This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the WCNC 2007 proceedings.

Convolutional Multiplexing for Multicarrier Systems Wei Jiang, Daoben Li

Xingpeng Mao

School of Information Engineering Beijing University of Posts and Telecommunications Beijing 100876, China Email: [email protected], [email protected]

Department of Communication Engineering Harbin Institute of Technology (Weihai) Weihai, Shandong 264209, China Email: [email protected]

I. I NTRODUCTION OFDM (Orthogonal Frequency Division Multiplexing) [1], [2] has been considered as a promising technology in the future wireless communications for its advantage of relatively high spectrum efficiency and immunity to the inter-symbol interference (ISI). As the data symbols are parallelized and transmitted on narrow subcarriers, the OFDM system suffers from frequency selective fading. Several improved schemes have been proposed to achieve diversity gain in frequency selective fading channels, such as Coded OFDM (COFDM), Multicarrier Code Division Multiple Access (MC-CDMA) [3]–[5], or OFDM Code-Division Multiplexing (OFDM-CDM) [6]. COFDM can achieve diversity gain and coding gain at the same time, but there is always a loss in spectral efficiency. The MC-CDMA system spreads the data symbols onto multiple tones according to the user-specific codes, and the signal of the different users can be multiplexed and transmitted on the same cluster of subcarriers. Though, the MC-CDMA system suffers from multiple access interference (MAI) and the diversity gain will be reduced when the system load is high [7]. In this paper, we propose a new scheme to multiplex the signal and transmit it on a group of orthogonal subcarriers. It’s called Multicarrier Convolutional Multiplexing (MCCM) system, in which the data symbols are spread onto several subcarriers in a convolutional manner. This system has the same spectrum efficiency with the conventional uncoded OFDM system using the same modulation. However, in frequency selective fading channel, the MCCM system can achieve significant diversity gain. As long as the spreading codes are well designed, the diversity order can be equal to the length of the codes, and there is no loss compared to the theoretical independent fading channel diversity with the maximum

Sy mb o l M ap p er

S

Co n v o lu tio n al Sp read er

X Interleaver

IFFT

CP

D/A

D e-In t erleav er

FFT

Remo v e CP

A/D

Channel

Abstract— A new multiplexing scheme with high diversity gain for multicarrier systems, which is called Multicarrier Convolutional Multiplexing (MCCM), is proposed. In this scheme the data symbols are spread onto several subcarriers by a convolutional spreader. Compared to the conventional OFDM (Orthogonal Frequency Division Multiplexing) system, the MCCM system using well designed spreading codes can achieve diversity with order equal to the length of the codes in frequency selective fading channels. A simple free distance searching algorithm is utilized to search the codes with the optimized performance. The best codes of length four are presented and their performance is evaluated by numerical simulations.

Y Detec tor

De-M ap p er

Fig. 1.

The structure of the MCCM system

ratio combining (MRC) when the maximum likelihood (ML) detector is used. The rest of the paper is organized as follows. Section II introduces the system model and describes the new multiplexing scheme in detail. Section III discusses the performance of the proposed system in AWGN (Additive White Gaussian Noise) channel and in frequency selective fading channel. Section IV proposes a free distance searching algorithm and presents several good-performance codes. The numerical simulation results are presented in the following section. Finally, a conclusion is drawn in the last section. II. MCCM S YSTEM M ODEL The model of the MCCM system is illustrated in Fig. 1. At the transmitter, the data stream is mapped into symbols and then passed through a convolution spreader, which introduces inter-symbol interference in the stream. Then, after interleaving, the symbols are modulated onto orthogonal subcarriers by inverse fast Fourier transform (IFFT), and padded with cyclic prefix (CP) to resist the ISI, just as the conventional OFDM system does. Correspondingly, at the MCCM receiver, after the FFT operation, the symbols are deinterleaved and detected. And the information data is retrieved after the symbol demapper. The convolutional spreader can be implemented by a transversal filter, as is shown in Fig. 2. The complex valued coefficients on the taps form a spreading code. The output of the spreader is the summation of the delayed symbols multiplied by the spreading code. The data bits within a block is mapped into a symbol sequence of length L, which is denoted as S = [S1 , S2 , · · · , SL ]. The spreading code is denoted as C = [C1 , C2 , · · · , CN ], where N is the length of the spreading code. Then, the output

1525-3511/07/$25.00 ©2007 IEEE

634

This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the WCNC 2007 proceedings.

Sl

S l-1 D

C1

S l-N+2

...

D C2

D C N-1

...

TABLE I M INIMUM E UCLIDEAN D ISTANCE OF M ODULATIONS

S l-N+1 CN

X (l) Fig. 2.

Modulation

BPSK

QPSK

8PSK

16QAM

2 Dmin (Eb )

4

4

1.7574

1.6

where D2 (Xi , Xt ) is the squared Euclidean distance between Xi and Xt , i.e.,

The structure of the convolutional spreader

D2 (Xi , Xt ) = of the convolutional spreader can be expressed as X(l) =

N 

Cn Sl−n+1 , 0 < l ≤ L,

(1)

where Sl = 0 for l ≤ 0. For the simplicity of the analysis, we normalize the spreading codes, i.e., 2

|Cn | = 1.

(2)

n=1

The received symbol vector after the deinterleaver is Y = [Y (1), Y (2), · · · , Y (L)]. In AWGN channel, it can be expressed as Y (l) = X(l) + n(l), 0 < l ≤ L,

(3)

where n(l) is the additive complex Gaussian noise with mean zero and variance N0 . As for the frequency selective Rayleigh fading channel, as long as the CP is larger than the delay spread of the channel, and the interleaving block length is large enough, the fading on the subcarriers can be assumed to be flat and independent. We denote the fading coefficient on the l-th subcarrier as h(l), and the received symbols are Y (l) = h(l)X(l) + n(l), 0 < l ≤ L.

2

|Xi (l) − Xt (l)| .

(7)

l=1

n=1

N 

L 

(4)

As is shown in Fig. 2 and given in (1), the convolutional spreader introduces inter-symbol constraint, just as the convolutional code. So it can also be represented by a trellis diagram and a symbol block can be represented by a path in the trellis which starts from and ends in the all-zero state [8]. The maximum likelihood sequence estimation (MLSE) [8], [9] algorithm can be used to detect the symbol sequence. III. P ERFORMANCE OF THE MCCM SYSTEM A. AWGN channel When the symbol sequence Y is received after the deinterleaver, the ML detection of the symbols can be expressed as ˆ = arg max P (Y|X) . (5) X X

In AWGN channel, it’s well known that the pairwise error probability [12] between the symbol vectors Xi and Xt is   2 (X , X ) D i t , Pe (Xi → Xt ) = Q  (6) 2N0

Let Df2 ree be the free squared Euclidean distance in the trellis: (8) Df2 ree = min D2 (Xi , Xt ), i,t

where Xi and Xt are two symbol sequences whose paths diverge from any state and remerge at the same, or another state after one or more transitions. Due to the lack of the linearity, we cannot assume a certain sequence, such as the all-zero sequence, is transmitted to find the free distance, just as we do for the convolutional codes. Based on the principle of the union bound, the event error probability [12] at high signal-to-noise ratio (SNR) is well approximate by   Df2 ree , (9) Pe ≈ Pf Nf ree Q  2N0 where Pf is the probability that a sequence with distanceDf2 ree sequences is transmitted, and Nf ree is the average number of sequences with distance Df2 ree to the transmitted sequence. When evaluating the performance of the MCCM system in AWGN channel, we neglect the effect of the Pf and Nf ree , and regard Df2 ree as the dominating factor. It’s reasonable to compare the MCCM system with the conventional uncoded OFDM system using the same modulation. Since the OFDM system is interference free in AWGN channel, its performance is dominated by the minimum squared Euclidean distance in the constellation, which is denoted as 2 2 . The parameter Dmin of some common modulations is Dmin listed in Table I. (Eb in the table represents the average energy per bit.) If the Df2 ree of the MCCM system is less than the 2 Dmin of the corresponding OFDM system, the MCCM system is inferior to the OFDM system, and vise versa. However, as regard to the free squared Euclidean distance of the MCCM system, there is a proposition as follows. Proposition 1: The free squared Euclidean distance of the MCCM system is no larger than the minimum squared Euclidean distance of the base modulation, i.e., 2 . (10) Df2 ree ≤ Dmin Proof: In fact, we only need to proof that given any transmitted symbol sequence, there is always another sequence 2 to the correct one. Suppose S = that have distance Dmin  [S1 , S2 , · · · , SL ] is transmitted, and let S be different from S only in one position, say l0 . Denoting the output sequences of

635

This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the WCNC 2007 proceedings.



the convolutional spreader generated by S and S as X and  X respectively, then according to (1) we have      |Cl−l0 +1 (Sl0 − Sl0 )|, l0 ≤ l < l0 + N   X(l) − X (l) = 0, others. (11) By substituting (2) and (11) into (7), we get 



D2 (X, X ) = |Sl0 − Sl0 |2 . As

(12)



2 = min |Sl0 − Sl0 |2 , Dmin Sl0 ,Sl

(13)

0

according to (8), the free squared Euclidean distance is upper 2 . bounded by Dmin When the equality in (10) holds, the MCCM system performs asymptotically the same as the OFDM system in AWGN 2 channel. We call the spreading codes having Df2 ree = Dmin the Maximum Euclidean Distance (MED) codes. Note that for the MED codes, Pf in (9) equals to one. B. Rayleigh fading channel When the subcarriers of the MCCM system undergo independent and flat Rayleigh fading, as is described in the section II, the pairwise error event probability of confusing the transmitted symbol sequence Xi with another sequence Xt is upper bounded [10] by  −1  |X (l) − X (l)|2  i t Pe (Xi → Xt ) ≤ , (14)   4N0 l∈Gi,t



where Gi,t = {l|1 ≤ l ≤ L, Xi (l) = Xt (l)}. Let Li,t = |Gi,t |, and  L1  i,t ∆ 2 2  |Xi (l) − Xt (l)| . (15) Dprod (Xi , Xt ) = l∈Gi,t

Li,t is the Hamming distance between Xi and Xt , and 2 (Xi , Xt ) can be called the product distance [11] beDprod tween the two sequences. Then (14) can be rewritten as  −Li,t 2 (Xi , Xt ) Dprod . (16) Pe (Xi → Xt ) ≤ 4N0 For the high SNR, the event error probability is dominated by the pairs of symbol sequences with the minimum Hamming distance in the event error, which is defined as the free Hamming distance: Lf ree = min Li,t . i,t

(17)

Furthermore, we define ∆

Df2 p =

min

(Xi ,Xt ):Li,t =Lf ree

2 Dprod (Xi , Xt )

(18)

as the minimum product distance of the pairs of sequences with Hamming distance Lf ree . Then, by the principle of the

union bound, the event error probability for high SNR can be approximated by  −Lf ree Df2 p   , (19) Pe ≈ Pf Nf ree 4N0 

where Pf is the probability that a sequence with Hamming  distance Lf ree is transmitted, and Nf ree is the average number of the distance-Lf ree sequences. As in the AWGN channel, we mainly consider the effect of   Lf ree and Df2 p , and neglect the effect of Pf and Nf ree when evaluating the performance of the MCCM system in frequency selective fading channels, since the former ones dominate the event error probability for high SNR. As is given in (19), the event error probability varies inversely with (Eb /N0 )Lf ree , so Lf ree is the diversity order of the system. Obviously, the free Hamming distance cannot be larger than the register length of the convolutional spreader, i.e., Lf ree ≤ N . When the spreading codes satisfy Lf ree = N , we call them the Maximum Hamming Distance (MHD) codes. Moreover, for the conventional OFDM system with diver2 be the minimum product distance of the OFDM sity, let Dmp system which has the same diversity order and spectrum 2 , there efficiency with the MCCM system. Then if Df2 p > Dmp is gain in performance relative to the conventional OFDM system with independent fading channel diversity of order Lf ree . Note that in order to the achieve diversity gain without loss in spectrum efficiency for the conventional OFDM system, other technologies must be employed, such as the space diversity. When the energy is uniformly distributed onto the P independent fading channels to achieve diversity gain, we have D2 2 (20) = min . Dmp P IV. D ESIGN OF THE S PREADING C ODES As discussed in the last section, in order to get the optimal MCCM system performance, we should maximize the free Euclidean distance Df2 ree in the AWGN channel, and the diversity order Lf ree , as well as the product distance Df2 p , in the frequency selective fading channel. Since the elements of the codes are complex valued, it’s quite difficult to find the optimal spreading codes. On the contrary, given a finite set of spreading codes, we can search for the best performance codes according to their parameters of Df2 ree , Lf ree , and Df2 p . This can be a scheme to design the spreading codes. A. Free Distance Searching Algorithm Due to the fact that the symbol sequences do not form a linear space, the distance property of the codes cannot be decided by assuming a specific sequence, like all-one sequence, is transmitted. Exhaustive search of the free distance by testing all of the possible transmitting sequence, and all state transition, is very time consuming. As the first step, a simple algorithm is proposed to check the distance property of spreading codes.

636

This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the WCNC 2007 proceedings.

TABLE II T HE S PREADING C ODES WITH N = 4 AND THEIR F REE S QUARED E UCLIDEAN D ISTANCES Df2 ree (Eb )

Spreading Ca : Cb : Cc : Cd :

TABLE III F REE H AMMING D ISTANCE AND P RODUCT D ISTANCE OF THE S PREADING C ODES Df2 p (Eb )

Lf ree

Spreading

Code

BPSK

QPSK

8PSK

Code

BPSK

QPSK

8PSK

BPSK

QPSK

8PSK

[1, 1, 1, 1] [1, −1, −1, −1] [1, −1, j, j] [1, j, −1, −j]

2 4 4 4

2 4 4 2

0.8787 1.7574 1.7574 0.8787

Ca Cb Cc Cd

2 3 4 4

2 3 4 2

2 3 4 2

1 1.5874 1 1

1 1.5874 1 1

0.4392 0.6975 0.4392 0.4392

The proposed searching algorithm is based on the well known Viterbi algorithm (VA) [13]. It’s known that VA is an ML algorithm that tests the metrices of all candidate sequences. As the path corresponding to a random symbol sequence that is long enough can almost definitely undergo all the possible state transition, if we detect the random sequence that is not infected with noise, we will find out the free distance, which is just the minimum metric of the competing branches at the nodes. The free distance searching algorithm is summarized as follows. Free Distance Searching Algorithm: • Generate a sufficiently long, e.g., 1000, random symbol sequence. Get the output sequence X of the convolutional spreader according to (1). • Pass X to the sequence detector. Initialize the distance register R with ∞. • Detect the sequence with the Viterbi algorithm. When choosing the survivor path at each stage, compare the metric of the incorrect path, denoted by M , with the value in the distance register. If M < R, set R = M . • When the detection is completed, R is the free distance. The proposed algorithm is suitable for both the free squared Euclidean Distance and the free Hamming distance. Its complexity is almost the same as the conventional Viterbi algorithm, except for the need of a distance register. Note that when searching for the free Hamming distance, the Euclidean distance is used for detection as usual, and the Hamming distance is the metric registered. If the algorithm is used for searching the product distance, it’s a little bit complicated. In this case, the Hamming distance should first be examined, and the minimum product distance for the corresponding Hamming distance is recorded. Of cause, we only care about the minimum product distance for the free Hamming distance. B. Spreading Codes for MCCM system It’s unrealistic to search the whole set of the possible spreading codes, because the set is infinite. In fact, the wholeset searching is also unnecessary, as it’s reasonable that the performance will not change dramatically when the spreading codes vary a little. In the following search, we confine the code symbols √ to be Cn ∈ {1, j, −1, −j} for 1 ≤ n ≤ N , where j = −1, and the normalization factor √1N to satisfy the condition (2) is neglected.

Taking N = 4 as the example, we first search the codes for the AWGN channel, where the free squared Euclidean distance is the dominating factor. After applying the proposed free distance searching algorithm to the codes with N = 4, we list some representative codes with their parameters Df2 ree 2 in Table II. Remember that Df2 ree is upper bounded by Dmin . Comparing Table II with Table I, we find that the codes except Ca are MED codes for BPSK, and Cb and Cc are MED codes for QPSK and 8PSK. In searching for the codes out of the all 64 codes with N = 4 and the first code symbols being 1 for BPSK modulation, 2 . They are we find that only two codes have Df2 ree < Dmin 2 Ca and [1, −1, 1, −1], both with Df ree = 2Eb . Though all the other 62 codes have the maximum Df2 ree , they also differ from each other in performance, because of the difference in parameters Pf and Nf in (9). Table II shows that a MED code for BPSK modulation is not necessary a MED code for high order modulation, such as QPSK, 8PSK. For example, Cd only has Df2 ree = 2Eb for QPSK, and Df2 ree = 0.8787Eb for 8PSK. So, compared 2 to the Dmin shown in Table I, there is 3dB loss for QPSK and 8PSK. On the other hand, Cb and Cc have no loss in Df2 ree . They are MED codes for all of the modulations, and are preferred in AWGN channel. As is derived in the last section, the free Hamming distance and the product distance are the two most important factors for the performance of the MCCM system in frequency selective fading channels. These parameters of the codes in Table II are provided in Table III. Obviously, the best codes in AWGN channel are not necessarily the best codes in the fading channel. For example, the MED code Cb only has Lf ree = 3. On the other hand, the code Cc has both the maximum free Euclidean distance and the maximum free Hamming distance for any modulation used. Also note that the code Cd is a MHD code for BPSK, but not for QPSK and 8PSK, where it only has 2-order diversity in frequency selective fading channels. In summary, the code Cc is the best code for all modulation types and both kinds of channels. The minimum product distances Df2 p of the codes are also provided in Table III. According to (20), we found that the MCCM system can have gain over the conventional OFDM system with the same spectrum efficiency and the same order of diversity. For example, the MCCM system with spreading

637

This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the WCNC 2007 proceedings.

code Cb can gain about 0.8dB relative to the OFDM system with the same diversity order. However, being a MHD code, Cc has no gain over the 4-order diversity OFDM system.

perform asymptotically the same as the OFDM systems with the same modulation. Since the Df2 ree of Ca is only one half 2 of Dmin for these modulations, it loses 3dB relative to the MED codes. The case is the same for Cd applied to 8PSK MCCM system. For BPSK modulation, the gap between the curves of Cd and the OFDM system can be attributed to the effect of Pf and Nf in (9), which is not taken into account when searching for the codes. Fig. 5 and Fig. 6 show the results for the frequency selective fading channel. The performance of the conventional modulation in independent Rayleigh fading channel with MRC is also shown in the figures. It can be seen that the diversity gain of the MCCM system is obvious. The diversity orders are interpreted as the slope of the BER-SNR curves in the log-log graph, which are in accordance with the parameters Lf ree given in Table III. It’s shown in the figures that the code Cc performs the best, and its curves are very close to the results of the independent MRC diversity with order four. So the code Cc is the optimum code both in AWGN channel and in frequency selective fading channel. Other codes simulated have loss in diversity gain, especially when the high order modulation is used. When comparing the performance of the MCCM system to that of the OFDM system with the same order of diversity, it can be found that Ca is 3dB worse than the counterpart 2-order diversity OFDM system. This is because its product 2 defined by (20). Cd distance Df2 p is the half of the Dmp applied to 8PSK MCCM systems also has the 3dB loss for the same reason. Besides, because the value of Df2 p for Cc 2 is the same as Dmp of the 4-order diversity OFDM system, this code has no loss in SNR. And interestingly, the code Cb can have about 0.8dB gain relative to the OFDM system with three-order diversity, as it has relatively high Df2 p . The performance of the uncoded OFDM-CDM system with 8PSK and length-four Walsh-Hadamard code is also shown in Fig. 6 for comparison. It’s obvious that it only achieves order-one diversity, thus is inferior to the proposed MCCM system.

V. S IMULATION R ESULTS

VI. C ONCLUSION

The performance of the proposed MCCM system is evaluated by numerical simulations, both in AWGN channel and frequency selective Rayleigh fading channel. The spreading codes for the system are those in Table II. We compare the MCCM system with the conventional OFDM system with the same spectrum efficiency by their bit error rate (BER). The power losses due to the cyclic prefix of both systems are not taken into account. For the situation of the frequency selective fading channel, the fading on each subcarriers is assumed to be flat and independent. And ideal channel estimation is used in the simulations, i.e., the fading coefficients are supposed to be known at the receiver. The comparison of the MCCM system and the conventional OFDM in AWGN channel is shown in Fig. 3 and Fig. 4, with BPSK and 8PSK respectively. As is predicted by the previous analysis, the MCCM systems with MED codes

In this paper, we propose a new multiplexing scheme used in multicarrier systems, which is called Multicarrier Convolutional Multiplexing (MCCM) system. In this system, data symbols are spread onto multiple subcarriers by convolutional spreader. The MCCM system can achieve significant diversity gain without loss of spectrum efficiency. In the MCCM system, the spreading codes have to be carefully designed. Since the free Euclidean distance determines the system performance in AWGN channel, and the free Hamming distance determines the diversity order in frequency selective fading channel, the two parameters can be used as the criterion to design the spreading codes. Moreover, the minimum product distance of the codes also plays an important role in fading channel. The best code in AWGN channel is not necessarily a good code in fading channel, and the best code for BPSK is not necessarily a good code for high order

0

10

−1

10

−2

BER

10

−3

10

−4

10

Theoretical MCCM, C

a

MCCM, Cb MCCM, C

−5

10

c

MCCM, Cd

−6

10

0

2

4

6 8 E / N (dB) b

Fig. 3.

10

12

14

0

Performance of the MCCM system with BPSK in AWGN channel

0

10

−1

10

−2

10

−3

BER

10

−4

10

OFDM MCCM, C

−5

10

MCCM, C −6

10

MCCM, C MCCM, C

−7

10

Fig. 4.

0

2

4

a b c d

6

8 10 Eb / N0 (dB)

12

14

16

18

Performance of the MCCM system with 8PSK in AWGN channel

638

This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the WCNC 2007 proceedings.

Only the MLSE algorithm is used for detection to the present, which is quite complex, especially when the spreading code is long and high order modulation is used. Some other reduced complexity algorithms, which have been studied in the decoding of the convolutional code and in the equalization to the ISI channel, may be applied in the MCCM system for practical use. Their impact on the system performance should be researched in the future.

0

10

Theoretical MCCM, Ca

−1

10

MCCM, C

b

MCCM, Cc MCCM, Cd

−2

10

−3

BER

10

−4

10

−5

ACKNOWLEDGMENT

−6

The research is supported by National Natural Science Foundation of China (NSFC) under grant no. 90604035.

10

10

−7

10

0

5

10

15

20 25 E / N (dB) b

30

35

40

0

Fig. 5. Performance of the MCCM system with BPSK in frequency selective fading channel. The dotted lines are the theoretical performance of BPSK with independent MRC diversity of order 1, 2, 3, 4 from up to down. 0

10

−1

10

−2

10

P=1

−3

10 BER

P=4

−4

10

OFDM, order P OFDM−CDM, WH MCCM, C

−5

10

P=3

a

MCCM, C −6

10

MCCM, C MCCM, C

−7

10

0

5

10

P=2

b c d

15

20 25 Eb / N0 (dB)

30

35

40

Fig. 6. Performance of the MCCM system and the OFDM-CDM system with 8PSK in frequency selective fading channel. The OFDM-CDM system uses the Walsh-Hadamard codes of length four. The dashed lines are the performance of the 8PSK OFDM system with independent MRC diversity of order P .

modulation. Fortunately, we have found several good codes for different modulations, both in AWGN channel and frequency selective fading channel, with the free distance searching algorithm proposed in this paper. And their performance is evaluated by numerical simulations.

R EFERENCES [1] S. Weinstein and P. Ebert, “Data transmission by frequency-division multiplexing using the discrete Fourier transform,” IEEE Transactions on Communications , vol. 19, no. 5, pp. 628–634, 1971. [2] J. A. C. Bingham, “Multicarrier modulation for data transmission: An idea whose time has come,” IEEE Communications Magazine, vol. 28, no. 5, pp. 5–14, 1990. [3] N. Yee, J. P. Linnartz, and G. Fettweis, “Multi-carrier CDMA in indoor wireless radio networks,” in IEEE international symposium on Personal, Indoor and Mobile Radio Communications (PIMRC ’93), Yokohama, Japan, 1993, pp. 109–113. [4] K. Fazel and L. Papke, “On the performance of convolutionally coded CDMA-OFDM for mobile communication system,” in IEEE international symposium on Personal, Indoor and Mobile Radio Communications (PIMRC ’93), Yokohama, Japan, 1993, pp. 468–472. [5] A. Chouly, A. Brajal, and S. Jourdan, “Orthogonal multicarrier techniques applied to direct sequence spread spectrum CDMA systems,” in Proceeding of IEEE Global Telecommunications Conference, vol. 3, Houston, USA, 1993, pp. 1723–1728. [6] S. Kaiser, “OFDM code-division multiplexing in fading channels,” IEEE Transactions on Communications, vol. 50, no. 8, pp. 1266–1273, 2002. [7] W. Jiang and D. Li, “Full-diversity spreading codes for multicarrier CDMA systems,” in MILCOM 2006, Washington, D.C., 2006. [8] J. Forney, G., “Maximum-likelihood sequence estimation of digital sequences in the presence of intersymbol interference,” IEEE Transactions on Information Theory, vol. 18, no. 3, pp. 363–378, 1972. [9] G. Ungerboeck, “Adaptive maximum-likelihood receiver for carriermodulated data-transmission systems,” IEEE Transactions on Communications, vol. 22, no. 5, pp. 624–636, 1974. [10] D. Divsalar and M. K. Simon, “The design of trellis coded MPSK for fading channels: Performance criteria,” IEEE Transactions on Communications, vol. 36, no. 9, pp. 1004–1012, 1988. [11] C.-E. W. Sundberg and N. Seshadri, “Coded modulation for fading channels: An overview,” European Transactionns on Telecommunications, vol. 4, no. 3, pp. 309–323, 1993. [12] J. G. Proakis, Digital Communications, 4th ed. New York: McGraw Hill, 2001. [13] J. Forney, G. D., “The Viterbi algorithm,” Proceedings of the IEEE, vol. 61, no. 3, pp. 268–278, 1973.

639

Convolutional Multiplexing for Multicarrier Systems - IEEE Xplore

School of Information Engineering. Beijing University of Posts and Telecommunications. Beijing 100876, China. Email: [email protected], lidaoben@vip.sohu.net. Xingpeng Mao. Department of Communication Engineering. Harbin Institute of Technology (Weihai). Weihai, Shandong 264209, China. Email: [email protected].

241KB Sizes 0 Downloads 378 Views

Recommend Documents

Convolutional Multiplexing for Multicarrier Systems - IEEE Xplore
Email: [email protected], [email protected]. Xingpeng Mao ... Email: [email protected] .... It's reasonable to compare the MCCM system with the con-.

Convolutional Multiplexing for Multicarrier Transmission
Convolutional Multiplexing for Multicarrier. Transmission: System Performance and Code Design. Wei Jiang and Daoben Li. School of Information Engineering, ...

Robust Power Allocation for Multicarrier Amplify-and ... - IEEE Xplore
Sep 11, 2013 - Abstract—It has been shown that adaptive power allocation can provide a substantial performance gain in wireless communication systems ...

Convolutional Multi-code Multiplexing for OFDM Systems
Jun 26, 2007 - h(l): i.i.d Rayleigh fading (Broadband, frequency interleaver). Wei Jiang .... survivor path at each stage, compare the metric of the incorrect path,.

Statistical Multiplexing-Based Hybrid FH-OFDMA ... - IEEE Xplore
of orthogonal frequency-division multiplexing (OFDM)-based ultra-wideband (UWB) indoor radio access networks (RANs). The downlink user capacity is here ...

Convolutional Multi-code Multiplexing for OFDM ... -
error rate (BER). The power loss due to the cyclic prefix of both systems is not taken into account. For the situation of the frequency selective fading channel, the ...

Convolutional Multi-code Multiplexing for OFDM ... -
with good performance are found by computer search. Compared ... such as Coded OFDM (COFDM) [3], Multicarrier Code ... efficiency for multi-carrier systems. ...... wireless radio networks,” in IEEE PIMRC'93, Yokohama, Japan, 1993, pp.

IEEE Photonics Technology - IEEE Xplore
Abstract—Due to the high beam divergence of standard laser diodes (LDs), these are not suitable for wavelength-selective feed- back without extra optical ...

Doppler Spread Estimation for Wireless OFDM Systems - IEEE Xplore
operating conditions, such as large range of mobile subscriber station (MSS) speeds, different carrier frequencies in licensed and licensed-exempt bands, ...

Power Control for Multirate DS-CDMA Systems With ... - IEEE Xplore
[25] B. M. Hochwald and S. ten Brink, “Achieving near-capacity on a multiple- antenna channel,” IEEE Trans. Commun., vol. 51, no. 3, pp. 389–399,. Mar. 2003.

Small Test Systems for Power System Economic Studies - IEEE Xplore
This paper will discuss two small test systems. The first system is based on the original PJM 5-bus system, which contains real power related data only, since it is ...

wright layout - IEEE Xplore
tive specifications for voice over asynchronous transfer mode (VoATM) [2], voice over IP. (VoIP), and voice over frame relay (VoFR) [3]. Much has been written ...

Device Ensembles - IEEE Xplore
Dec 2, 2004 - time, the computer and consumer electronics indus- tries are defining ... tered on data synchronization between desktops and personal digital ...

wright layout - IEEE Xplore
ACCEPTED FROM OPEN CALL. INTRODUCTION. Two trends motivate this article: first, the growth of telecommunications industry interest in the implementation ...

Evolutionary Computation, IEEE Transactions on - IEEE Xplore
search strategy to a great number of habitats and prey distributions. We propose to synthesize a similar search strategy for the massively multimodal problems of ...

I iJl! - IEEE Xplore
Email: [email protected]. Abstract: A ... consumptions are 8.3mA and 1.lmA for WCDMA mode .... 8.3mA from a 1.5V supply under WCDMA mode and.

Gigabit DSL - IEEE Xplore
(DSL) technology based on MIMO transmission methods finds that symmetric data rates of more than 1 Gbps are achievable over four twisted pairs (category 3) ...

IEEE CIS Social Media - IEEE Xplore
Feb 2, 2012 - interact (e.g., talk with microphones/ headsets, listen to presentations, ask questions, etc.) with other avatars virtu- ally located in the same ...

Grammatical evolution - Evolutionary Computation, IEEE ... - IEEE Xplore
definition are used in a genotype-to-phenotype mapping process to a program. ... evolutionary process on the actual programs, but rather on vari- able-length ...

Throughput Maximization for Opportunistic Spectrum ... - IEEE Xplore
Abstract—In this paper, we propose a novel transmission probability scheduling scheme for opportunistic spectrum access in cognitive radio networks. With the ...

SITAR - IEEE Xplore
SITAR: A Scalable Intrusion-Tolerant Architecture for Distributed Services. ∗. Feiyi Wang, Frank Jou. Advanced Network Research Group. MCNC. Research Triangle Park, NC. Email: {fwang2,jou}@mcnc.org. Fengmin Gong. Intrusion Detection Technology Divi

striegel layout - IEEE Xplore
tant events can occur: group dynamics, network dynamics ... network topology due to link/node failures/addi- ... article we examine various issues and solutions.

Digital Fabrication - IEEE Xplore
we use on a daily basis are created by professional design- ers, mass-produced at factories, and then transported, through a complex distribution network, to ...