading impairments). Small-scale fading is called Rayleigh fading if there are multiple reflective paths that are large in number and there is no line-of-sight signal component; the envelope of such a received signal is statistically described by a Rayleigh pdf. When a dominant nonfading signal component is present, such as a line-of-sight propagation path, the small-scale fading envelope is described by a Rician pdf [6]. In other words, the small-scale fading statistics are said to be Rayleigh whenever the line-of-sight path is blocked, and Rician otherwise. The two manifestations of small-scale fading, signal time-spreading (signal dispersion) and the time-variant nature of the channel are examined in two domains: time and frequency, as indicated in Figure 2.5 blocks 7, 10, 13, and 16. For signal dispersion, the fading degradation types are categorized as being frequency-selective or frequency-

17

nonselective (flat), as listed in blocks 8, 9, 11, and 12. For the time-variant manifestation, the fading degradation types are categorized as fast-fading or slow-fading, as listed in blocks 14, 15, 17, and 18. Channel correlation functions

Channel correlation functions are used to exploit the channel characterization. Since the nature of the channel is random, the channel impulse response function can be replaced by a set of autocorrelation functions, which gives a better description of the unpredictable behavior of the channel. The channel (baseband) impulse response function can be seen as a complex random process. The autocorrelation function of h(τ;t) is then defined as follows

φh (τ 1 ,τ 2 ; t1 , t 2 ) = E [h* (τ 1 ; t1 )h(τ 2 ; t 2 )] 1 2

(2.14)

where h* denotes the complex conjugation. In many situations it is reasonably to assume that the channel is wide sense stationary. This implies, that the given autocorrelation function depend on the time difference between them ∆t= t2 - t1 only. Consequently,

φh (τ 1 ,τ 2 ; ∆t ) = E [h* (τ 1 ; t )h(τ 2 ; t + ∆t )] 1 2

(2.15)

If we now assume uncorrelated scattering, which means that the signals coming via different paths experience uncorrelated attenuations, phase shifts and time delays, the formula (9) transforms to

[

]

1 E h* (τ 1 ; t )h(τ 2 ; t + ∆t ) = φh (τ 1 ; ∆t )δ (τ 1 − τ 2 ) 2

(2.16)

In this case, the channel is said to be a wide sense stationary uncorrelated scattering channel. If now the time difference ∆t is set to zero, the resulting autocorrelation function

φh(τ) = φh(τ;0) describes the time spread of the channel. This function is called multipath intensity profile or the delay power spectrum and represents the average power output of the channel as a function of the time delay τ. The function is decaying since there is a limited time during which all the multipath components arrive at the receiver. Hence, the function also provides a measure for the time dispersion of the channel. The measure is called the rms delay spread of the channel, is denoted by τrms and defined as the square root of the second central moment of the power delay profile (where PDP = |h(t)|2) by the formula

18

τ rms =

(t − τ m )2 PDP(t ) dt

(2.17)

Gc

where τm is the average delay time and Gc is the average channel power response . By analogy, the equivalent autocorrelation function in the frequency domain is defined by

φ H ( f1 , f 2 ; ∆t ) = E [H * ( f1 ; t )H ( f 2 ; t + ∆t )] 1 2

(2.18)

The function is derived under the same assumption that the channel is wide sense stationary. If we now assume the uncorrelated scattering, then the function depends only on the frequency difference ∆f = f2 - f1 and not on the particular frequencies. Then function (2.18) transforms to

φ H ( f1 , f 2 ; ∆t ) = φ H (∆f ; ∆t )

(2.19)

φH is called the spaced-frequency, spaced-time correlation function. Again, if ∆t=0, the derived function φH(∆f) = φH(∆f;0) is the Fourier transform of the multipath intensity profile. It provides the information about the channel’s coherence in the frequency domain. The measure for this coherence is called the coherence bandwidth of the channel Bc, which is related to the rms delay spread as BC ≈

1

(2.20)

ατ rms

where α = 2π in case of the exponentially decaying PDP. When the coherence bandwidth is small compared to the bandwidth of the transmitted signal, the channel affects different frequencies of the signal spectrum differently; the channel is said to be frequency selective. However, if the bandwidth of the transmitted signal is narrow compared to the coherence bandwidth of the channel, all the frequency components of the signal undergo the same attenuation; then the channel is said to be frequency nonselective. Table 2.3. Typical Delay Spread Environment or cause

Delay Spread

Maximum Path Length Difference

Indoor (room)

40 nsec- 200 nsec

12m –60m

Outdoor

1µsec – 20 µsec

300m –6km

Doppler shift

In this section we investigate the Doppler shift, which is caused by the time variations of the channel. The spaced-frequency, spaced-time correlation function is considered again.

19

We define the Fourier transform of this function with respect to ∆t. The resulting function is given by ∞

S H ( ∆f ; λ ) = ∫ φ H (∆f ; ∆t )e − j 2πλ∆t d∆t

(2.21)

−∞

where λ is the Doppler frequency. If we set ∆f =0, relation (15) becomes ∞

S H (λ ) = ∫ φ H ( ∆f ; ∆t )e − j 2πλ∆t d∆t

(2.22)

−∞

The resulting function SH(λ) is the Doppler power spectrum of the channel and represents the power spectrum of the signal as a function of the Doppler frequency λ. The function gives a measure for the spectral broadening of the channel due to the Doppler effect. This measure is called the Doppler spread of the channel (Bd). The Doppler spread has also its equivalent in the time domain, which is the coherence time Td ≈

1 Bd

(2.23)

The coherence time is a measure for the time span over which the channel remains approximately constant. The scattering function is expressed by the formula below ∞

S (τ ; λ ) = ∫ φ h (τ ; ∆t )e −∞

− j 2πλ∆t



d∆t =

∫S

H

( ∆t ; λ )e j 2πλ∆f d∆f

−∞

20

(2.24)

2.5

OFDM System

A complete OFDM transceiver system is described in Figure 2.6. In this model, Forward Error Control/Correction (FEC) coding and interleaving are added in the system to obtain the robustness needed to protect against burst errors. An OFDM system with addition of channel coding and interleaving is referred to as Coded OFDM (COFDM).

Figure 2.6 Complete transmission model of OFDM system

Each block of the system is briefly explained in this section. Implementation detail is being discussed in upcoming chapters pertaining to specific applications. Scrambler

Nulls in the frequency response of the channel can cause the information sent in neighboring carriers to be destroyed, resulting in a clustering of the bit errors in each symbol. Most Forward Error Correction (FEC) schemes tend to work more effectively if the errors are spread evenly, rather than in large clusters, and so to improve the performance most systems employ data scrambling as part of the serial to parallel conversion stage. This is implemented by randomising the subcarrier allocation of each sequential data bit. At the receiver the reverse scrambling is used to decode the signal. This restores the original sequencing of the data bits, but spreads clusters of bit errors so that they are approximately uniformly distributed in time. This randomisation of the location of the bit errors improves the performance of the FEC and the system as a whole. Error Control Coding and Interleaving

OFDM has potential to convert the frequency selective fading case in a flat fading case, provided the length of cyclic prefix is greater than the delay spread of the channel. An efficient FEC coding in flat fading situations leads to a very high coding gain, especially

21

if soft decision decoding is applied. In a single carrier modulation, if such a deep fade occurs, too many consecutive symbols may be lost and FEC may not be too effective in recovering the lost data [23]. Experiences show that basic OFDM system is not able to obtain a BER of 10−5 or 10−6 without channel coding. Thus, all OFDM systems now a day are converted to COFDM. The benefits of COFDM are two-fold in terms of performance improvement. First, the benefit that the channel coding brings in, that is the robustness to burst error. Secondly, interleaving brings frequency diversity. Different systems employs different kind of FEC schemes, like convolutional coding, Reed Soloman coding, Trellis Coding, Turbo Coding etc. Turbo coding provides data rates of near Shannon limits but not suitable for many of the applications because of large processing delays. Deep fades in the spectrum may cause groups of OFDM subcarriers to be less reliable than others, thereby causing bit errors to occur in bursts rather than being randomly scattered. Interleaving is applied to randomize the occurrence of bit errors prior to decoding. The interleaver ensures that adjacent outputs from channel encoder are placed far apart in frequency domain. Specifically for a ½ rate encoder, the channel encoder provides two output bits for one source bit. When they are placed far apart from each other (i.e. placed on subcarriers that are far from each other in frequency domain), then they experience unique gain (and/or unique fade). It is very unlikely that both of the bits will face a deep fade, and thus at least one of the bits will be received intact on the receiver side, and as a result, overall BER performance will improve Serial to Parallel Conversion

Data to be transmitted is typically in the form of a serial data stream. In OFDM, each symbol typically transmits 40 - 4000 bits, and so a serial to parallel conversion stage is needed to convert the input serial bit stream to the data to be transmitted in each OFDM symbol. The data allocated to each symbol depends on the modulation scheme used and the number of subcarriers. For example, for a subcarrier modulation of 16-QAM each subcarrier carries 4 bits of data, and so for a transmission using 100 subcarriers the number of bits per symbol would be 400. For adaptive modulation schemes, the modulation scheme used on each subcarrier can vary and so the number of bits per subcarrier also varies. As a result the serial to parallel conversion stage involves filling the data payload for each subcarrier. At the receiver the reverse process takes place, with the data from the subcarriers being converted back to the original serial data stream.

22

Subcarrier Modulation (Constellation Mapping)

Once each subcarrier has been allocated bits for transmission, they are mapped using a modulation scheme to a subcarrier amplitude and phase, which is represented by a complex In-phase and Quadrature-phase (IQ) vector. Figure 2.7 shows an example of subcarrier modulation mapping with gray coding. This example shows 64-QAM, which maps 6 bits for each symbol. Each combination of the 6 bits of data corresponds to a unique IQ vector, shown as a dot on the figure. A large number of modulation schemes are available allowing the number of bits transmitted per carrier per symbol to be varied.

Figure 2.7 Constellation diagram for 64 QAM Modulation

Subcarrier modulation can be implemented using a lookup table, making it very efficient to implement. In the receiver, mapping the received IQ vector back to the data word performs the subcarrier demodulation function. For each received IQ vector the receiver has to estimate the most likely original transmission vector. This is achieved by finding the transmission vector that is closest to the received vector. Errors occur when the noise exceeds half the spacing between the transmission IQ points, making it cross over a decision boundary. Frequency To Time Domain Conversion

After the subcarrier modulation stage each of the data subcarriers is set to an amplitude and phase based on the data being sent and the modulation scheme; all unused subcarriers are set to zero. Constellation mapping process maps the given M bits to a symbol X(k) = XI(k)+jXQ(k). At the transmitter, OFDM system treats these symbols as though they are in

23

the frequency domain. An IFFT is thus used to convert the signal to time domain, allowing it to be transmitted. The IFFT drastically reduce the amount of calculations by exploiting the regularity of the operations in IDFT. Using the radix-2 algorithm, an Npoint IFFT requires only (N / 2 ) log 2 ( N ) complex multiplications [5]. For instance, in a 16-point transform a reduction by a factor of 8 can be achieved as 256 multiplications are required for the IDFT whereas only 32 for the IFFT. This difference grows for larger numbers of subcarriers. Use of radix-4 algorithm can reduce the number of multiplications in the IFFT even further. Figure 2.8 shows the IFFT section of the OFDM transmitter. In the frequency domain, before applying the IFFT, each of the discrete samples of the IFFT corresponds to an individual subcarrier. Most of the subcarriers are modulated with data. The outer subcarriers are unmodulated and set to zero amplitude. These zero subcarriers provide a frequency guard band before the Nyquist frequency and effectively act as an interpolation of the signal and allows for a realistic roll off in the analog anti-aliasing reconstruction filters.

Figure 2.8. Baseband implementation of OFDM scheme Guard time and Cyclic Prefix

OFDM deals with multipath very efficiently. The parallel transmission implies that the input data stream is divided in N subcarriers and the symbol duration is made N times smaller, which also reduces the relative multipath delay spread, relative to the symbol time, by the same factor.

24

Figure 2.9 Use of Cyclic Prefix in OFDM (a) multipath with small relative delay, (b)

multipath with large delay The intersymbol interference is almost completely eliminated by introducing a guard time for each OFDM symbol. This important contribution was due to Peled and Ruiz [4] in 1980, who introduced the cyclic prefix (CP) or cyclic extension, solving the orthogonality problem. Instead of using an empty guard space, they filled the guard space with a cyclic extension of the OFDM symbol (Figure 2.9 a) to eliminate the sudden change in waveform (which contain higher spectral components) and hence intercarrier interference (ICI). This effectively simulates a channel performing cyclic convolution, which implies orthogonality over dispersive channels when the CP is longer than the impulse response of the channel. . The guard time is chosen larger than the expected delay spread such that multipath components from one symbol cannot interfere with the next symbol. Using this method, the delay replicas of the OFDM symbol always have an integer number of cycles within the FFT interval, as long as the delay is smaller than the guard time. Cyclic Prefix ensures that all the information integrated comes from the same symbol and appears constant during it. Multipath signals with delays smaller than the guard time cannot cause ICI. Introduction of Cyclic Prefix adds energy loss proportional to the length of the CP, but the zero ICI generally compensate for this loss. If the integration period spans two symbols (as for the delayed paths in Figure 2.9 b), not only there will be same carrier ISI, but in addition there will be inter-carrier interference (ICI) as well. This happens because the beat tones from other carriers may no longer integrate to zero if they change in phase and/or amplitude during the period. Multipath delays exceeding the guard time by a small fraction of the FFT interval (for example 3%), the subcarriers are not orthogonal anymore, but the interference is still small enough to get a reasonable constellation. Considering that the multipath delay exceeds the guard time by 10% of the FFT interval, the constellation is seriously affected and an unacceptable error rate is obtained.

25

Windowing

Essentially, an OFDM signal consists of a number of unfiltered QAM subcarriers. This means that the out-of-band spectrum decreases rather slowly, following a sinc function. For larger number of subcarriers, the spectrum goes down rapidly in the beginning, which is caused by the fact that the sidelobes are closer together. To make the spectrum decrease faster, windowing is applied to the OFDM signal. Several conventional windows were simulated including raised cosine, Hanning, Hamming, Blackman and Kaiser. RF Modulation (Up Conversion)

The output of the OFDM modulator generates a base band signal, which must be mixed up to the required transmission frequency. This can be implemented using analog techniques as shown in Figure 2.10 (a) or using a Digital Up Converter as shown in Figure 2.10 (b). Both techniques perform the same operation, however the performance of the digital modulation will tend to be more accurate due to improved matching between the processing of the I and Q channels, and the phase accuracy of the digital IQ modulator.

Figure 2.10 (a) RF up conversion using analogue technique, (b) RF up conversion using

direct digital synthesis Real v/s Complex OFDM Generation

For most wireless applications the OFDM signal is generated at base band using complex samples, then modulated up to the required frequency using an IQ modulator, as shown in Figure 2.10 (a) and (b). The IQ modulator frequency shifts the OFDM signal from DC to the required RF frequency, and converts the complex signal into a real signal. A transmitted RF signal is always a real signal as it is just a variation in field intensity. It is

26

however possible to directly generate a real OFDM signal. This is useful in wired applications, such as ADSL. In these applications the transmitted signal is generally from just above DC to an upper limit determined by the required signal bandwidth. The required transmission signal is a real signal as only a single cable is used. If a complex signal were used then two wires would be needed, one for the real signal and one for the imaginary signal. A real signal is equivalent to a complex base band signal, centered on DC, mixed to the new center frequency using an IQ modulator. The real signal can be generated directly using the IFFT stage instead of requiring the use of an IQ modulator for frequency translation. To create a real waveform the upper frequency bins of the IFFT must be set to the complex conjugate of the mirror of the lower half. With a real waveform the useable bandwidth of the signal is only half the sampling frequency, and so to generate a real OFDM signal only one half of the available subcarriers can be used for data modulation. This can be contrasted with the construction of a complex base band OFDM signal. In this case all of the frequency bins can be used for subcarrier modulation, with the main limitation being that the outer bins must be kept as zero to allow reconstruction of the analog signal, without aliasing. In most applications the subcarrier corresponding to DC is not used. Its removal simplifies the implementation hardware. In order for the DC subcarrier to be used it requires that the IQ outputs are DC coupled to the IQ mixer. This is difficult to achieve in hardware as offset errors result in large errors in the generated IQ vector. Using AC coupling reduces the complexity of the implementation and so the DC subcarrier is usually not used. If digital modulation is used as shown in Figure 2.10 then the DC subcarrier can be used. Channel Estimation

In wideband mobile channels, the pilot based signal correction scheme has been proven a feasible method for OFDM systems [24]. Most Channel estimation methods for OFDM transmission systems have been under the assumption of a slow fading channel, where the channel transfer function is assumed stationary within one OFDM data block. In addition, the channel transfer function for the previous data block is used as the transfer function for the present data block. Based on the principle of OFDM transmission scheme, it is easy to assign the pilot both in time domain and in frequency domain. Several types of pilot arrangement have been studied [24]. Mainly there are two kind of pilot arrangement as shown in Figure 2.11. The

27

first kind of pilot arrangement shown in Figure 2.11 (a) is denoted as block type pilot arrangement. The pilot signal is assigned to a particular OFDM block, which is sent periodically in time domain. This type of pilot arrangement is especially suitable for slow fading radio channels. Because the training block contains all pilots, channel interpolation in frequency domain is not required. Therefore, this type of pilot arrangement is relatively insensitive to frequency selectivity. The estimation of channel response is usually obtained by LS or MMSE estimate of training pilots [25].

Figure 2.11 Pilot subcarrier arrangement in OFDM symbol (a) Block type pilot

subcarrier arrangement (b) Block type pilot subcarrier arrangement The second arrangement is known as comb-type pilots. The pilot signals are uniformly distributed within each OFDM block. Assuming that the payloads of pilot signals of the two arrangements are the same, the comb-type pilot assignment has a higher retransmission rate. Thus, the comb-type pilot arrangement system provides better resistance to fast fading channels. Since only some subcarriers contain the pilot signal, the channel response of non-pilot signal will be estimated by interpolating pilot subchannels [26]. Thus comb-type pilot arrangement is sensitive to frequency selectivity when comparing to the block type pilot arrangement system. That is the pilot spacing ∆f must be smaller than the coherence bandwidth BC.

2.6

Major Applications of OFDM

Advanced and fast digital signal processors have made the implementation of FFT, IFFT and other signal processing very easy and cost effective. Therefore, OFDM applications are increasing day by day [11]. OFDM has been adopted as the new European DAB standard as well as for the Terrestrial DVB systems. The primary applications are in multimedia push technology and in wireless LAN. In recent years, new systems and 28

standards for wireless communication are coming with Orthogonal Frequency Division Multiple Access (OFDMA) and applications based on Multi Carrier CDMA. For fixed-wire applications, OFDM is employed in the ADSL and HDSL systems. It has also been suggested for power line communications systems due to its resilience to time dispersive channels and narrow band interferers. It has also been suggested for Powerline communication systems. More recently, OFDM applications were studied within the European 4th Framework ACTS program. The MEDIAN project investigated a 155 Mbps WATM network, while Magic WAND group developed a WLAN. Hallman and Rohling presented a range of different OFDM systems that were applicable to the ETSI recent personal communication oriented air interface concept. OFDM and its variant (MC-CDMA) have been considered as strong contenders for the 4G wireless communications. Wireless Personal Area Networks (WPAN) based on OFDM will provide a continuous network connection to the

user. This will revolutionize the future home, where wireless communications appliances will be an integral part of home life. WPANs will be very similar to WLANs in terms of operation, application and implementation. The IEEE 802.16a uses Wideband OFDM (W-OFDM) a patented technology of Wi-LAN to server up to 1 km radius of high data rate fixed wireless connectivity. Thus OFDM will be vividly present in all future wireless devices as it appears now. OFDM applications namely Wireless LAN, Digital Audio Broadcasting and Digital Subscriber Lines have been investigated in this thesis in the subsequent chapters.

2.7

Literature Survey and Review of OFDM

Synchronization

OFDM system can be extremely sensitive to synchronization errors. Study [27] present scheme for performing timing recovery that include symbol synchronization and sampling clock synchronization in OFDM systems. The scheme is based on pilot subcarriers. It uses a path time delay estimation method to improve the accuracy of the correlation based symbol synchronization methods, and the study use a delay locked loop (DLL) to do the sampling clock synchronization. The study shows that, by using this scheme, the mean square values of symbol timing estimation error can be decreased by several orders of magnitude compared to the common correlation methods in both the AWGN and multipath fading channels. 29

Study [28] propose scheme for Inter carrier interference self-cancellation for OFDM mobile communication system. The scheme works in two very simple steps. At the transmitter side, one data symbol is modulated onto a group of adjacent subcarriers with a group of weighting coefficient. The weighting coefficients are designed so that the ICI caused by the channel frequency errors can be minimized. At the receiver side, by linearly combining the received signals on these subcarriers with proposed coefficient, the residual ICI contained in the received signals can be then further reduced. The carrier to interference power ratio (CIR) can be increased by 15 and 30dB if the group size is two or three respectively. The study shows that OFDM system using the proposed ICI selfcancellation scheme performs much better than standard system while having the same bandwidth efficiency in multipath mobile radio channels with large Doppler frequencies. OFDM is also sensitive to the carrier interference offset, which destroys orthogonality, and cause ICI. The statistical average of the ICI could be used as a performance measure or the bit error rate (BER) caused by carrier frequency offset could be approximated by assuming the ICI to be a Gaussian. Study [29] propose a numerical technique for calculating the effect of carrier frequency offset on the bit error rate in an OFDM system. The study use an infinite series expression for the error function in order to express the average probability of error in terms of a 2-D Fourier transform of the ICI. This method can be used to study the use of error correction codes to suppress the ICI caused by carrier frequency offset. Phase Noise

By definition, multi-carrier modulation requires very close proximity of the adjacent individual carriers. This is possible due to the relatively low data rate for each carrier. However, upon down-conversion in the receiver, any phase noise associated with the local oscillator (LO) synthesizer will be superimposed onto the low data rate modulation. As a result, maintaining sufficiently low phase noise levels close to the LO frequency becomes extremely important in achieving low bit rate performance in an OFDM modem, increase in the BER for each carrier can result in a dramatic increase in the cumulative error rate over a packet. Thus, phase noise must be carefully contained in the OFDM modem system. Study [30] show that the error performance after applying some phase correction scheme depends on the number of subcarriers that compose the OFDM signal. In most common

30

situations, when the noise bandwidth is not too big compared to the inter carrier spacing, a system with lower number of subcarriers will exhibit a better error performance. Channel Estimation

Most channel estimation schemes try to exploit the correlation of the channel response of subchannels to reduce the noise and improve the estimation, though the subchannels are considered to be independent in principle when performing signal detection. Minimum mean squared error (MMSE) estimation can be obtained if the channel correlation function of is known by using the singular value decomposition of the correlation matrix [31]. Study [32] instead of finding the channel correlation matrix, it approximate the channel response by a certain model basis and minimize the estimation error by controlling the model error and residual noise. The polynomial model can be used as such a model to approximate the fading multipath channel if it is viewed as a smoothly varying function. The study uses the polynomial approximation in both the time and frequency domains. Therefore the noise can be further suppressed because fewer coefficients need to be estimated. Study [33] investigated channel estimation techniques for OFDM system based on pilot arrangement. The channel estimation based on pilot arrangement is performed by sending pilots at every sub-channel and using this estimation for a specific number of following symbols. Some papers proposes a robust pilot assisted channel estimation method for OFDM signals in Rayleigh fading. It is based on nonlinear regression channel models. Unlike the linear minimum mean squared error (LMMSE) channel estimation, this method does not have to know or estimate channel statistics like the channel correlation matrix and the average signal to noise ratio (SNR) per bit. Also some papers studied increased the OFDM system capacity with enhanced channel estimation. Study [34] considered Multiple-input Multiple-output (MIMO) OFDM to increase the capacity by a factor of the minimum number of transmit and receive antennas. The study proposed using MIMO-OFDM for wideband transmission to mitigate inter symbol interference and enhance system capacity. The MIMO-OFDM use two independent space-time codes for two sets of two transmit antennas. At the receiver, the independent space-time codes are coded using prewhitening, followed by minimum Euclidean distance decoding based on successive interference cancellation. The study shows that increasing the number of the receive antennas improve the system 31

performance. When the number of receive antenna is increased from four to eight, the required SNR 10% and 1% word error rates are reduced to 4dB and 6dB respectively, the study conclude that MIMO-OFDM is a promising technique for high spectrally efficient wideband transmission. Peak to Average Power Ratio (PAPR)

One disadvantage of OFDM is that the peak of the signal can be up to N times the average power (where N is the number of carriers). These large peaks increase the amount of intermodulation distortion resulting in an increase in the error rate. The average signal power must be kept low in order to prevent the transmitter amplifier limiting. Minimising the PAPR allows a higher average power to be transmitted for a fixed peak power, improving the overall signal to noise ratio at the receiver. It is therefore important to minimise the PAPR. A number of approaches for reduction the PAPR of the OFDM signals have been proposed. In [35], novel combination schemes of packet power reduction and forward error correction (FEC) are introduced. In the coding approach, PAPR reduction is achieved by introducing the redundancy that can be also efficiently used for FEC. The coding schemes may expand the bandwidth for PAPR reduction, but the bandwidth expansion can be also exploited for FEC. However, the problem of the coding scheme is its coding rate that rapidly diminishes as the number of subcarriers increases. Therefore, these schemes may not be necessarily efficient for the OFDM system with a relatively large number of subcarriers, say more than 100. The deliberate clipping [36] may be one of the simplest solutions when the number of subcarriers is large. The clipping operation causes degradation due to the nonlinear operation, which require some compensation.

Summary of solution for problems associated with OFDM Problem of channel estimation

Channel estimation is required to: • Cancel the phase rotation of the channel •

To estimate the value of channel transfer function H(t,τ) for detection

Solutions: 1. Using pilot to estimate the channel 2. Dual of a training sequence is a pilot 3. Time and frequency interpolation.

32

Problem of Peak to Average Power

The OFDM signal is basically a sum of N complex random variables. All the signal components may add up in phase and produce a large output or they may cancel each other producing zero output at different times. Thus the peak to average ratio (PAR) of the OFDM system is very large. Solutions: 1. Signal distorting (clipping, peak widowing , and peak cancellation) For peak windowing solution the window should be as narrow as possible, and it should not be too large in the time domain, because that implies many signal samples are affected which increase BER. The peak cancellation involves a peak power (Amplitude) detector, and a comparator. 2. By using a cluster OFDM, we can reduce the effect of peak to average and create space diversity. 3. Coding across frequencies is more effective. Problem of time selective fading in OFDM

Solutions: Diversity is the best solution for time selective fading, particularly in slow fading such as indoor wireless channels. 1. space diversity can significantly improve the capacity and performance in uplink and downlink 2. Software radio can provide low cost diversity for handset 3. Combined adaptive antenna and interference cancellation improve capacity and performance in the uplink 4. Adaptive (smart) antenna scheme can provide optimum beamforming through baseband signal processing. Problem of synchronization

OFDM is very sensitive to synchronization errors which include: •

Timing error - Sample timing (clock drift) -



Symbol timing

Frequency error - Transmitter and receiver RF osillator mismatch

33

-

Channel Doppler shift

Solutions: 1. Pilot symbols (training sequences) based techniques 2. Blind synchronization techniques 3. Cyclic prefix (Redundancy) based techniques, which is used anyway to remove multipath effect. OFDM v/s Single Carrier Transmission

Under the assumption of perfect synchronization, the performance in AWGN and/or flat or frequency non-selective channels then the performance of OFDM system is exactly the same as that of a single carrier coherent transmission system using the same modulation scheme. If we look at just a single OFDM subcarrier (since the subcarriers are orthogonal to each other, this does not effect the performance in any way) then this is exactly the same as a single carrier transmission that is quadrature modulated with no band pass filtering. The transmitted amplitude and phase is held constant over the period of the symbol and is set based on the modulation scheme and the transmitted data. This transmitted vector is then updated at the start of each symbol. This results in a sinc frequency response, which is the required response for OFDM. The optimal receiver for such a single carrier transmission is to use a coherent matched receiver, which can be implemented by mixing the signal to DC using an IQ mixer. This results in an IQ output that describes the amplitude and phase of the received modulated carrier. The amplitude and phase of the transmitted signal is constant over the symbol period, and so the optimal method of removing the most noise from the signal is to use an integrate-and-dump filter. This filter averages the received IQ vector over the entire symbol, then performs IQ demodulation on the average. The demodulation of an OFDM signal is performed in exactly the same manner. In the receiver a FFT is used to estimate the amplitude and phase of each subcarrier. The FFT operation is exactly equivalent to IQ mixing each of the subcarriers to DC then applying an integrate-and-dump over the number of samples in the FFT. From this we can see that the FFT performs the same operation as the matched receiver for the single carrier transmission, except now for a bank of subcarriers. From this we can conclude that in AWGN, OFDM will have the same performance as a single carrier transmission with no band limiting.

34

In a single carrier system implementation complexity is dominated by equalization, which is necessary when the delay spread is larger than 10% of the symbol duration. OFDM does not require an equalizer. Instead, the complexity OFDM system is largely determined by the FFT, which is used to demodulate the various subcarriers. It can be learned that at least 8 feedforward and 8 feedback taps are required to handle a delay spread of 100ns for a GMSK modem at a data rate of 24 Mbps. We can use this information to compare a single carrier system with the IEEE 802.111a 24 Mbps mode, which can handle delay spread up to 250ns using a 64-point FFT. In order to increase the tolerance of GMSK modem to the same level, the equalizer length has to be increased by a factor of 250/100, so it has 20 feedforward and feedback taps. Number of real multiplication per second in GMSK becomes 2*20*24*106 = 960*106. For a OFDM system with 64-point FFT and 4µs symbol duration, with radix 4 algorithm, this requires 96 complex multiplications, which gives 96*106 real multiplications second. So in terms of multiplication per second, the equalizer of the single carrier system is 10 times more complex than the FFT of the OFDM system. In previous example for doubling the bit rate while having the same delay spread tolerance, single carrier system requires quadruple multiplications per second while the complexity of FFT grows only slightly faster than linear ( N log 2 ( 2 N ) / N log 2 N = 2(1 + 1 / log 2 N ) , where N is the FFT size of the half rate 2

system) with the bandwidth delay spread product, which explains why OFDM is more attractive than a single carrier system with equalization for relatively large bandwidth delay spread products (values around 1 or larger) . Another complexity advantage of OFDM is the fact that the FFT does not really require full multiplications, but the phase rotations, which can be efficiently implemented by the CORDIC algorithm. The performance of the OFDM system will be primarily determined by the noise seen at the receiver. However, the performance of a single carrier transmission will degrade rapidly in the presence of multipath. Single carrier systems are more sensitive to timing errors than the OFDM systems. On the other hand, the OFDM system is more sensitive to frequency errors.

35

Chapter 3

Simulation of OFDM in Wireless LAN application 3.1

Wireless Local Area Networks Description

Wireless Local Area Networks can potentially be a promising tool for providing high speed internet access and data connectivity in different user environments, namely home, airports, hotels, corporate, high-rising offices, city centers etc. A major WLAN application will be in public sectors, where WLAN can be used to connect a user to the backbone network. will be target area for such public WLAN usage. It is becoming more and more evident that WLANs will play a greater role in future. A popular vision of future generations of telecommunications systems suggests that it will be an amalgamation of high data-rate wireless wide area networks (such as UMTS) and newly standardized WLANs. However systems of the near future will require WLANs with data rate of greater than 100 Mbps, so there is a need to further improve the capacity of existing WLAN systems. In a typical WLAN configuration, a transmitter/receiver (transceiver) device, called an access point, connects to the wired network from a fixed location using standard Ethernet cable. Access point receives, buffers, and transmits data between the WLAN and the wired network infrastructure. A single access point can support a small group of users and can function within a range of several 100 feet. The access point (or the antenna attached to the access point) is usually mounted high but may be mounted essentially anywhere. End users access the WLAN through wireless LAN adapters, which are implemented as PC cards or use ISA or PCI adapters in notebook and desktop computers or as fully integrated devices within handheld computers. WLAN adapters provide an interface between the client network operating system (NOS) and the airwaves (via an antenna). Present Wireless LAN technology uses OFDM in the physical layer (PHY) to provide high data rate in the limited bandwidth. Earlier WLAN PHY were mainly based on Direct Sequence Spread Spectrum technology, which can provide data rates up to 11 Mbps. OFDM has been rightly identified as a technique for supporting high data rates in the range of 50 to 100 Mbps in hostile multipath channel. WLAN physical layer uses Scrambling, Forward Error Control coding, Interleaving and Diversity techniques with OFDM to achieve these high data rates.

36

In this thesis, the OFDM system was modeled using Matlab to allow various parameters of the system to be varied and tested, including those established by the standard. The aim of doing the simulations was to measure the performance of OFDM under different selective channel conditions, and to allow for different OFDM configurations to be tested. The IEEE 802.11 standard committee has developed the standard for 5GHz PHY for wireless networks with OFDM technique. But, the industry has not offered any interface yet. Many companies are still researching and developing, over all for the receiver, which is the key part of the system. The standard does not give rules about it and its implementation is up to the designer.

3.2

Channel Model for 5 GHz Wireless LANs

For WLAN environments, majority of time rms delay spreads are relatively small, but occasionally, there are worst-case multipath scenarios that lead to much larger delay spreads. Measurements in outdoor and large open space indoor environments shows that rms delay spread can very over an order of magnitude, within the same environment. Although large delay spread occur relatively infrequently, they can have a major impact on system performance. To evaluate accurately the relative performance of candidate systems, it is desirable to model the variability of delay spread as well as the locations where delay spread is relatively large. For example, in a office type of environments, the upper limit of rms delay spread is about 50-60 ns for distances up to 30 m while the typical value is 10-20 ns. Moreover, the assumption that the power has an exponential decline agrees very well with the measurements. For large open space indoor environments, like airport terminals, larger delay spreads are expected. One measurement in a 130x100 m car manufacturing assembly-hall reports a 20 dB delay interval of 460 ns which corresponds to a rms delay spread of 100 ns [43]. Considering such a variation of the delay spread, channel assumed for the simulation are non fading channel as AWGN, flat fading channel as Rayleigh and Rician channel (at different velocities) and frequency selective channel as JTC channel model A, B and C and a set of indoor channel models A to E decided by ETSI BRAN. ETSI Channel Models for frequency selective fading channels at 5GHz

Five models A, B, C, D and E have been suggested by J. Medbo and adopted by ETSI for working in 5GHz radio environments. A tapped delay line type of model, which is basically described in [42], has been chosen. In order to reduce the number of taps 37

needed, the time spacing is non-uniform. For shorter delays, a more dense spacing is used. The average power declines exponentially with time. Except for the first tap, which can have a Ricean K factor of 10, all taps have Rayleigh fading statistics (K=0). A classical Doppler spectrum (Jake's model [6]) corresponding to a terminal speed of 3 m/s is assumed for all taps. These channels represent frequency selective slow fading case. Model A corresponds to a typical office environment. Model B corresponds to a typical large open space environment with NLOS conditions or an office environment with large delay spread. Models C and E correspond to typical large open space indoor and outdoor environments with large delay spread. Model D corresponds to LOS conditions in a large open space indoor or an outdoor environment. Table 3.1 Channel model for HIPERLAN/2 at 5GHz Channel Name A B C D E

RMS delay spread 50 ns 100 ns 150 ns 140 ns 250 ns

Characteristic Rayleigh Rayleigh Rayleigh Rice Rayleigh

Environment Office NLOS NLOS NLOS LOS NLOS

Table 3.2 Delay profile for channel A to E Channel A

Channel B

Channel C

Channel D

Channel E

Delay

Power

Delay

Power

Delay

Power

Delay

Power

Delay

Power

(ns)

(dB)

(ns)

(dB)

(ns)

(dB)

(ns)

(dB)

(ns)

(dB)

0

0

0

-2.6

0

-3.3

0

10

0

-4.9

10

-0.9

10

-3

10

-3.6

10

-10

10

-5.1

20

-1.7

20

-3.5

20

-3.9

20

-10.3

20

-5.2

30

-2.6

30

-3.9

30

-4.2

30

-10.6

40

-0.8

40

-3.5

50

0

50

0

50

-6.4

70

-1.3

50

-4.3

80

-1.3

80

-0.9

80

-7.2

100

-1.9

60

-5.2

110

-2.6

110

-1.7

110

-8.1

140

-0.3

70

-6.1

140

-3.9

140

-2.6

140

-9

190

-1.2

80

-6.9

180

-3.4

180

-1.5

180

-7.9

240

-2.1

90

-7.8

230

-5.6

230

-3

230

-9.4

320

0

110

-4.7

280

-7.7

280

-4.4

280

-10.8

430

-1.9

140

-7.3

330

-9.9

330

-5.9

330

-12.3

560

-2.8

170

-9.9

380

-12.1

400

-5.3

400

-11.7

710

-5.4

200

-12.5

430

-14.3

490

-7.9

490

-14.3

880

-7.3

240

-13.7

490

-15.4

600

-9.4

600

-15.8

1070

-10.6

290

-18

560

-18.4

630

-13.2

630

-19.6

1280

-13.4

340

-22.4

640

-20.7

880

-16.3

880

-22.7

1510

-17.4

390

-26.7

730

-24.6

1050

-21.2

1050

-27.6

1760

-20.9

38

Impulse response in the time and frequency domain of these five channels have been shown in Figure 3.1 (a) and (b) respectively Channel Model A "Time domain impulse response"

1

Channel Model A "Frequency domain impulse response" 20

0.5 0 0 1

0 -20

50

Channel Model B "Time domain impulse response" 350

400

0 20

0.5 0 0 1

1

Channel Model C "Frequency domain impulse response"

1

Channel Model D "Frequency domain impulse response" 2

9

10

1

Channel Model E "Frequency domain impulse response"

9

10

9

10

9

10

0

100

Channel Model C "Time domain impulse response" 700

800

0 20

10

0 -20

0 0 4

Channel Model D "Time domain impulse response" 200 1000

1200

0 20 0

2

-20

0 0 1

Channel Model E "Time domain impulse response" 200 1000

Magnitude (dB) --->

relative Magnitude --->

Channel Model B "Frequency domain impulse response"

-20

0.5

1200

0.5 0 0

1

0 20 0

-20

200

400

600

800

1000

time (n sec)--->

1200

1400

1600

1800

0

1

2

3

4

5

6

frequency (MHz)--->

7

8

Figure 3.1 (a) Time domain, (b) Frequency domain impulse response of different

frequency selective ETSI channel model A to E. Joint Technical Committee Channel Models for fading channels at 5GHz

There is a different set of channel model provided by Joint Technical Committee [44] (JTC) US for indoor office applications. These frequency selective fading channel models are A, B and C, having maximum delay spread of 100ns, 700ns and 1650 ns respectively. There delay profiles are given in the Table 3.3. Channel model C is the most severe model out of these. Channels are modeled as taped delay line filter. Slow fading (stationary channel for one frame duration) has been assumed, as user terminal does not move with high velocity in the indoor office environments. Table 3.3 JTC Channel Model Parameters for Indoor Office Areas Channel A rms spread = 50 ns Relative Average Power Delay (dB) (nsec) 0 0 50 -3.6 100 -7.2 -

Channel B rms spread = 100 ns Relative Average Power Delay (dB) (nsec) 0 0 50 -1.6 150 -4.7 325 -10.1 550 -17.1 700 -21.7 -

39

Channel C rms spread = 450 ns Relative Average Power Delay (dB) (nsec) 0 0 100 -0.9 150 -1.4 500 -2.6 550 -5 1125 -1.2 1650 -10

3.3

Simulation of OFDM based Wireless Local Area Network

In Wireless LAN, data for transmission is supplied by the MAC layer to the physical layer via a PDU train. The PDU train contains a sequence of 1’s and 0’s. Preparation for transmission and data recovery are performed by the functional blocks shown in Figure 2.6. In the simulation, MAC layer has not been implemented. It is assumed that the data from the MAC layer (PDU) is available for transmission at physical layer. For the performance evaluation of WLAN we have taken different combination of physical layer parameters. Some of those parameters have been described in Table 3.4. Table 3.4 Physical Layer parameters for WLAN simulation Parameters

Values

Channel Bandwidth

20 MHz

No of Subcarriers

32, 64, 128 and 256

Cyclic Prefix Length

50ns to 4µs

Modulation Used

BPSK, QPSK, 16QAM and 64 QAM

Forward Error Control Coding

Convolution Encoding and Viterbi Decoding

Coding Rates

1/2 , 2/3, 3/4 AWGN, Flat Fading Channel, Frequency selective

Channel Models

channel Model (JTC A, B and C and Medbo Model A to E)

Performance has been evaluated for different channel conditions, different number of subcarriers and different length of cyclic prefix for OFDM signal, through simulations. All the simulations have been repeated with different combination of modulation and error control coding. We have also simulated the IEEE 802.11a standard, which is explained in subsequent section. As there are no significant difference between the IEEE 802.11a and HIPERLAN/2, the simulation is also applicable to HIPERLAN/2 standard. In practice, the OFDM signal for the WLAN is generated as follows: Packet Data Unit (PDU) from MAC layer is first scrambled. Then this data sequence is FEC encoded with a ½ rate mother convolutional encoder and output is punctured to achieve different data rates. Next, the coded and/or punctured bits are interleaved. The interleaved coded bits are grouped together to form symbols. The symbols are modulated with one of the modulation scheme such as BPSK, QPSK, 16-QAM, 64-QAM or higher order QAM modulations. Complex modulated symbols are mapped on to subcarriers for time domain conversion. The dc subcarrier is left unmodulated and filled with zero value. 40

Pilot and null subcarriers are inserted in the OFDM symbol as per the requirement of channel estimation. N point IFFT converts all the subcarriers to time domain. The output of the IDFT/ IFFT is converted to a serial sequence and a guard interval or CP is added. Thus, total duration of the OFDM symbol is the sum of the CP or guard interval plus the useful symbol duration. The guard or CP is considered overhead in the OFDM frame along with the preamble. Windowing is applied after addition of CP to get a narrower output spectrum. OFDM symbols are appended one after another to form the transmission frame, Using an IQ modulator, the signal is converted to analog, which is up-converted to the 5 GHz band, amplified and transmitted through the antenna. RF conversion has not been implemented in simulation. All the simulations have been done on the baseband only. Receiver is responsible for performing the inverse operations of the transmitter in reverse order. Before any receiver algorithms can be employed, timing must be recovered; that is, the system clock at the receiver must become synchronized with that at the transmitter, while taking into account the delay associated with propagation across the channel. Since OFDM is a frequency domain modulation technique, it is essential to have accurate estimates of the frequency offset, caused by oscillator instability, at the receiver. Training sequences are provided in the preamble for the specific functions mentioned above. The training sequence is used to estimate the channel impulse response or channel state information (CSI). With the CSI, the received signal can be demodulated. Demodulated QAM values are then demapped into binary values, de-interleaved and finally a decoded to give the information bits. Detailed description of different blocks of the OFDM system has been given below: Scrambler and Descrambler

The PDU data has been scrambled scrambler shown in Figure 3.2. The octets of the PDU are placed in transmit serial bit stream, bit 0 first and bit 7 last. The frame synchronous scrambler uses the generator polynomial S(x). S ( x) = x 7 + x 4 + 1

(3.1)

41

Figure 3.2 Data Scrambler Forward Error Correction Coding

In simulation, data has been encoded with a convolutional encoder of coding rate R = 1/2, 2/3, or 3/4, corresponding to the desired data rate. The convolutional encoder uses the generator polynomials g0 = 1338 and g1 = 1718 as shown in Figure 3.3.

Figure 3.3 Convolutional Encoder (Constraint length k = 7)

The bit denoted as “A” shall be output from the encoder before the bit denoted as “B” Higher rates are derived from it by employing “puncturing”. Puncturing is a procedure for omitting some of the encoded bits in the transmitter reducing the number of transmitted bits and increasing the coding rate and inserting a dummy zero metric into the convolutional decoder on the receive side in place of the omitted bits. Even though the convolutional code is established by the standard, block codes may be more desirable in certain applications, such as packet voice or data communications, in which the length of the packet may be made equal to a multiple of the code length. In these applications, block codes are more attractive than convolutional codes, since the memory of the convolutional codes must be brought to a known state to terminate the trellis, which lowers the effective code rate. But only convolutional coding has been simulated for WLAN. Figure 3.4 shows the coding gain in AWGN and in ETSI Channel A. For Coded QPSK and without encoded BPSK Modulation Convolutional coding and

42

soft Viterbi decoding give a gain of around 4.5dB in AWGN channel, where as in Channel Model A, SNR gain of 3dB is achievable. Interleaver has been simulated for the IEEE 802.11a standard only hence explained in the later section.

Figure 3.4 ½ rate Convolutional Coding and soft Viterbi Decoding with 64 subcarriers

for the same data rate of 6 Mbps in (a) AWGN channel, (b) ETSI Channel model A Subcarrier Modulation and Mapping

OFDM subcarriers can be modulated with different modulations. We have used BPSK, QPSK, 16-QAM, or 64-QAM to evaluate the performance of WLAN. Modulation used determines the data rate of link. The encoded, punctured and interleaved binary serial input data is first divided into groups of NBPSC (Number of bits per subcarrier) which could be 1, 2, 4, or 6 bits depending on the modulation used and converted into complex numbers representing BPSK, QPSK, 16-QAM, or 64-QAM constellation points. The conversions have been performed according to Gray-coded constellation mappings, illustrated in Figure 3.5 and Appendix A, with the input bit, b0, being the earliest in the stream. The output values, d, are formed by multiplying the resulting (I+jQ) value by a normalization factor KMOD, as described in equation (3.2). d = (I + jQ) × KMOD

(3.2)

The normalization factor, KMOD, depends on the base modulation mode, as prescribed in Table 3.5. The purpose of the normalization factor is to achieve the same average power for all mappings. Table 3.5 Modulation-dependent normalization factor KMOD

43

Modulation

KMOD

BPSK

1

QPSK

1/√2

16 QAM

1/√10

64 QAM

1/√42

Figure 3.5 (a) Transmitted Constellation with QPSK modulation with 128 subcarriers

(before normalization), (b) Received Constellation with 6 dB SNR in AWGN channel

Figure 3.6 (a) Transmitted Constellation with 16-QAM modulation (before

normalization), (b) Received Constellation with 12dB SNR in AWGN channel IFFT and Serial to Parallel Conversion

After mapping the data to respective complex constellation, though pilot have been inserted in the frequency domain but not used for the channel estimation. DC subcarrier is modulated with null (zero). Not all the available subcarriers have been used for the data transmission instead null carriers are inserted at outer side of the frequency spectrum to avoid channel interference. Then 64, 128 or 256 etc. point IFFT has been taken to convert

44

the signal in time domain. CP which copy of some last samples is appended to the output of the IFFT and all the samples are transmitted serially for D/A conversion. Transmitted OFDM signal (baseband) in time domain can be seen in Figure 3.7. Power spectral density of the OFDM signal is shown in Figure 3.8

Figure 3.7 Transmitted waveforms of OFDM signal with 64 QAM Modulation

Figure 3.8 Power Spectral Density of the transmitted OFDM signal 64 subcarrier (48

data, 4 pilot and 12 null subcarriers) with 64QAM Modulation Channel Estimation and Equalization

Based on the principle of OFDM transmission scheme, it is easy to assign the pilot both in time domain and in frequency domain. In simulation, only Block type pilot arrangement (see section 2.7) has been considered for channel estimation, though four pilots have been inserted in the OFDM signal and can be used to estimate the channel even in the fast fading case. Channel estimation is done in frequency domain only. Effect

45

of channel is first estimated on two long training sequence and then assuming that channel is stationary for one block of OFDM symbols, the average estimation of two training sequences is applied to remaining data on each subcarrier.

Figure 3.9 (a) Received Constellation without equalization in 24 Mbps mode, (b) with

equalization, in Channel model A with 12dB SNR

Figure 3.10 (a) Received Constellation without equalization in 24 Mbps mode, (b) with

equalization, in Channel model E with 12dB SNR

46

Figure 3.11 (a) Received Constellation without equalization in 54 Mbps mode, (b) with

equalization, in Channel model A with 24dB SNR

3.4 Wireless Local Area Networks Standards In July 1998, the IEEE 802.11 standardization group decided to select OFDM as the basis for their new 5 GHz standard, targeting a range of data rates from 6 to 54 Mbps. This new standard is the first to use OFDM in packet based communications, the use of OFDM was previously limited to continuous transmission systems like digital audio broadcasting (DAB) and digital video broadcasting (DVB). Following the IEEE 802.11 decision, ETSI BRAN HIgh Performance LAN (HIPELAN) and Multimedia Mobile Access Communication (MMAC) also adopted OFDM for their physical layer standards. The three bodies have worked in close cooperation since then to make sure that differences among the various standards are kept to a minimum, thereby enabling manufacturing of equipment that can be used worldwide. The main difference between the IEEE 802.11a and the HIPERLAN type 2 is in the medium access control (MAC). The IEEE 802.11a uses a distributed MAC based on carrier sense multiple access with collision avoidance (CSMA/ CA), whereas the HIPERLAN/2 uses a centralized and scheduled MAC based on time division multiple access with dynamic slot assignment (TDMA/DSA). The MMAC supports both of these MACs. As far as the physical layer specifications are concerned, there are only a few minor differences between the IEEE 802.11a and the HIPERLAN/2 standards such as: 1. HiperLAN/2 uses extra puncturing to accommodate the tail bits in order to keep an integer number of OFDM symbols in 54 byte packets required for ATM transmission. For example, the 16-QAM mode of HiperLAN/2 uses a rate 9/16 convolutional

47

encoder rather than the rate 1/2 convolutional encoder used by IEEE 802.11a and MMAC. Puncturing 2 out of every 18 coded bits generate the rate 9/16. 2.

HiperLAN/2 uses different training sequences. The long training is the same as IEEE 802.11, but the preceding sequence of short training symbols is different. A downlink transmission starts with 10 short symbols as IEEE 802.11, but the first 5 symbols are different in order to detect the start of the downlink frame. Uplink packets may use 5 or 10 identical short symbols, with the last short symbol inverted.

3.

HiperLAN/2 has an optional mode that uses a 400 µs cyclic prefix.

Table 3.6. Rate dependent parameter for the IEEE 802.11a standard Data

Modulation

Rate

Coding

Coded Bits per

Coded bits per

Data bits per

Rate

subcarrier

OFDM symbol

OFDM symbol

(Mbps) 6

BPSK

½

1

48

24

9

BPSK

¾

1

48

36

12

QPSK

½

2

96

48

18

QPSK

¾

2

96

72

#

16-QAM

½

4

192

96

27*

16-QAM

9/16

4

192

108

36

16-QAM

¾

4

192

144

#

64-QAM

2/3

6

288

192

54

64-QAM

¾

6

288

216

24

48

Table 3.7. Physical layer parameters for the IEEE 802.11a standard Symbol

Parameters

Values

NSD

Number of data subcarriers

48

NSP

Number of pilot subcarriers

4

NS

Number of subcarriers, total

52 (NSD + NSP)

∆f

Subcarrier frequency spacing

0.3125 MHz (=20 MHz/64)

TFFT

IFFT/FFT period

3.2 µs (1/∆f)

TPREAMBLE

PLCP preamble duration

16 µs (TSHORT + TLONG)

TSIGNAL

Duration of the SIGNAL BPSK-OFDM symbol

4.0 µs (TGI + TFFT)

TGI

GI duration (Cyclic Prefix)

0.8 µs (TFFT /4)

48

TGI2

Training symbol GI duration

1.6 µs (TFFT /2)

TSYM

Symbol interval

4 µs (TGI + TFFT)

TSHORT

Short training sequence duration

8 µs (10 ×TFFT /4)

TLONG

Long training sequence duration

8 µs (TGI2 + 2×TFFT)

PLCP Frame Format

PLCP Protocol Data Unit (PPDU) is given in Figure 3.12. It includes the OFDM Physical Layer Convergence Protocol (PLCP) preamble, OFDM PLCP header, PLCP Service Data Unit (PSDU), tail bits, and pad bits. The PLCP header contains the following fields: LENGTH, RATE, a reserved bit, an even parity bit, and the SERVICE field. In terms of modulation, the LENGTH, RATE, reserved bit, and parity bit (with 6 “zero” tail bits appended) constitute a separate single OFDM symbol, denoted SIGNAL, which is transmitted with the most robust combination of BPSK modulation and a coding rate of R = 1/2. The SERVICE field of the PLCP header and the PSDU (with 6 “zero” tail bits and pad bits appended), denoted as DATA, are transmitted at the data rate described in the RATE field and may constitute multiple OFDM symbols. The tail bits in the SIGNAL symbol enable decoding of the RATE and LENGTH fields immediately after the reception of the tail bits. The RATE and LENGTH are required for decoding the DATA part of the packet. In addition, the CCA mechanism can be augmented by predicting the duration of the packet from the contents of the RATE and LENGTH fields, even if the station does not support the data rate.

Figure 3.12 PPDU Frame format for the IEEE 802.11a standard

The modulation parameters dependent on the data rate used shall be set according to Table 3.6. List of timing parameters associated with the PLCP is given in Table 3.7. HIPERLAN/2 provide one extra data rate mode of 27 Mbps using 9/16 code rate with 16 QAM Modulation, whereas 24Mbps data rate and 48 Mbps data rate modes are available in the IEEE 802.11a standard only. All other modes are available in both the standards.

49

PLCP Header Encoding Process

PLCP header field is decided by the RATE, LENGTH, and SERVICE fields of the TXVECTOR and formed by filling the appropriate bit fields. The RATE and LENGTH fields of the PLCP header are encoded by a convolutional code at a rate of R = 1/2, and are subsequently mapped onto a single BPSK encoded OFDM symbol, denoted as the SIGNAL symbol. In order to facilitate a reliable and timely detection of the RATE and LENGTH fields, 6 “zero” tail bits are inserted into the PLCP header. The encoding of the SIGNAL field into an OFDM symbol follows the same steps for convolutional encoding, interleaving, BPSK modulation, pilot insertion, Fourier transform, and pre-pending a GI as described subsequently for data transmission at 6 Mbps. The contents of the SIGNAL field are not scrambled. Number of data bits per OFDM symbol (NDBPS), the coding rate (R), the number of bits in each OFDM subcarrier (NBPSC) and the number of coded bits per OFDM symbol (NCBPS) can be calculated from RATE field of the TXVECTOR. PSDU is appended to the SERVICE field of the TXVECTOR and the resulting bit string is extended with “zero” bits (at least 6 bits) so that the resulting length will be a multiple of NDBPS. The resulting bit string constitutes the DATA part of the packet. PLCP Preamble (SYNC)

To reduce the uncertainty in the channel estimation, two OFDM symbols containing training sequences are provided: short training and long training. The short training is used to provide coarse and fine estimation of time and frequency errors. PLCP preamble field, composed of 10 repetitions of a “short training sequence” (used for AGC convergence, diversity selection, timing acquisition, and coarse frequency acquisition in the receiver) and two repetitions of a “long training sequence” (used for channel estimation and fine frequency acquisition in the receiver), preceded by a guard interval (GI). As shown in Figure 3.13.

Figure 3.13 OFDM training symbol structure (from IEEE 802.11a standard)

50

In PLCP preamble t1 to t10 denote short training symbols and T1 and T2 denote long training symbols. The SIGNAL field and DATA follow the PLCP preamble. The total training length is 16 µs. The dashed boundaries in the figure denote repetitions due to the periodicity of the inverse Fourier transform. A short OFDM training symbol consists of 12 subcarriers, which are modulated by the elements of the sequence S, given by S-26, 26 =√(13/6) × {0, 0, 1+j, 0, 0, 0, -1-j, 0, 0, 0, 1+j, 0, 0, 0, -1-j, 0, 0, 0, -1-j, 0, 0, 0, 1+j, 0, 0, 0, 0,0, 0, 0, -1-j, 0, 0, 0, -1-j, 0, 0, 0, 1+j, 0, 0, 0, 1+j, 0, 0, 0, 1+j, 0, 0, 0, 1+j, 0,0}

(3.3)

The multiplication by a factor of √(13/6) is in order to normalize the average power of the resulting OFDM symbol, which utilizes 12 out of 52 subcarriers. The fact that only spectral lines of S-26:26 with indices that are a multiple of 4 have nonzero amplitude results in a periodicity of TFFT/4 = 0.8 µs. The interval TSHORT is equal to ten 0.8 µs periods (i.e., 8 µs). A long OFDM training symbol consists of 52 subcarriers plus a zero value at dc, which are modulated by the elements of the sequence L, given by L-26, 26 = {1, 1, -1, -1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 0,1, -1, -1, 1, 1,

(3.4)

-1, 1, -1, 1, -1, -1, -1, -1, -1, 1, 1, -1, -1, 1, -1, 1, -1, 1, 1, 1, 1}

Interleaving

According to the IEEE 802.11a standard, a block interleaver must interleave all data bits with a block size corresponding to the number of bits in a single OFDM symbol (NCBPS). The interleaver is defined by a two-step permutation. The first permutation ensures that adjacent coded bits are mapped onto nonadjacent subcarriers. The second ensures that adjacent coded bits are mapped alternately onto less and more significant bits of the constellation and, thereby, long runs of low reliability (LSB) bits are avoided. Considering k the index of the coded bit before the first permutation, i the index after the first and before the second permutation and j the index after the second permutation, just prior to modulation mapping, the first permutation is defined by the rule: i = (NCBPS / 16) × mod (k, 16) + floor(k/16) ;

k = 0,1,… NCBPS –1

(3.5)

The function floor (.) denotes the largest integer not exceeding the parameter. The second permutation is defined by the rule: j = s × floor(i/s) +mod (i + NCBPS

-

floor(16 × i/NCBPS), s)

i=0,1,… NCBPS –1 (3.6)

Number of coded bits per subcarrier, NBPSC, determines the value of s, as follows

51

s = max(NBPSC / 2 , 1)

(3.7)

The deinterleaver, which performs the inverse relation, is also defined by two permutations. Here, j denotes the index of the original received bit before the first permutation, I the index after the first and before the second permutation, and k the index after the second permutation, just prior to delivering the coded bits to the convolutional (Viterbi) decoder. The first permutation is defined by the rule: i = s × floor(j/s) + mod(j + floor(16 × j/NCBPS) , s) ;

j =0,1,… NCBPS –1 (3.8)

where s is given by equation (3.7) The second permutation is defined by the rule: k = 16 × i .(NCBPS –1 ) × floor(16 × i/NCBPS)

i = 0,1,… NCBPS –1 (3.9)

Following graphs show the effect of Convolutional Coding, Puncturing and Interleaving in different fading and non-fading channels. From Figure 3.14 it is clear that interleaving does not provide any benefit if the channel is AWGN only. Next Figure shoes the advantage of interleaving and convolutional coding in frequency selective channel model A. Coding with interleaving gives highest performance for selective channels.

Figure 3.14 Coding and interleaving performance of 12 Mbps mode (a) in non fading

channel and (b) frequency selective fading ETSI channel model A Pilot subcarriers

In each OFDM symbol, four of the subcarriers are dedicated to pilot signals in order to make the coherent detection robust against frequency offsets and phase noise. These pilot signals shall be put in subcarriers –21, –7, 7 and 21. The pilots shall be BPSK modulated by a pseudo binary sequence to prevent the generation of spectral lines. The stream of

52

complex numbers is divided into groups of NSD = 48 complex numbers. We shall denote this by writing the complex number dk,n, which corresponds to subcarrier k of OFDM symbol n, as follows: d k ,n = d k + N SD xn ,

k = 0,K N SD − 1; n = 0,K N SYM − 1

(3.10)

where NSYM are number of OFDM symbols M(k), defines a mapping from the logical subcarrier number 0 to 47 into frequency offset index -26 to 26, while skipping the pilot subcarrier locations and the 0th (dc) subcarrier.  k − 26  k − 25  k − 24 M (k ) =  k − 23 k − 22   k − 21

0< k < 4 0< k < 17 0< k < 23 0< k < 29

(3.11)

0< k < 42 0< k < 47

The contribution of the pilot subcarriers for the nth OFDM symbol is produced by Fourier transform of sequence P, given by P–26, 26 = {0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0,

(3.12)

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, –1, 0, 0, 0, 0, 0}

The polarity of the pilot subcarriers is controlled by the sequence, pn, which is a cyclic extension of the 127 elements sequence and is given by p0..126v = {1,1,1,1, -1,-1,-1,1, -1,-1,-1,-1, 1,1,-1,1, -1,-1,1,1, -1,1,1,-1, 1,1,1,1, 1,1,-1,1, 1,1,-1,1, 1,1,-1,1, 1,1,-1,1, -1,-1,-1,1, -1,1,-1,-1, 1,-1,-1,1, 1,1,1,1, -1,-1,1,1, -1,-1,1,-1, 1,-1,1,1, -1,-1,-1,1, 1,1,-1,-1, -1,1,-1,-1, 1,-1,1,1, 1,1,-1,1, -1,1,-1,1, -1,-1,-1,-1, -1,1,-1,1, 1,-1,1,-1, 1,1,1,-1, -1,1,-1,-1, -

(3.13)

1,1,1,1, -1,-1,-1,-1, -1,-1,-1}

To avoid difficulties in D/A and A/D converter offsets and carrier feedthrough in the RF system, the subcarrier falling at DC (0th subcarrier) is not used.

Figure 3.15 Subcarrier frequency allocation

53

Discrete Time Implementation

Complex number string after modulation is divided into groups of 48 complex numbers. Each such group will be associated with one OFDM symbol. In each group, the complex numbers will be numbered 0 to 47 and mapped hereafter into OFDM subcarriers numbered –26 to –22, –20 to –8, –6 to –1, 1 to 6, 8 to 20, and 22 to 26. The subcarriers – 21, –7, 7, and 21 are skipped and, subsequently, used for inserting pilot subcarriers. The “0” subcarrier, associated with center frequency, is omitted and filled with zero value.

Figure 3.16 Inputs and Outputs of IFFT

In 64-point IFFT, the coefficients 1 to 26 are mapped to the same numbered IFFT inputs, while the coefficients –26 to –1 are copied into IFFT inputs 38 to 63. The rest of the inputs, 27 to 37 and the 0 (dc) input, are set to zero. This mapping is illustrated in Figure 3.16. After performing an IFFT, the output is cyclically extended to the desired length. Windowing

To make the spectrum decrease faster, windowing is applied to the OFDM signal. The standard does not specify the kind of window to be used. In implementation, the windowing function will be represented in discrete time. With parameters T = 4.0 µs, TTR = 100 ns and the signal is sampled at 20 Msamples/s, windowing function becomes 1  wT [n] = wT (nTS ) =  0.5 0 

1
(3.14)

0, 80 otherwise

TTR is the transition time between two consecutive periods of FFT, as it can be seen in Figure 3.17.

54

Figure 3.17 OFDM frame with cyclic extension and windowing for two receptions of the

FFT period Figure 3.17 also illustrates the possibility of extending the windowing function over more than one period, TFFT, and additionally shows smoothed transitions by application of a windowing function, as exemplified in equation (3.14). In particular, window functions that extend over multiple periods of the FFT are utilized in the definition of the preamble. Receiver

Before an OFDM receiver can demodulate the subcarriers, it has to perform at least two synchronization tasks. The first one is to find out where the symbol boundaries and what the optimal timing instants are to minimize the effects of intercarrier interference (ICI) and intersymbol interference (ISI). The second task is to estimate and correct the carrier frequency offset of the received signal to avoid the ICI. Also, for coherent receivers, the carrier phase has to be synchronized. Further, a coherent QAM receiver needs to detect the amplitudes and phases of all subcarriers to define the decision boundaries for the QAM constellation of each subcarrier. Synchronization using Special Training Symbols

The synchronization technique based on the cyclic extension is particularly suited to tracking or to blind synchronization in a circuit-switched connection, where no special training signals are available. For packet transmission, however, there is a drawback because an accurate synchronization needs an averaging over a large (>10) number of OFDM symbols to attain a distinct correlation peak and a reasonable SNR. For high-rate packet transmission, the synchronization time needs to be as short as possible, preferably a few OFDM symbols only. To achieve this, special OFDM training symbols are used, for which the data content is known to the receiver. In this, the entire received training signal can be used to achieve synchronization, whereas the cyclic extension method only uses a fraction of each symbol. 55

At receiver, the received signal is correlated with itself with a delay of one short symbol, given by N

A(n) = ∑ r (k + n)r ∗ (k + n + L)

(3.15)

k =0

Where r(n) is the received sequence, A(n) is the correlation output and L is the length of the short symbol (16 samples). The incoming frame at receiver can be detected by comparing the magnitude of auto-correlation result with some threshold. In simulation we detect OFDM symbol boundary using auto-correlation and cross correlation of short preamble. In equation (3.15) the value of N should be in between 16 and 144 and a multiple of 16. For N=80, if we plot the auto-correlation magnitude values, we get a curve as shown in Figure 3.18 (a). The curve rises to some value, remains flat for about N-CP=80-16=64 samples duration and then falls down as shown. In our algorithm, we detect the index of the (N-CP+1)th sample when counted from the start of the preamble. The auto-correlation magnitude values are passed through a moving average filter to smoothen the curve. The moving average filter is defined by Y ( n) =

l 1 ∑ A(k + n) + A(n) 2l + 1 k = − l

(3.16)

where A(n) is the auto-correlation magnitude and l is the size of the moving average filter and it is chosen as 3 in the simulation. We can detect this falling edge (N-CPth sample ) by observing the slope of the curve. However, at low SNRs and high delay spread situations, exact detection of this edge is difficult. This edge can be localized, if we do cross correlation of the received sequence with the local copy of the short symbol. By this, we get peaks at the end of each short symbol. However, the frequency offset of the local oscillator disturbs the magnitude of these cross correlation peaks significantly. Instead of averaging this cross correlation for one short symbol, if we average over more short symbols, as indicated by equation (3.16), we can still detect the peak. M

N

C (n) = ∑∑ r (l * N + k + n) s ∗ (l * N + k )

(3.17)

l =0 k =0

Where s(n) is the local copy of the short symbol. M (5 in the simulation) is the number of short symbols over which we are averaging the cross correlation. The simulation result shows that this type of averaging can with stand ±20ppm frequency offset, which is the worst-case possible frequency offset specified in 802.11a standard.

56

Autocorrelation and Crosscorrelation cruves for SNR=10 dB, multipath delay spread 60 ns and no frequency offset 1.6

1.4

Auto correlation Magnitude Averaged Auto correlation Cross correlation magnitude

1.2

Magnitude

1

0.8

0.6

0.4

0.2

0 0 8 16 24 32 40 48 56 64 72 80 88 96 104112120128136144152160168176184192200 Received sample index

Figure 3.18 (a) Auto-Correlation curve and Cross-Correlation peaks for ideal case (No

noise, no multipath), (b) Auto-Correlation curve and Cross-Correlation peaks for SNR=10dB and multipath delay spread 60 ns and no frequency offset Figure 3.18 (a) shows the auto-correlation curve and the cross correlation peaks in the case of an ideal channel. Our objective is to detect the cross correlation peak at which the falling edge of the auto-correlation curve starts. This can be achieved by tracking the slope of the curve with the help of another dynamically set threshold. To detect the corresponding cross correlation peak, we need to do peak search by taking a window of 16 cross correlation magnitude values around that falling edge. The window size can be decided in simulations. The detected peak corresponds to the index of the (N-CP+1)th sample when counted from the start of the preamble. Thus, in simulation, cross correlation is used to localize the exact boundary of the short symbol. The difference between the detected boundary and the actual boundary is the boundary detection error. This boundary detection error results in corresponding rotation of the signal constellation in frequency domain. This rotation can be taken care by channel estimation and equalization up to some extent. In simulation the exponential channel model A is considered for 60 ns rms delay spread. Figure 3.18 (b) shows the auto-correlation magnitude curve and cross correlation magnitude peaks at 10dB SNR, with an RMS multipath delay spread of 60ns and with zero frequency offset.

57

3.4

Performance Results

Various graphical results are first presented for WLAN with different physical layer parameters and then results for the IEEE 802.11a and HIPERLAN/2 standards have been given in this subsection. Cyclic Prefix

Effect of Cyclic Prefix length on the performance of WLAN can be seen through the following results. We have used a multipath channel having rms delay spread = 50 ns and max. delay spread of 300 ns and 128 subcarriers. From the simulation graphs it has been observed that as we increase the CP length from 100 ns to 800 ns the SNR requirement for BPSK and QPSK modulation reduces only 1 to 2 dB but in the case of 16 QAM and 64QAM very high SNR is required to get 10-5 BER with 100 ns.

(a) BPSK Modulation

(b) QPSK Modulation

(c) 16 QAM Modulation

(d) 64 QAM Modulation

58

Figure 3.19 SNR requirements for CP length of 100, 200, 400 and 800 ns in channel

model A (max delay spread = 300 ns), v=50 km/hr for different modulation schemes Table 3.8 SNR comparison of various modulation schemes and different length of cyclic

prefix in channel model A for BER of 10-4 Cyclic Prefix 100 ns 200 ns 400 ns 800 ns

Modulation used BPSK

QPSK

16 QAM

64 QAM

8 dB 7.5 dB 7.25 dB 7 dB

11.5 dB 11 dB 11 dB 10.5 dB

32 dB 21 dB 20 dB 18 dB

32 dB 32 dB 30 dB

This concludes that with 64 subcarriers at least 200 ns cyclic prefix is required in channel A for higher order modulation than QPSK. SNR requirements have been summarized in Table 3.8 Subcarriers

Comparison of different subcarriers in ETSI channel E, JTC channel C and AWGN channel has been given in Figure 3.20 (a), (b) and (c) and is summarized in Table 3.9. Table 3.9 SNR comparison of different number of subcarriers for BER of 10-4 Channel Model ETSI E JTC C AWGN

No. of subcarriers in 20 MHz bandwidth 64 26 dB 12 dB

128 23 dB 19 12 dB

59

256 21 dB 17.5 12 dB

Figure 3.20 Comparison of SNR requirements for number of subcarriers 64, 128 and 256

with 16 QAM Modulation and CP = 800ns (a) in channel E (rms delay spread = 250 ns), (b) in JTC channel C (rms delay spread = 450 ns) v = 50 km/hr, (c) AWGN channel Coding and Interleaving

Comparison of different data rates with and without, coding and interleaving have been done in shown in Figure 3.21. The comparison is made between (i) uncoded BPSK and ½ rate QPSK coded for the same data rate of 12Mbps, (ii) uncoded QPSK and ½ rate 16 QAM coded for the data rate of 24 Mbps and (iii) uncoded 16QAM and 2/3 rate 64 QAM convolutional coded for 48 Mbps data rate. A gain of 7 dB in SNR for BER of 10-5 for 12 Mbps mode can be achieved with the help of coding and interleaving in frequency selective channel model A. Without interleaving the gain reduces to 4 dB only. For 24 Mbps mode the gain is 4dB only with coding and interleaving. This gain can be improved by 2.5 dB if we use soft decoding in the Viterbi decoder. For 48 Mbps data rate we are able to achieve gain of only 2dB for BER of 10-4 . Reason for the low gain in SNR can be that even with coding and interleaving because of punctured output of convolutional encoder is not able cope with the selective fading without soft decoding.

60

Figure 3.21 Effect of FEC and Interleaving at different data rates in frequency selective

fading channel model A The IEEE standard 802.11a and HIPERLAN/2 standard data rates

Various data rates of the IEEE 802.11a standard & the HIPERLAN/2 standard have been summarized in Table 3.10. Different graphical results have been plotted in Figure 3.22 and 3.23. Table 3.10 SNR comparison for different data rates for the IEEE 802.11a for BER of 10-4 Channel Model

Data Rates 6 Mbps

12 Mbps

24 Mbps

36 Mbps

48 Mbps

54 Mbps

AWGN

0.5 dB

5 dB

13 dB

16dB

20.5 dB

22 dB

A

2.25 dB

8 dB

15 dB

22 dB

25 dB

28 dB

B

1.75 dB

5.75 dB

13.5 dB

19 dB

23 dB

27 dB

C

2 dB

6 dB

15 dB

19.5 dB

24.5 dB

28 dB

D

0 dB

0 dB

4.5 dB

7 dB

13 dB

15 dB

E

7.5 dB

12 dB

20.5 dB

26 dB

30.5 dB

34 dB

61

Figure 3.22 The IEEE 802.11a standard for Data rate of (a) 6 Mbps, BPSK, ½ rate

coding, (b) 12 Mbps, QPSK, ½ rate coding, (c) 24 Mbps, 16-QAM Modulation, ½ rate coding, with interleaving in ETSI channels A to E

62

Figure 3.23 (a) 36 Mbps Data rate, 16-QAM, 3/4 rate coding, (b) 48 Mbps Data rate, 64-

QAM, 2/3 rate coding, (c) 54 Mbps Data rate, 64-QAM, 3/4 rate coding, with interleaving in Medbo frequency selective fading channels A to E 63

Figure 3.24 Performance of OFDM in ETSI Channel model A for different data rates of

the IEEE 802.11a standard From Table 36, Figures 3.22 and 3.23, it can be seen that as the delay spread increases the performance is improved in the Rayleigh channels until the delay spread becomes so large that ISI and ICI become limiting factors (channel E). Channels B, C and D have increasingly better performances than channel A due to the increased frequency diversity of the channels. As expected channel D has better performance than channel C because it is modelled as a Rician channel. In channel E the excess delay (1760ns) of the channel is much larger than the guard interval (800ns) so ISI cannot be completely eliminated and SNR requirements are highest. Figure 3.24 shows the performance of OFDM for different data rates of the WLAN standards in ETSI channel model A. Following results are shown for AWGN and JTC channel model A, B and C [12]. In Figure 3.25 (a) simulation results for AWGN (non-fading) channel is plotted with the theoretical curve. In AWGN, OFDM does not provide any advantage in BER performance but it transmits the data in limited bandwidth. With the single carrier modulation, data can be transmitted at the maximum speed of 2 Mbps, 1 Mbps and 220 kbps in channel A (rms delay spread 50 ns), channel B (rms delay spread 100 ns) and channel C (rms delay spread 450 ns) respectively. Figure 7 and 8 shows that for both channel A and B, we can transmit at 48 Mbps (16 QAM modulation) with the BER of 105

and SNR less than 30 dB. Figure 3.26 (b) shows that in channel C because of large

delay spread (more then the cyclic prefix duration), maximum data rate achievable is 24 Mbps (QPSK modulation) at an error probability of 3x10-3.

64

Figure 3.25 BER performance of OFDM with different modulation schemes in (a)

AWGN channel, (b) JTC channel model A without coding and interleaving

Figure 3.26 BER performance of OFDM with different modulation schemes in (a) JTC

channel model B and C without coding and interleaving Performance of OFDM is summarised in the Table 3.11 given below. This table shows the SNR requirement for Bit Error Rate of 10-4 for different modulation schemes. Table 3.11 SNR comparison for various modulation schemes in different channels Cyclic Prefix AWGN A B

BPSK 7.5 dB 15 dB 14.5 dB

Modulation used QPSK 16 QAM 10.5 dB 17.0 dB 18.5 dB 25.5 dB 17.5 dB 24.5 dB

64 QAM 23.0 dB 31.5 dB 31.0 dB

For the JTC channel B again BPSK requires lower SNR then QPSK, 16QAM and 64QAM. However higher data rates are obtainable with higher order modulation for example for both channel A & B 16 QAM gives a data rate of 48 Mbps at BER of 10-5 whereas BPSK gives only 12 Mbps. 64 QAM can provide data rates of up to 72 Mbps but for the 10-5 BER it requires much higher values of SNR in fading channels. We find that it is not possible to achieve high data rates at BER of 10-5 for channel model C. For channel model C error probability better then 10-3 is not achievable using OFDM without FEC and interleaving. 65

Chapter 4

Performance of OFDM in Digital Audio Broadcasting 4.1

Digital Audio Broadcasting

OFDM have been adopted by the Digital Audio Broadcasting (DAB) System, standardized by ETSI as the European system. DAB is used for the broadcasting of sounds and voice in digital form, through the terrestrial radio channel, to fixed, portable and mobile receivers. DAB standard provides three modes of operation 1-3. Mode 1 is for terrestrial Single Frequency Network (SFN). Mode 2 applies to conventional terrestrial local broadcasting. Mode 3 is for satellite broadcasting. The standard [17] defines in full details the transmission, coding and control protocols for the broadcasted signal. The most challenging operational environment for a radio receiver is, of course, the mobile one, where the channel experiences fast variations due to Doppler phenomena, fading, shadowing, and interference from multiple paths. In addition, the DAB system considers the possibility of operation in a Single Frequency Network mode that is by broadcasting the same program on the same carrier frequency (but synchronized in time) with different transmitters over a national area. This solution would eliminate the need for retuning of the receiver when moving between the coverage area of different transmitters and also fills in dead spots because of shadowing at a particular receiver location. On the other hand, this causes more co-channel interference, due to the adjacent transmitters to reach the mobile receiver. Any receiver therefore receives a sum of signals from more than one transmitter, coincident in frequency format and time, except for differences in propagation delay. The necessity to cope with time-varying multipath channels led to the choice of OFDM modulation system with cyclic prefix, which is also more appropriate for SFN operation than single-carrier systems. Received signal in an SFN Assuming that each path provides a Rayleigh distributed signal, the powers will add. If the spread of the arrival times, which include both multipath spread and spread of propagation times from different transmitters, is less than the guard interval between OFDM symbols, then the orthogonality between subcarriers is preserved. If this is not the case, then degradation caused by interference between subcarriers will result. This interference may be approximated as Gaussian noise, and is proportional to the degree that the inter-symbol interference duration exceeds the guard interval [20].

66

As an example of guard interval requirement, let us assume a receiver receiving direct signals from two transmitters, the distance between them is 40Km. The time separation could be up to 133µs. Considering the addition of multipath from each transmitter, and reception from additional transmitters, the guard interval should be substantially greater than this value. A constraint in the other direction, due to Doppler shift and frequency variation in the receiver’s local oscillator, sets a minimum spacing between subcarriers, and thus a maximum symbol duration. For a vehicle traveling at 80 mph (31m/s), the Doppler shift at 240 MHz carrier frequency can be up to 25Hz. The subcarrier spacing must be large compared to this value in order to minimize this source of inter-carrier interference.

4.2

Channel Models for DAB

There are five different kind of channel models used for the simulation. These models have been defined in the Table 4.1. There are two models for rural area and two for urban area. One model is provided for free space channel. Other than this simulation has been done for only AWGN channel for the purpose of comparison between different channel models. Table 4.1 Delay profile of different channels for DAB Rural Area 1 Delay Power (µs) 0 1 0.2 0.63 0.4 0.1 0.6 0.01 -

Rural Area 2 Delay Power (µs) 0 1 0.1 0.4 0.2 0.16 0.3 0.06 0.4 0.03 0.5 0.01 -

Typical Urban 1 Delay Power (µs) 0 0.4 0.1 0.5 0.3 1 0.5 0.55 0.8 0.5 1.1 0.32 1.3 0.2 1.7 0.32 2.3 0.22 3.1 0.14 3.2 0.08 5.0 0.1

Typical Urban 2 Delay Power (µs) 0 0.5 0.2 1 0.5 0.63 1.6 0.25 2.3 0.16 5.0 0.1 -

Free Space Delay Power (µs) 0 1 80 0.55 160 0.40 -

-

Figure 4.1 shows the time domain impulse response of Typical Urban area and Figure 5.2 shows output signal after passing through this channel.

67

channel Impulse Response -Time Domain-

0.25

channel Impulse Response -Frequency Domain-

0 -10

0.2

H(f)

-20 -30 -40

0.15 h(t)

-50

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0.3 0.4 0.5 0.6 0.7 Normalized Frequency (×π rad/sample)

0.8

0.9

1

f 0

Phase (degrees)

0.1

0.05

0 0

5

10

15

20 25 30 t (micro sec) -->

35

40

45

-100

-200

-300

-400

50

0

0.1

0.2

Figure 4.1 (a) Time domain (b) Frequency Domain impulse response of Urban Area Input of the channel -Frequency Domain-

80

X(f)

60 40 20 0

0

0.5

1

1.5 f

2

2.5

Output of the channel -Frequency Donain-

30

3 x 10

5

25

Y(f)

20 15 10 5 0

0

0.5

1

1.5 f

2

2.5

3 x 10

5

Figure 4.2 Effect of frequency selective channel on the transmitted OFDM signal

4.3

Simulation of DAB System

The DAB system has three distinct modes of operation with different values of the OFDM modulation parameters as can be seen in Table 4.2. The Mode 1 standard meets all the constraints by providing for 1536 subcarriers with 1KHz spacing and cyclic prefix of 246 µs duration. Since the useful symbol duration is 1msec, the loss in spectral efficiency is approximately 20%. Each subcarrier is modulated by π/4-DQPSK. A 2048point IFFT is performed in the transmitter, treating the unused subcarrier as zero, so the bandwidth remains 1.536MHz. The signal is complex modulated, using I and Q component, onto an RF carrier in the range 175-240MHz.

68

The transmitted OFDM signal carries several audio programs, each of which may be monophone or stereo, and of varying quality. Each audio channel is encoded using subband encoding, at one of several allowed bit rates between 32 and 384Kb/s. That bit stream is then convolutionally encoded at rate approximately ½ and interleaved. The bit stream are then time multiplexed and input to the OFDM modulator. The gross bit rate is 2.3Mb/s. Because the variability of the original audio encoding, the number of channels carried is also variable. A typical system carries six programs each using 192Kb/s. The audio encoder accepts digital samples of the audio input, which in general is 2 channel stereo. Samples occur at 48KHz, rate 16 bits per sample, for a total rate of 768Kb/s per channel. A sub-band encoding technique is used to reduce the rate to a lower value, depend on the desired subjective quality. The output of the audio encoder is scrambled by modulo-2 addition with a pseudorandom sequence formed from 9-bit feedback shift register. This is different from the more common scrambling technique of division by a randomizing polynomial. It does not suffer from error multiplication effects, but it does require synchronization of the descrambling sequence at the receiver [38]. The purpose of this scrambling is to ensure that the final transmitted frequency spectrum is suitable dispersed. In addition, the standard allows for additional encryption scrambling if appropriate. The scrambled data is then convolutionally encoded. This is essential for satisfactory operation over a radio channel. The first step is a mother code of rate ¼ with constraint length 7. That code is then subject to puncturing to yield a rate of the form 8/n, where n can be any integer value between 9 and 32. Each audio channel can have different code rate, depending on the required error rate, to produce a given audio quality over the expected worst-case channel. Typically rate of approximately ½ is used [20]. Interleaving by a factor of 16 is then applied. Several audio channels are multiplexed and combined with other signals, which may include data channels in addition to audio. The signals are arranged in frames, as shown in Figure 4.4. A frame consists of a time sequence of 2 synchronization symbols, 3 digital overhead symbols, followed by 72 symbols of multiplexed audio information. A symbol is a block of 3072 bits, which are mapped into an OFDM symbol. The length of a frame is therefore sec 77 x 1.246 ≈ 96 ms. Overhead and information symbols are interleaved before assignment to sub-carriers. This provides further randomization of the signal. The synch symbols are added and the OFDM modulation performed. The raw bit rate can be calculated as:

69

72 symbols × 1536 subcarriers / symbol × 2 bits / subcarriers = 2.3 Mb / s 0.096 sec

(4.1)

For satisfactory performance, the OFDM symbol rate must be large compared to a maximum Doppler shift. Complete transmission model for DAB system is given in Figure 4.3.

Figure 4.3 Block diagram of a DAB transmitter Structure of the DAB signal

The DAB signal each transmission frame consist of consecutive OFDM symbols. The number of OFDM symbols in a transmission frame is dependent on the transmission mode. The synchronization channel in any transmission mode occupies the first two OFDM symbols of each transmission frame. The first OFDM symbol of the transmission frame is the Null symbol of duration TNULL. > Ts. The remaining part of the transmission frame L OFDM symbols of duration TS, of which the first one is a fixed Phase Reference Symbol (PRS) and the remaining L - 1 carry DQPSK modulated data. The frame structure can be seen in Figure 4.1 and different frame parameters for the three operation modes are shown in Table 4.2.

Figure 4.4 Structure of the DAB transmission frame

Each of these OFDM symbols made up of a set of equally-spaced carriers, with a carrier spacing equal to 1/Tu. Any OFDM symbol consists of N subcarriers, indexed from –N/2+1 to N/2. However, only K < N carriers with indices –K/2,…,-1 and 1,…,K/2 are modulated, whereas no symbols are transmitted over the N-K-1 outer subcarriers, to

70

avoid interfering on adjacent bands, nor over the zero-th subcarrier. The main signal s(t) can be defined using the following formula: K   +∞ L 2  2 jπfct  s (t ) = Ree z m,l ,k . g k ,l (t − mTF − TNULL − (l − 1)TS ) ∑ ∑ ∑ K m = −∞ l = 0   k =− 2  

0 g k ,l (t ) =  2 jπk (t −∆ ) / TU . Re ct (t / TS ) e

(4.2)

for l = 0

(4.3)

for l = 1,2,K, L

and TS = TU + ∆

(4.4)

where Zm,l,k is the complex D-QPSK symbol associated to carrier k of OFDM symbol l during transmission frame m. For k = 0, Zm,l,k = 0, so that the central carrier is not transmitted and fc is the central frequency of the signal. These parameters are specified in Table 4.2 for transmission modes I, II and III. The values of the various time related parameters are given in multiples of the elementary period T = 1/2048000 seconds, and approximately in milliseconds or microseconds. Table 4.2 Definition of the parameters for transmission modes I, II and III Parameter

Mode I

Mode II

Mode III

L: # of symbols per transmission frame

76

76

153

N: # of total subcarriers

2048

512

256

K: # of active subcarriers

1536

384

192

196608 T

49152 T

98304 T

96 ms

24 ms

48 ms

2656 T

664 T

345 T

~1.297 ms

~324 µs

~168 µs

2552 T

638 T

319 T

1.246 ms

312 µs

156 µs

2048 T

512 T

256 T

1 ms

250 µs

125 µs

504 T

126 T

63 T

~246 µs

~62 µs

~31 µs

Subcarrier spacing

1 KHz

4 KHz

8 KHz

Nominal maximum transmitter separation for SFN

96 km

24 km

12 km

Nominal frequency range (for mobile reception)

≤ 375 MHz

≤ 1.5 GHz

≤ 3 GHz

TF: Frame duration

TNULL: Null Symbol duration

TS: duration of the OFDM Symbol

TU: useful symbol duration

∆: duration of guard interval

71

Null symbol

As previously described, the first OFDM symbol of the transmission frame is the null symbol. During the time interval [0, TNULL] , the main signal s(t) is equal to 0. Phase reference symbol

The second OFDM symbol of the transmission frame is the phase reference symbol. It constitutes the reference for the differential modulation for the next OFDM symbol. The phase reference symbol is defined by the values of Zl,k for l = 1.

 jφ e z l ,k =   0

K −K <= k < 0 and 0 < k <= 2 2 for k = 0

for

(4.5)

As the Null symbol and the PRS represent overhead that is explicitly inserted synchronization purposes. During the Null symbol, no signal is transmitted, so that the receiver can immediately recognize the start of a new frame, by simply observing a drop in the received power. The PRS is built starting from a Constant Amplitude Zero Auto Correlation (CAZAC) block of 16 symbols of a 4-PSK constellation which is repeated with different offsets and integrated to yield a sequence of K 4-PSK symbols again with good correlation properties. The overhead bits constitute a fast information channel, which carries parameters necessary for decoding subsequent information. QPSK Symbol Mapper

For any of the OFDM symbols of index l = 2, 3, 4 ,..., L, the 2K-bit vector ( pl ,n ) 2n =K0−1 , whose elements pl,n are mapped on the K complex QPSK symbols ql,n according to the following relation: q l ,n =

1 2

[(1 − 2 p ) + j (1 − 2 p l ,n

l ,n + K

)]

for

n = 0,1,2, K , K − 1

(4.6)

Frequency interleaving

In frequency interleaving the correspondence between the index n of the QPSK symbols ql,n and the carrier index (-K/2 ≤ k < 0 and 0 < k ≤ K/2). The QPSK symbols are re-ordered according to the following relation y l ,k = ql ,n

for

l = 2,3, K , L

(4.7)

72

with k = F(n), where F is a function defined in the standard for the different transmission modes. Differential Modulation

DAB uses differential modulation to modulate the data on different subcarriers. Therefore frequency-domain channel equalization is not required, since the information is associated with the phase difference of the transmitted and received symbols. Differential modulation is applied to the QPSK symbols on each carrier and is defined by the following rule: Z l ,k = Z l −1,k . y l ,k

(4.8)

for l = 2,3,4,...L

(4.9)

and



k k <= k <= 2 2

(4.10)

This means that each carrier is modulated using a π/4-shift D-QPSK. All together, they form the main signal. The generation of the complex D-QPSK symbols Zm,l,k does not depend on the transmission frame index m, which appears on the formula defining the main signal s(t). The main signal s(t) is therefore defined for all values of t. It is generated from the DQPSK symbols Zm,l,k by the OFDM symbol generator of Figure 4.1. OFDM Symbol Generation

OFDM symbol is generated using N point IFFT. Value of N depends on the transmission mode of DAB. Complex output of IFFT is first fed to digital to analogue converter and RF conversion is done using IQ modulation to get the real signal. In simulation we have upsampled the signal four times and converted to real signal at the baseband level using IQ conversion.

73

I -time-

|I| -frequency-

1

120 100 80

n

|I(f)|

0.5

0

60 40 20

-0.5

0

1

2 time

0

3 x 10

0

1

2 frequency

5

3 x 10

5

|Q LPF| -frequency-

Q -time0.2

120 100

0.1 (f)|

LPF

60

|Q

n

80 0

40 -0.1 20 -0.2

0

1

2 time

0

3 x 10

0

1

2 f

5

3 x 10

5

Figure 4.5 OFDM signal after D/A converter in time and frequency domain ILPF -time-

|ILPF| -frequency-

0.8

120

0.6

100 80 LPF

I(n)

(f)|

0.4

40

0 -0.2

60

|Q

0.2

20 0

1

2 n

0

3 x 10

0

1

2 f

5

3 x 10

5

Q LPF -time0.2

120 100

0.1

n

80 0

60 40

-0.1 20 -0.2

0

1

2 time

0

3 x 10

5

0

1

2

3 x 10

5

Figure 4.6 OFDM signal after low pass filtering in time and frequency domain

4.4

Performance Results

For performance evaluation phone.wav file has been read using waveread function of Matlab and converted to bits to be transmitted. Results have been obtained. All channel have been simulated as Rayleigh channel at pedestrian speed of 1km/hr. No channel estimation has been done as the modulation technique used is DQPSK.

74

Figure 4.7 shows the transmitted symbol in time domain and frequency domain. Figure (a) shows one peak in starting of the signal, which is the phase reference symbol. Figure (b) shows that outer subcarriers are null carriers to avoid interference to other bands. D AB transmission signal in time-domain 1

s(n)

0.5 0 -0.5 -1

0

0.5

1

1.5

2

2.5

n

3 x 10

D AB transmission signal frequency-domain

5

80

|S(f)|

60 40 20 0

0

0.5

1

1.5

2

fre que ncy

2.5

3 x 10

5

Figure 4.7 DAB Transmitted signal (a) in time domain (b) in frequency domain, for

mode 1 having 2048 subcarriers Figure 4.8 show the Rayleigh fading envelope at 100km/hr speed. Channel changes quite rapidly within one frame duration for this speed and have deep fades in the time domain.

Figure 4.8 Rayleigh fading Envelope and phase response at 100 km/hr speed

75

As can be seen from Figure 4.9 that at the pedestrian speed of around 1km/hr we can achieve 0 bit error rate at 11 dB SNR but as the velocity increases curve changes to irreducible BER floors. Main reason of this is that we are not using any error control coding for recovery of the lost bits. For BER les than 10-5 FEC is required in such fading channels.

Figure 4.9 BER v/s SNR Curves for Rayleigh fading channels at different speed for

transmission mode 1 For different frequency selective channels performance of OFDM varies differently. Figure 4.10 and 4.11 shows the performance in such channels for transmission mode 1 and mode2. SNR requirements are minimum for AWGN channels and about same for both the transmission modes. Rural area have some less reflectors and obstruction for the signal propagation so having less multipath as compared to urban area. Free space have less multipath component but these arrives at the receiver after very much delay that is why SNR requirements are most critical for this channel model. In Figure 4.11 it is clear that we can not achieve BER of 10-5 for free space channel even for higher SNR values. That is because mode 2 have smaller symbol duration and cyclic prefix length (61.512 µs) whereas maximum delay spread of free space channel is 160 µs. For mode 1 cyclic prefix is sufficient enough (246 µs) to overcome this delay spread. Typical Urban area requires around 6-9 db more SNR than rural area for the same BER of 10-4. DAB doesn’t use any kind of training sequence. So it is not possible to do any channel estimation at receiver. The information is recovered differentially from the previous symbol received. If one of the symbols is in more error than other then all the further received symbols will be in error till the next frame comes with fresh phase 76

reference symbol. Results for two different transmission modes in different channels have been summarized in the Table 4.3.

Figure 4.10 BER v/s SNR Curves for different fading channels for transmission mode 1

Figure 4.11 BER v/s SNR Curves for different fading channels for transmission mode 2 Table 4.3 SNR requirements for Transmission Mode 1 and 2 for BER 10-4 Channel Model

DAB Transmission Mode Mode 1

Mode 2

AWGN

9.25 dB

10 dB

Rural Area 1

11.75 dB

12.5 dB

Rural Area 2

10.25 dB

11 dB

Urban Area

17 dB

20.5 dB

Free Space Area

26 dB

Not achievable

77

Chapter 5

Study of OFDM in Asymmetric Digital Subscriber Line 5.1

Digital Subscriber Lines

In the 1980s, T1/E1 (1.544 / 2.048 Mbps) lines became available to businesses for voice and data transmission. T1/E1 lines required repeaters every 3,000 to 5,000 feet, and all bridged taps had to be removed for proper use of these lines. Therefore, a T1/E1 line was expensive to install and the installation as well as maintenance was time consuming. This leads o the development of the Digital Subscriber Lines. Description of different wireline standards and their data rates is given in the table 5.1 for the purpose of comparison. Table 5.1 High speed data communication standards Standard

Data Rate (kbps)

Description

V.32 (voice band modem)

9.6

Full duplex using PSK

V.34 (voice band modem)

33.6

Channel precoding

V.90 (voice band modem)

56 down

Pulse code modulation

33.6 up ISDN (Integrated service digital

144

Two 64 kbps and

network) HDSL (High bit rate DSL)

one 16 kbps channel 1544/2048

Two wire pairs, reach of 12,000 feet

ADSL (Asymmetric DSL) G.lite

1500-8000 down

One wire pair, reach of 18,000

16-640 up

feet require splitters

up to 1500 down

no splitter

up to 512 up VDSL (Very high rate DSL)

13000-52000 down

One wire pair reach of 4500 feet

1500-6000 up DOCSIS (Data over cable)

27000 or 36000 down

Cable TV infrastructure

320-10240 up IEEE 802.14 (cable modem)

27000 or 36000 down

Cable TV infrastructure

DSL technology is not limited to businesses and communication between central offices. Consumer applications such as video-on-demand required high throughput in the downstream and smaller throughput in the upstream hence the concept of Asymmetric data rate came, which lade to Asymmetric Digital Subscriber Lines (ADSL). ADSL was originally proposed for video-on-demand applications to transmit MPEG-1 video streams.

78

Before the standardization, the bit rate requirements changed due to the development of MPEG-2. For residential and commercial users with an ongoing need for broadband data access, but who do not send out correspondingly large data streams, asymmetric digital subscriber line (ADSL) services work well. This service is so named because the data rate sent to the user (downstream) is much greater than the data rate sent from the user (upstream). This asymmetric model is based on typical Internet usage patterns. Rate-adaptive ADSL automatically determines the highest rate it can provide over a given loop. Rate-adaptive ADSL (RADSL) supports downstream rates up to 7-10 Mb/s and upstream rates up to 512 - 900 kb/s. Spectrum Allocation

The ADSL PHY was designed so that it could peacefully co-exist with the standard POTS spectrum. The two services can co-exist because the ADSL spectrum only uses the frequencies above POTS. The POTS spectrum goes from near DC to approximately 4 kHz. A frequency guard band is placed between the POTS spectrum and the ADSL spectrum to help avoid interference. The ADSL spectrum starts above the POTS band and extends up to approximately 1.1 MHz. The lower part of the ADSL spectrum is for upstream transmission (from the customer to the CO) and the upper part of the spectrum is for downstream transmission. There are actually two different ways that the upstream and downstream spectra can be arranged. In a frequency division multiplexed (FDM) system, the upstream and downstream spectra use separate frequency ranges. They can vary for different implementations, but typically the upstream band is from 25 to 200 kHz and the downstream band is from 200 kHz to 1.1 MHz. Other divisions are also permitted within the ADSL standard. This system is free from the occurrence of a type of interference called self-crosstalk. One drawback, however, is that the downstream bandwidth is reduced in comparison to an echocancelled system. An echo-cancelled system allows the downstream band to overlap with the upstream band. The upstream band still uses the frequencies from 25 to 200kHz, but the downstream band can now extend over the upstream band. The main advantage of this system is that it significantly extends the available downstream bandwidth. However, it does require echo-canceling circuitry due to the full-duplex transmission. In addition, the presence of self-crosstalk causes additional interference. Because most of the

79

consumer products are very cost sensitive, and it is cheaper to use a non-overlapping method, that is the most usual. For a downstream transmission 256 different carriers are used but for a upstream transmission only 32 carriers are used. The 256 carriers downstream and the 32 carriers upstream use the frequency interval from 0 Hz up to 1.104 MHz and 138 kHz, respectively. The number of carriers that are actually used are lower.

Figure 5.1. ADSL Frequency Plan

5.2

Application of OFDM in Asymmetric Digital Subscriber Lines

An ADSL system uses existing telephone wire to allow bi-directional data communications between a user and the telephone company's central office (CO). An important advantage of ADSL is that it allows the plain old telephone system (POTS) signal to co-exist with the ADSL data signal. ADSL was the first DSL standard to adopt multicarrier modulation. The emerging Very High Bit Rate DSL (VDSL) standards will support two line codes {multicarrier modulation and carrierless amplitude/phase modulation). Multicarrier modulated VDSL will likely be an extension of ADSL. The goal for VDSL is to achieve up to 52 Mb/s downstream for distances up to 1,000 feet and 13 Mb/s downstream for distances up to 3,750 feet. VDSL is proposed as a way to connect a consumer to a fiber optical communication network in the consumer's neighborhood.

80

The PHY of ADSL uses a multicarrier modulation technique known as discrete multitone (DMT). A DMT system transmits data on multiple subcarriers in a manner very similar to the OFDM technique that is used in many wireless applications. A DMT modulator takes in N data symbols in parallel and transmits the symbols on N subcarriers. The data rate on each subcarrier is 1/N the original data rate. Reducing the data rate results in a DMT symbol period that is N times as long as the original symbol period. Increasing the symbol period can make the symbol longer than the time span of the channel. This situation can make it easier to combat the effects of intersymbol interference.

5.3

Implementation of OFDM based ADSL

Different physical layer parameters for the implementation of Digital subscriber lines with OFDM are given in Table 5.2. Number of subcarrier used for the downstream and upstream is different as the data rate in downstream and upstream is different. Table 5.2. Physical Layer Parameters for DMT (OFDM) based DSL Downstream Overall symbol rate

4 kHz

Number of carriers per DMT

Symbol 256

Subcarrier spacing

4.3125 kHz

Cyclic prefix length

32 samples

Operational modes

FDM or echo cancelled

FDM mode frequency range

64 to 1100 kHz

Echo cancelled mode frequency range

13 to 1100 kHz

Number of bits assigned per subcarrier

0 to 15 (no bits assigned to 64k QAM)

Synchronization

Pilot tone at subcarrier 64, f = 276 kHz Upstream

Number of subcarriers per DMT symbol

32

Cyclic prefix length

4 samples

FDM mode frequency range

11 to 43 kHz

Echo cancelled mode frequency range

11 to 275 kHz

Synchronization Pilot tone at subcarrier

16, f = 69 kHz

DMT Transmitter

The DMT signal is formed using an Inverse Fast Fourier Trans-form (IFFT) at the transmitter. The data symbols at the transmitter are treated as being in the frequency domain and act as complex weights for the basis functions (orthogonal sinusoids at 81

different frequencies) of the IFFT. The IFFT then converts the data symbols into a timedomain "sum of sinusoids" signal. The block of IFFT output samples is known as a DMT symbol. This time-domain signal is transmitted across the channel, and an FFT is used at the receiver to bring the signal back into the frequency domain. A block diagram of a typical ADSL transmitter/receiver pair is shown in Figure 5.2.

Figure 5.2 Block diagram of a ADSL Transceiver using Discrete Multitone Modulation Convolutional Codes

A Reed-Solomon block code is used on top of the convolutional code. Reed-Solomon codes are powerful codes that are good at detecting and correcting burst errors, such as those generated by the Viterbi decoder. The ADSL specification allows Reed-Solomon code-word lengths of up to 255 bytes with the addition of up to 16 parity bytes for each code word. The outermost code is a cyclic redundancy check (CRC) code. The CRC can detect errors, but it cannot correct them. The CRC code is used as a top-level errordetection mechanism in order to detect any errors that remain after Viterbi and ReedSolomon decoding. We have not used any error correcting coding scheme in our simulations. Tone Order

The dynamic bit loading algorithms allows DMT to vary the number of bits per symbol for each subcarrier based on the subcarrier's signal-to-noise ratio (SNR). Subcarriers with a low SNR transmit binary phase-shift keying (BPSK) or Quadrature PSK (QPSK) because they are robust modulation formats. If the subcarrier's SNR is very low, that subcarrier will not be used to transmit data at all. Subcarriers with a higher SNR transmit 82

higher-order Quadrature Amplitude Modulation (QAM) in order to achieve an increased throughput. Unlike DMT, in OFDM systems, the number of bits in each channel is equal and constant. Thus, there is no need for a bit-loading algorithm. The tone order assigns bits to different carriers. The most important thing to know is how many bits that can be assigned for each symbol. In the initialization process, a known bit pattern is transmitted for the test transmission period and received at the receiver. SNR will be calculated at the receiver. This process is repeated for several times to find out the SNR at each subcarrier. Then this SNR information is transferred to the transmitter for making the calculation of bit allocation table before the training time has expired. We have used 5 rounds to find out the average SNR on each subcarrier. SNR values and the corresponding bit-table is presented in Figure 5.3. SNR is the ratio between signal and noise and this is the main parameter to decide how much data that can be transmitted over the channel. SNR is calculated through the formula in equation (5.1), where x is the transmitted and y the received signal.

Figure 5.3. (a) SNR (b) bit allocation for given SNR at each subcarrier for CSA Loop-1  x   (5.1) SNR = 20 × log  ( x − y )   The bit table shown in Figure 5.3 (b) is correlated to the SNR with a simple bit allocation

algorithm. The bit-table can be calculated with several different methods but all give more bits to the carriers with the highest SNR. A signal with the double power has 3 dB higher values. An increase with one bit doubles the number of possible constellations.

83

The distance between two successive constellation points then approximately is half the length. A good approximation is to give 3 dB for each new bit. To increase the performance it is also common to have a margin down to zero. In the simulation we have followed a simple algorithm that calculate the bit-table, b as:  SNR − 6  b= , here 6 is the margin in dB  3 

(5.2)

The tone order function has two incoming paths, one fast and one interleaved that are multiplexed together to an incoming bit stream, see Figure 5.4. When the bits are assigned, the bits from these two paths append in different areas.

Figure 5.4. The fast and interleaved bit streams are merged together and are thereafter

transmitted to the tone order The algorithm for tone ordering starts with a bit stream with the N bits that will be transmitted. N is the number of bits that are possible to transmit. In these N bits the fast bits come first and then the interleaved bits. First allocate bits to the tones that can transmit the smallest number of bits and after that in increasing order. The result is that the fast bits are transmitted over the carriers with the fewest bits. Subcarrier Modulation and Mapping

The DMT subcarriers shall be modulated as BPSK, QPSK, 16-QAM, or 64-QAM using constellation encoding. The constellation encoding is independent for each tone. The number of points for each tone depends on the number of bits that are assigned to each tone. The smallest tones with two bits can give four different constellation points and the biggest with 15 bits can give 32768 different points. b bits give 2b constellation points. If b is odd it is more difficult but the idea is to never have the constellation points further away than necessary. In Figure 3.6 shows the smallest even constellations are presented. Figure 5.5 shows the two smallest odd constellations are presented.

84

QASK Constellation

3

1

5

1

0

4

-1

7

3

2

6

-3

-1

1

3

Quadrature

(a)

-3

In-phase

QASK Constellation

5

28

20

22

30

3

12

13

9

8

24

25

1

4

5

1

0

16

17

-1

6

7

3

2

18

19

-3

14

15

11

10

26

27

29

21

23

31

1

3

Quadrature

(b)

-5

-5

-3

-1

5

In-phase

Figure 5.5 The constellation points for odd number of bits. (a) 8-QAM and (b) 32-QAM IFFT and FFT

The efficiency of DMT and OFDM lies in the modulation of the subcarriers. Instead of having two independent modulators, the modulators are implemented with 2N-point inverse FFT (IFFT). In DMT, the N negative-frequency IFFT bins are the complex conjugate of the N positive-frequency bins. This symmetric spectrum results in a real time-domain signal. The DMT signal is centered at DC with the subcarriers around DC zeroed out (not used) to create a hole in the DMT spectrum in order to make room for the POTS spectrum. DMT is thus a true baseband system. 85

Figure 5.6 Generation of real signal from IFFT

In the full rate downstream direction, a block of 255 complex data symbols, including several of value zero, are assembled together. Subcarriers which can not support at least a 9dB SNR (6dB margin + 3 dB for each bit) have not been used for data transmission Conjugate appending is performed on the block followed by a 512 point IFFT as shown in Figure 5.5. This results in frame of 512 real values. A cyclic prefix of 32 samples is added, and the resultant 2.208M samples per second transmitted over the line. Cyclic Prefix

DMT supports inclusion of a cyclic prefix. A cyclic prefix is a block of samples with a length, LP, that is a replica of the last LP samples of the DMT symbol. The prefix is transmitted first, followed by the 2N (512) samples of the DMT symbol. ISI is completely eliminated for channels with impulse responses of length less than or equal to LP + 1. The prefix is selected as the last 32 samples of the symbol in order to convert the linear convolution effect of the channel into circular convolution. The cyclic prefix contains redundant information. However, the DMT receiver exploits the presence of the prefix in order to mitigate the effects of the channel. Channel

In case of the DSL the channel is the telephone line. It must be pretty short because the performance decreases with the length of the copper wire. A telephone line can have a lot of different forms. It can be one very long cable or it can be a cable with a lot of crossings that disturb the signal. In a simulation some standard loops, called csaloops are used. In the simulation, eight different channel models called csaloop1 - csaloop8 are used. They 86

can be viewed in Figure 5.7 and 5.8. They are presented in more detail in [49]. Different models for testing can be found in [50]. Impairments There are several significant types of impairments encountered in an ADSL system: additive white Gaussian noise (AWGN), crosstalk, impulse noise, bridged taps, and radio noise. In a digital system such as ADSL, AWGN can cause symbol errors to occur at the receiver when noise pushes the received sample beyond a decision boundary. Like many other digital communication systems, ADSL employs error-control coding and interleaving to help mitigate the effect of AWGN. Time Domain Equalizer (TEQ)

The main idea with the TEQ filter [46] [48] is to mitigate the intersymbol interference (ISI) that appears between two different symbols. ISI appears because two symbols overlap each other. TEQ filter pushes the ISI to a small range. If the range is shorter than the cyclic prefix, the entire problem can be removed. A MATLAB toolbox [47], where different TEQ filters are implemented is included in the toolbox. In the simulation the minimum-ISI method that optimizes for shortest possible length of the ISI is used that is described below. Minimum-ISI The idea with this method is to force the ISI to change its location from a big part of the symbol to only the part with the cyclic prefix. The method that is called Minimum-ISI will minimize the ISI outside the area of the cyclic prefix. The only effect that TEQ has on the channel capacity is the way it spreads ISI power over different frequencies. This experience is used in the minimum-ISI method. If the total sum of the ISI power is minimized it would be better but this is not the optimal way. The ISI from the frequencies with a dominant noise has no effect on SNR so it can be ignored. The channel impulse response h and the equalizer w are mixed. Then it is one part that causes ISI, h * w and one part that does not. Also only the part that extends beyond the cyclic prefix causes ISI. The Optimization Problem Goal [44]: • Find w that minimizes a weighted sum of the ISI power gains in each subchannel.

87

min diag ( S ) .Q.D.H .w

2

(5.3)

• Prevent w from also minimizing the desired part of the h⊕w: G.H .w = 1 ; G = I − D

(5.4)

w: The equalizer. This is the vector that is the answer. H: The convolution matrix, such that H.w= h ⊕ w D: The windowing matrix. This is a diagonal matrix that isolates the part of h ⊕ w

causing ISI. Q: The FFT matrix. Takes FFT of D.H.w S: The weighting matrix diag(S). amplitude -->

6

Actual channel impulse function

-3

4 2 0 -2 6

amplitude -->

x 10

0 -3 x 10

0.5

0

0.5

1.5

2

2.5

3 x 10

-4

4 2 0 -2

0.04

amplitude -->

1

C hannel impulse function w ith splitter

1

1.5

2

Shorted channel impulse function

2.5

3 x 10

-4

0.02 0 -0.02 -0.04

0

0.5

1

1.5

2

2.5

time (sec) -->

3 x 10

-4

Figure 5.7 Channel impulse response for CSA Loop – 1 in time domain before and after

channel shortening Effect of time domain channels shortening can be clearly seen in Figure 5.7 (c), where response of the channel made shorter then the cyclic prefix length.

88

Magnitude (dB) --> Magnitude (dB) --> Magnitude (dB) -->

Actual channel impulse function

0

-50

-100

0

2

0

4

6

8

Channel impulse function with splitter

10

12 x 10

5

-50

-100

0

2

0

4

6

8

Shorted channel impulse function

10

12 x 10

5

-50

-100

0

2

4

6

frequency (Hz)) -->

8

10

12 x 10

5

Figure 5.8 Frequency response of CSA Loop – 1 before and after channel shortening

Frequency Domain Equalizer (FEQ) The Frequency Domain Equalizer is a vector with complex values that is multiplied row wise with the subchannels, if the cyclic prefix is sufficiently large and the TEQ removes the ISI completely. That also means that if the prefix length is longer than the length of the channel impulse response, then the FEQ is only one single complex coefficient for each subchannel. In the calculations it is assumed that the condition is fulfilled. The Frequency Domain Equalizer uses an adaptive algorithm. One of the simplest algorithms is the Least Mean Square (LMS) [27] [28] algorithm, which we have used in the simulations see Figure 5.9. The algorithm does not need off-line gradient estimations or data repetitions. For this reason and because it is simple and easy to compute, the LMS algorithm is often used.

Figure 5.9 The adaptive LMS algorithm that is used in FEQ

89

In each iteration of the algorithm the error is calculated as the difference between the transmitted signal and the signal after the equalization process, see Equation 2. The received signal after the transmission, r is calculated in Equation 3. This signal, the error signal and the old filter are all applied to an adaptive algorithm, Equation 4. This algorithm has different values for different applications depending on how fast the function must adapt and how much variation that is acceptable. At last the signal is filtered through the equalizer in equation 5.5 to 5.8 and everything would take a new round, possibly a little closer to the correct result.

e= x− y

(5.5)

r = xH

(5.6)

FN = f ( FN −1 , e, r )

(5.7)

y = r.H

(5.8)

DMT Receiver

The receiver is basically the dual of the transmitter with the exception of the addition of time-domain and frequency domain equalizers. The time-domain equalizer ensures that that the equalized channel impulse response is shortened to be less than the length of the cyclic prefix. If the TEQ is successful, then the received complex symbols after the FFT are the multiplication of the transmitted symbols with the FFT of the shortened (equalized) channel impulse response. The frequency domain equalizer (also called a onetap equalizer) divides the received symbols by the FFT coefficients of the shortened channel impulse response. After mapping the symbols back to the corresponding bits using the QAM constellation, they are converted to serial bits. Bit rate has been calculated with the formula given below: Bit Rate (in Mbps) = [Σ(Bit Table)]* 2.208e6 / 544 / 1e6

5.4

(5.9)

Performance Results

The simulation has eight different channels models, without any noise at all. From these 24 different cases the bit rate and the bit error rate have been calculated. The bit error rate (BER) is often chosen to 10-7 but in this model that is difficult because a lot of bits would be transmitted and that takes time. Another reason is that the BER would not be so small because no coding operations are used in the model. The coding operations (ReedSolomon and Trellis) decrease the BER a lot but they are not implemented in the present simulation.

90

Unequalized and Equalized Constellations 1 Unequalized Constellation Equalized Constellation

0.8 0.6 0.4

Imaginary

0.2 0 -0.2 -0.4 -0.6 -0.8 -1 -1

-0.8

-0.6

-0.4

-0.2

0 Real

0.2

0.4

0.6

0.8

1

Figure 5.10 Effect of frequency domain equalization on constellations

The received constellation is shown in Figure 5.10 in blue dots. We have to apply Frequency domain equalization to remove the effect of ISI caused by the channel. The results from my model are presented in Table 5.3. Simulations that give these values are optimized for the highest possible rate under the condition that the bit error rate would be lower than approximately 1%. The results in the model are far from the optimal result. The most important reason for that is the TEQ. TEQ function is a very big issue that has not been prioritized in this thesis. The TEQ functions that are used in the toolbox were found on Internet and that was the best model for TEQ that was possible to get. Table 5.3. Simulation results for different CSA Loop channels, showing achievable data

rate in downstream with Bit Error Probability Channel CSA Loop # 1 2 3 4 5 6 7 8

Rate (Mbps) 2.2486 1.9239 1.3151 2.7154 3.4297 0.8929 0.8158 0.6494

BER 0.0082 0.0066 0.0061 0.0058 0.0067 0.0058 0.0071 0.0022

Maximum achievable data rate with the simulation is 3.4297 Mbps in the case of CSA Loop 5 with BER of 6.7x10-3. Minimum achieved BER is 2.2x10-3 for CSA Loop 8 but that gives only 649.4 Kbps of data rates.

91

Chapter 6

Summary and Conclusion Discussion of Results In Wireless LAN application of OFDM increasing the number of subcarriers does not have any significant effect on SNR requirements until the cyclic prefix is sufficiently higher than the rms delay spread. Effect of increasing the number of subcarriers can be seen only when the multipath delay spread is high. ETSI channel model E and JTC channel model E have sufficiently high multipath delay spread for which OFDM does not perform well with 64 subcarriers but as we increase the number to 256, SNR requirement decreases by 5dB (Figure 3.20 a and b). More increase in subcarriers does not give much improvement. In AWGN channel required SNR does not changes with change in number of subcarriers (Figure 3.20 c). System performance improves as the RMS delay spread increases, until the excess delay significantly exceeds the guard interval length. This characteristic is due to the use of OFDM instead of a single carrier system. OFDM exploits the increased frequency diversity that results from high RMS delay spread. However, when the excess delay exceeds the guard interval length ISI impairs performance. To conclude for WLAN application SNR requirements are least in the case of Rician channel model C and in general in AWGN channel. Our performance evaluation shows that for all channel models used in the simulation BPSK is the best and 64 QAM is the worst Maximum data rate of 54 Mbps is achievable only with sufficient FEC and interleaving. However higher data rates are obtainable with higher order modulation only. Increasing modulation order higher than 64 QAM will demand very high SNR values which are not available in practical situations. In Digital Audio Broadcasting application we have simulated different transmission modes. Performance of Mode 1, Mode 2 and Mode 3 were found having no difference in AWGN (non fading) channel. Performance is almost same for two different rural area (non hilly) channel but for urban area channel, Mode-1 with 1536 number of subcarriers require 3.5 dB less SNR than Mode-2 with 384 subcarriers. Typical Urban area requires around 6-9 db more SNR than rural area for the same BER of 10-4 in Mode 1. Free space channel have maximum delay spread of 160µs and rms delay spread of around 90µs.

92

Faithful transmission in free space area is possible only with Mode-1 because it have a guard interval of duration 246 µs as compared to 62 µs guard interval in Mode-2. Even in Mode-1 SNR requirements are highest (26dB) for this channel. In genereal, DAB can provide data rates of 2.3 Mbps for broadcasting of very good quality sounds and voice in digital form, to fixed, portable and mobile receivers. For DAB, Mode 1 performs better than Mode 2 because of large symbol time and cyclic prefix duration. In Digital Subscriber Lines eight different CSA Loop channel has been implemented. Maximum data rate of 3.4297 Mbps have been achieved with simple bit loading algorithm applied to DMT. In DMT each subcarrier can be modulated with up to 15 bits but because of channel impairments we are able to achieve a maximum of 8 bit on few subcarriers. The performance shown by simulations is not ideal because no error correcting technique has been used and there can be some improvement in the time domain equalizer, which was not optimized for this simulation.

Conclusion OFDM appears to be a suitable modulation technique for high performance wireless and wired telecommunication systems. OFDM has been confirmed to work very good by using MATLAB simulations. Different types of channels have been used for different applications to evaluate OFDM performance like Gaussian Channel, Rayleigh fading channel Frequency selective slow and fast fading channels and twisted pair channels. Also the effect of guard period, number of subcarriers, different modulation schemes, forward error correction and interleaving schemes, synchronization and channel estimation technique have been tested for OFDM performance. OFDM was found to perform very well in multipath channel as long as the delay spread less than the guard period. OFDM performance in Gaussian channel was the best but similar to the single carrier systems, among the other types of channels tested, but this kind of channel is very difficult to achieve in the mobile radio environment. OFDM performance in Fast fading frequency selective channel was the worst case, especially with excessive multipath delay, which result in high Inter-symbol interference. This thesis has concentrated on OFDM, however most practical system would use forward error correction to improve the system performance. FEC has been used, only for the WLAN application of OFDM. In all the three applications, frequency domain interleaving has been used to reduce the burst errors. Several modulation techniques for 93

OFDM were investigated in this thesis including BPSK, QPSK, 16PSK, 64QAM, higher order QAM and Differential QPSK. Duration of cyclic prefix, modulation scheme and number of subcarriers have critical effect on data rates in case of fading channels. OFDM cannot achieve higher data rates efficiently without error correction and interleaving. Some factors were not tested here like peak power clipping, start time error and the effect of frequency stability errors. The codification used for the system could be improved by using turbo codes instead of convolutional codes. Also, the pilot signal distribution could be modified to reduce the redundancy. Adaptive techniques for bit loading and dynamically choosing the modulation technique based on the type of data being transmitted can improve the system performance further. More work could be done on investigating suitable techniques for doing this. OFDM promises to be a suitable modulation technique for high capacity wireless and wired communications. The future for OFDM is very bright as it gains significant momentum in the industry.

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97

2001],

Appendix A For BPSK, b0 determines the I value, as illustrated in Table A.1. For QPSK, b0 determines the I value and b1 determines the Q value, as illustrated in Table A.2. For 16-QAM, b0b1 determines the I value and b2b3 determines the Q value, as illustrated in Table A.3. For 64-QAM, b0b1b2 determines the I value and b3b4b5 determines the Q value, as illustrated in Table A.4 Table A.1 BPSK encoding table

Table A.2 QPSK encoding table

Input bit (b0)

I

Q

Input bit (b0)

I

Q

Input bit (b1)

I

Q

0

-1

0

0

-1

0

0

-1

0

1

1

0

1

1

0

1

1

0

Table A.3 16 QAM encoding table

Table A.4 64 QAM encoding table

Input bit (b0 b1)

I

Input bit (b0 b1 b2)

I

Input bit (b3 b4 b5)

Q

00

-3

000

-7

000

-7

01

-1

001

-5

001

-5

11

1

011

-3

011

-3

10

3

010

-1

010

-1

110

1

110

1

111

3

111

3

Input bit (b0 b1)

Q

101

5

101

5

00

-3

100

7

100

7

01

-1

11

1

10

3

98

Performance Evaluation of OFDM Technique for High ...

PRS. Phase reference symbol for DAB. PBCC. Packet Binary Convolutional Coding. PHY. Physical Layer. QAM. Quadrature Amplitude Modulation. QoS.

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