2011 International Conference on Advanced Technologies for Communications (ATC 2011)

Joint Adaptive Modulation and Switching Schemes for Opportunistic Cooperative Networks Vo Nguyen Quoc Bao

Bui Pham Lan Phuong

Tran Thien Thanh

Telecom. Dept. School of EE Faculty of EE Posts and Telecom. Inst. of Tech., Vietnam Ho Chi Minh Internaltional Uni. Ho Chi Minh City Uni. of Transport. Email: [email protected] Email: [email protected] Email: thienthanh [email protected]

adaptive modulation, it still suffers from spectral efficiency penalty due to the need of orthogonal channels for relay transmission. Using the same approach as in [6], Bao et al. studied the effect of adaptive modulation on opportunistic cooperative networks where only the best relay is selected to forward the source information and thus only two time slots are needed regardless of the number of cooperative relays [7]. By providing additional redundancy only on demand, opportunistic incremental relaying networks in conjunction with adaptive modulation was introduced in [8] as efficient relaying protocols to increase the system capacity and performance. However, it can be straightforwardly observed that the opportunistic incremental relaying network is not the optimal one in terms of spectral efficiency because it does not fully use the relaying link even it can provide better spectral efficiency than the direct link. Very recently, to address this concern, in [9], a switched cooperative network with adaptive modulation is proposed for one and two relays equipped with amplifyand-forward (AF) to maximize the overall system spectral efficiency; however, its performance evaluation is restricted to the outage probability and spectral efficiency. To the best of the authors’ knowledge, there is no published work concerning the performance of switched cooperative networks in conjunction with selection relay schemes. In this paper, for the first time, we propose a novel switched relaying network in conjunction with relay selection under adaptive modulation. By choosing either the relaying link via the best relay or the direct link for data transmission, the proposed network is able to achieve a considerable gain in spectral efficiency while satisfying a certain error performance. Assuming Rayleigh fading channels, we derive a tight approximation in closed form for the occurrence probability, the outage probability, the spectral efficiency, and the system bit error rate. Numerical results verify the validity of the theoretical analysis by comparison with Monte Carlo simulation, showing that the analysis results are tight approximations, particular at medium and high signal-to-noise ratio (SNR) regimes. The rest of this paper is organized as follows. In Sect. II, we introduce the model under study and describe the proposed protocol. Sect. III shows the formulas allowing for evaluation of occurence probability, outage probability, bit error rate and achievable spectral efficiency of the system. In Sect. IV, we contrast the simulations and the results yielded by theory.

Abstract—In this paper, we propose a novel scheme, which combines both advantages of adaptive modulation and the concept of distributed switching. Unlike previous incremental relaying protocols under adaptive modulation, we consider a more realistic scenario where the link providing higher spectral efficiency is chosen for data transmission. We also examine the outage probability, bit error rate, and spectral efficiency, which are important performance measures for the proposed system. Based on the derived expression and its approximate form, we demonstrate that the proposed network enhances the system performance in terms of spectral efficiency by around 3 dB, compared to the conventional incremental relaying networks. Finally, the derivation is validated through Monte Carlo simulations. Index Terms—amplify-and-forward, Rayleigh fading, outage probability, spectral efficiency, bit error rate, adaptive transmission, incremental relaying.

I. I NTRODUCTION Cooperative communication is a technique by which mobile agents with a single antenna share their antennas with other agents to mitigate the adverse effect of fading [1], [2]. The basic idea is that by relaying data for each other, a virtual antenna array is created having the potential to provide high data rate with wide coverage. Indeed, this technology is already included in recent wireless standards such as LTE, IEEE 802.11 and WiMax [3], [4], [5]. Motivated by studies on incremental relaying first introduced by Laneman [2], there have been works concerning the multi-node relay network that combines the cooperative diversity and adaptive modulation together to improve the system spectral efficiency even further. The adaptive transmission exploits the fact that adjusting the modulation level according to wireless channel conditions can significantly improve spectral efficiency whereas fixed-rate transmission, however, results in low bandwidth efficiency when the wireless channels are reliable. In [6], the performance of repetition-based cooperative networks under adaptive modulation was studied. Also in [6], the authors investigated the effect of optimum switching and fixed switching for both independent identically distributed (i.i.d.) and independent but not identically distributed (i.n.d.) fading Rayleigh channels showing that in terms of spectral efficiency, optimum switching thresholds gain around 3 dB compared to fixed switching. Although such the protocol can combine both advantages offered by cooperative diversity and

978-1-4577-1207-4/11/$26.00 ©2011 IEEE

70

Furthermore, some discussions on the behavior of the proposed system at low and high SNR regime are provided. Finally, the paper is closed in Sect. V.

Making use the fact that the minimum of two exponentially distributed random variables is again an exponentially distributed variable, thanks to [13], we have the probability density function (PDF) of γR as follows:

II. S YSTEM M ODEL fγR (γ) =

Consider an opportunistic cooperative system having a source (S), N relay denoted as R1 , . . . , RN and a destination (D) operating over Rayleigh fading channels. The channel gain is assumed to remain constant during the entire time of a packet transmission (frame), but independently change over frame intervals. We further assume that all nodes in the network employ only one antenna each. The communication between the source and the destination occurs two time slots where the source node broadcasts its data in the first time slot and then the best relay, operating in the half-duplex mode, cooperates to forward the received signal toward the destination in the second time slot by amplify-and-forward (AF) relaying approach. The relay selection algorithm selects the best relay using the opportunistic (distributed timer) approach suggested by Bletsas [10], [11] such that the best relay is the relay having the highest instantaneous SNR composed of instantaneous SNRs for the first hop and the second hop, namely γR =

max γn

n=1,...,N

FγR (γ) =

max min(γSRn , γRn D )

  N 1 − γ¯γ e R n γ¯R

(5)

(−1)

n−1

   N − γ 1 − e γ¯R . n

(6)

With the direct link from the source to the destination, the PDF and CDF of the instantaneous SNR, γD , can be expressed as fγD (γ) =

1 − γ¯γ − γ e D , FγD (γ) = 1 − e γ¯D γ¯D

(7)

where γ¯D = Ps /N0 E{|hSD }|2 = Ps /N0 λ0 with E{.} denoting expectation. Different from the incremental relaying scheme in conjunction with adaptive modulation [8] where the relaying link will be active when the direct link cannot support the lowest rate, our proposed scheme aims to maximize the instantaneous spectral efficiency by direct comparing the supportable spectral efficiency of the two links. The link with higher instantaneous spectral efficiency will be chosen to convey the source data to the destination. Stated another way, the relaying link will be employed whenever it can provide better spectral efficiency as compared to the direct link. To that effect, the destination needs to monitor the instantaneous channel conditions of both the direct link and relaying link. This can be accomplished by transmitting a short pilot signal from the source, which is then forwarded by the relay in the beginning of each data burst. Finally, the information about the chosen link as well as the chosen transmission mode will be fed back to the source node. We further assume that there exists an error-free feedback channel between the source and the destination. It should be noted that in this scheme, no diversity combining technique is used at the destination. Based on partitioning the entire range of the received SNR at destination corresponding to transmission modes, adaptive modulation can achieve high spectral efficiency over wireless fading channels. According to the channel condition, the system changes the modulation rate, i.e. it shifts up the modulation level when the channel is good and shifts down the modulation level when the channel is bad. Specially, it stops data transmission if the system cannot support the given target bit error rate, BERT . If the system supports K discrete adaptive modulation modes, there should be K + 1 0 values of the switching threshold, {γTk }K+1 k=0 with γT = 0 and K+1 = +∞. Denoting γΣ as the end-to-end received SNR of γT the system, modulation mode k is used if γΣ ∈ [γTk , γTk + 1).

(1)

(3)

Combining (1) and (3) yields n=1,...,N

N  n=1

γSRn γRn D (2) γSRn + γRn D + N0   2 2 where γSRn = Ps |hSRn | N0 and γRn D = Pr |hRn D | N0 are the instantaneous SNRs for the S → Rn and Rn → D link, respectively. hRn D and hRn D denote the corresponding channel coefficients. Under the assumption of independent and 2 identical distributed Rayleigh fading channels, |hSRn | and 2 |hRn D | are exponentially distributed with parameters λ1 and λ2 , respectively. Ps and Pr are the transmit powers for the source and the selected node with N0 denoting the additive noise terms at the relays and the destination. From (2), it is obvious that γn follows MacDonald distribution with parameters γ¯1 = Ps λ1 /N0 and γ¯2 = Pr λ2 /N0 [12]. However, it seems to be impossible to further analytical study the proposed scheme with the exact form of the PDF and CDF for γn provided in [12, eq. (2-3)]. To circumvent the difficulty in the exact analysis, the noise figure in (2) is usually ignored along with using the well-known relationship of SNRs in dual-hop link at high SNRs rendering γn in an analytically more tractable form, namely [2]

γR =

n−1

γ ¯2 where γ¯R = n1 (¯γγ¯11+¯ γ2 ) . The cumulative distribution function (CDF) associated to γR can be obtained by integrating fγR (γ) between 0 and γ as

γn =

γSRn γRn D ≈ min(γSRn , γRn D ). γSRn + γRn D

(−1)

n=1

where γn is the end-to-end instantaneous SNR of the dual AF link (S → Rn → D), given by [2]

γn ≈

N 

(4)

71

guarantee the target BER, i.e. γΣ ≤ γT1 . As such, the system outage probability is written as

In adaptive modulation, it is convenient to use approximate BER expressions. In particular, the bit error rate (BER) of a system which implements M -QAM modulation over an additive white Gaussian noise (AWGN) channel, with coherent detection and Gray mapping from bits to symbols can be approximated as [14, eq. (9.32)]   (8) βk γΣ BER(k, γΣ ) ≈ αk Q 1, k = 1, 2 where αk = and βk = 4/k, k ≥ 3 2/k, k = 1, 2 1

k . Having the BER expression 3 (2 − 1), k ≥ 3 in hand, ones can obtain the switching threshold for k = 1, . . . , K by solving the inverse approximate BER expression as follows:   2 BERT 1 Q−1 . (9) γTk = βk αk

OP

(12) Pr(γD ≤ γT1 ) Pr(γR ≤ γT1 )       N γ1 γ1 − T − T n−1 N 1 − e γ¯R . (−1) 1 − e γ¯D n n=1

= =

C. Average Spectral Efficiency Recalling that due to the constraint of half-duplex transmission, the spectral efficiency of the direct link and relaying link of mode k are log2 (Mk ) and log2 (Mk )/2, respectively. Therefore, the total average spectral efficiency of the proposed system can be calculated as ASE = =

K 

k

k/2

K 

k/2

+mk /2 Pr(γD ≤ γT

III. P ERFORMANCE A NALYSIS

k=K/2+1

Here we present the asymptotic analysis, which provides an insight to the performance of the proposed system under adaptive modulation.

D. Bit Error Rate

We first consider the concurrence probability defined as the probability or the percentage of time that mode k is used. In steady-state, according to the operation of the proposed scheme, adaptive modulation mode k is selected with probability as shown at the top of the next page where Pr(γZ ≤ x) = FγZ (x) with Z ∈ {D, R}. Furthermore, x and x denote the floor and ceiling function, respectively. Assuming the independence of γD and γR , πk can be rewritten as follows: ⎧ (1) ⎪ k=0 ⎪ ⎨ πk , (2) (11) πk = k = 1, . . . , K/2 πk , ⎪ ⎪ ⎩ (3) πk , k = K/2 + 1, . . . , K

γk

⎧T Ik (¯ γD ), ⎨ N =  n−1 N  ⎩ (−1) γR ), n Ik (¯ n=1

with =

Pr(γD ≤

=

Pr(γTk < + Pr(γTk

(3)

πk

=

Pr(γTk < + Pr(γTk

Z=D Z=R

.(15)

γ ) is defined as shown in the next page with Furthermore, Ik (¯ ∞ a−1 −t e dt [16]. Γ(a, x) = t

γT1 ) Pr(γR ≤ γT1 ), γD ≤ γTk+1 ) Pr(γγR ≤ γT2k+1 ) k/2 < γR ≤ γTk+1 ) Pr(γD ≤ γT ), k+1 K+1 γD ≤ γT ) Pr(γγR ≤ γT ) k/2 < γR ≤ γTk+1 ) Pr(γD ≤ γT ).

x

IV. N UMERICAL R ESULTS AND D ISCUSSION In this section, we provide Monte Carlo simulation to demonstrate the validity and usefulness of the analytical expressions. In the following numerical examples, we set the desired BER as BERT = 10−3 . We consider flat Rayleigh fading in two relaying scenarios: balanced networks (λ0 = λ1 = λ2 = 1) and unbalanced networks (λ0 = λ1 /5 = λ2 /5 = 1). For simplicity, the equal transmit power profile is employed at the source and the relay, i.e., Ps = Pr . Fig. 1 shows the occurrence probability of the proposed system versus average SNR for 8 mode transmission, K = 8. It is shown that the lowest and highest mode dominate

B. Outage Probability Outage probability is one of the most important performance measures for wireless communication systems. In discrete adaptive modulation, the system outage probability, OP, is the probability that the end-to-end SNR at the destination cannot 1 Note

) Pr(γTk < γR ≤ γTk+1 )

in which BERZ,k denotes the average BER of link Z in a specific region of [γTk γTk+1 ), given by  γ k+1 T BERZ,k = BER(k, γ)fZ (γ)dγ

that here BPSK is considered as a special case of M -QAM (M = 2).

72

(13)



The average BER for the proposed networks can be calculated, as in [15], as   K/2 Pr(γR ≤ γT2k+1 )BERD,k  mk k/2 + Pr(γ )BERR,k k=1  D ≤ γT  K Pr(γR ≤ γTK+1 )BERD,k  + mk k/2 + Pr(γD ≤ γT )BERR,k k=K/2+1 BER = (14) K k=1 mk πk

A. Occurrence Probability

(1) πk (2) πk



Pr(γR ≤ γT2k+1 ) Pr(γTk < γD ≤ γTk+1 )

) Pr(γTk < γΣ ≤ γTk+1 ) +m T  k /2 Pr(γD ≤ γK+1 mk Pr(γR ≤ γT ) Pr(γTk < γD ≤ γTk+1 )

k=1

+

log2 (Mk ) Pr(γTk < γΣ ≤ γTk+1 )

k=1  K/2 m 

.

πk

= Pr(γTk < γΣ ≤ γTk+1 ) ⎧ k=0 Pr(γD ≤ γT1 ) Pr(γR ≤ γT1 ), ⎪ ⎪   ⎪ ⎪ 2k+1 k+1 2k+1 k ⎪ Pr(γR ≤ γT ) Pr(γT < γD ≤ γT |γγR ≤ γT ) ⎪ ⎨ , k = 1, . . . , K/2 k/2 k/2 = ) Pr(γTk < γR ≤ γTk+1 |γD ≤ γT )  + Pr(γD ≤ γT  ⎪ ⎪ ⎪ Pr(γR ≤ γTK+1 ) Pr(γTk < γD ≤ γTk+1 |γγR ≤ γTK+1 ) ⎪ ⎪ ⎪ , k = K/2 + 1, . . . , K ⎩ k/2 k/2 ) Pr(γTk < γR ≤ γTk+1 |γD ≤ γT ) + Pr(γD ≤ γT ⎧ k=0 Pr(γD ≤ γT1 ) Pr(γR ≤ γT1 ), ⎪ ⎪   ⎪ ⎪ k+1 2k+1 k ⎪ Pr(γT < γD ≤ γT , γγR ≤ γT ) ⎪ ⎨ , k = 1, . . . , K/2 k/2 = )  + Pr(γTk < γR ≤ γTk+1 , γD ≤ γT  ⎪ ⎪ ⎪ Pr(γTk < γD ≤ γTk+1 , γγR ≤ γTK+1 ) ⎪ ⎪ ⎪ , k = K/2 + 1, . . . , K ⎩ k/2 ) + Pr(γTk < γR ≤ γTk+1 , γD ≤ γT 

Ik (x)

=

k+1 γT k γT



=

αk

αk Q

(10)

 1 γ e− γ¯ βk γ γ¯

(16)

 − 12    γTk+1  1  1 1 β γ  β β   γ 1 β 1 1 k k k k −γ Γ , − + , + γ Q βk γ 1 − e ¯ − Γ 2 π 2 2 2π 2 γ¯ 2 2 γ¯ k+1 γT

at low and high SNRs, respectively, confirming that adaptive modulation is only suitable for systems operating in mediumto-high SNRs. Fig. 2 gives the outage probability variation for different network configurations and it shows that the outage probability of the system over unbalanced channels is much better as compared to that over balanced channels. Furthermore, the analyzed values, obtained using (12), are also compared with that provided by Monte Carlo simulation. It is observed that the simulated and computed values are in good agreement, thus validating our analysis approach. The effect of adaptive modulation on the proposed scheme can be further ascertained by referring to Fig. 3 where the average BER as a function of average SNRs is shown. As predicted by the analysis, the average of the system is always well below the target BER and hence satisfies the QoS requirement. Fig. 4 plots the average spectral efficiency versus the number of relays with balanced links. The figure shows that increasing number of relays (N ) leads to relatively important but diminishing performance gain in the low-to-medium SNR regime. On the other hand, as the average SNR becomes sufficiency large, the ASE improvement decreases, as all curves converge asymptotically to the performance of the same system using the highest modulation level. This can be explained by the fact that at high SNR regime, the highest modulation level is used on the direct link level most of the time. Finally, we compare the average spectral efficiency from (13) with that of the conventional incremental opportunistic

cooperative networks. In incremental opportunistic cooperative networks, the relaying link is demanded since the direct link is in outage. Note that both networks do not utilize diversity combiners, i.e. maximal ratio combining (MRC) or selection combining (SC), hence the same hardware complexity is maintained at the destination. We see from the figure that for the same level of ASE, the proposed protocol attains a SNR advantage over the incremental relaying (IR) networks and this SNR advantage increase with K. For example, at the ASE of 3 bps/Hz, the SNR advantage of the proposed protocols over the IR networks increases from 2 to 3 dB as K increases from 6 to 8. V. C ONCLUSION In this paper, we propose a joint adaptive modulation and link switching scheme for opportunistic cooperative networks. The performance of the proposed networks in flat Rayleigh fading has been presented. From the analysis, we demonstrate that overall system spectral efficiency can be maximized by choosing the link having higher spectral efficiency for data transmission and the proposed scheme outperforms the opportunistic incremental relaying networks in terms of spectral efficiency. This feature makes this scheme an attractive candidate from practical point of view for cooperative networks under adaptive modulation. ACKNOWLEDGMENT This research was supported by the Vietnam’s National Foundation for Science and Technology Development (NAFOSTED) (No. 102.99-2010.10).

73

−3

10

1 iid channels ind channels simulation

0.9 0.8

Occurence Probability

−4

BER

10

−5

10

0.7 0.6 0.5 0.4 0.3 0.2 0.1

−6

10

0

5

Fig. 3.

10

15

20 25 30 35 Average SNR per symbol

40

45

0

50

Average bit error rate versus average SNR per symbol.

0

Fig. 1.

5

10

15 20 25 Average SNR per symbol

30

35

40

Occurrence probability versus average SNR per symbol.

0

4.5

10 N=1 N=2 N=3 N=4 N=5

4 3.5

iid channels ind channels simulation −2

10

3 N increasing −4

10

ASE

OP

2.5 2

−6

10

1.5 1

−8

10 0.5 0

0 0

2

4

6

8 10 12 14 Average SNR per symbol

16

18

20

Fig. 2. Fig. 4.

10

15 20 Average SNR per symbol

25

30

35

Outage probability versus average SNR per symbol.

Average spectral efficiency versus average SNR per symbol.

R EFERENCES

7 MSE IR

6

[1] A. Nosratinia, T. E. Hunter, and A. Hedayat, “Cooperative communication in wireless networks,” Communications Magazine, IEEE, vol. 42, no. 10, pp. 74–80, 2004. [2] J. N. Laneman, D. N. C. Tse, and G. W. Wornell, “Cooperative diversity in wireless networks: Efficient protocols and outage behavior,” IEEE Transactions on Information Theory, vol. 50, no. 12, pp. 3062–3080, 2004, 0018-9448. [3] Q. Li, X. E. Lin, J. Zhang, and W. Roh, “Advancement of mimo technology in wimax: from ieee 802.16d/e/j to 802.16m,” Communications Magazine, IEEE, vol. 47, no. 6, pp. 100–107, 2009. [4] K. Loa, W. Chih-Chiang, S. Shiann-Tsong, Y. Yifei, M. Chion, D. Huo, and X. Ling, “Imt-advanced relay standards [wimax/lte update],” Communications Magazine, IEEE, vol. 48, no. 8, pp. 40–48, 2010. [5] L. Rong, S. E. Elayoubi, and O. B. Haddada, “Impact of relays on lte-advanced performance,” in Communications (ICC), 2010 IEEE International Conference on, pp. 1–6.

K=8

5 K=6 ASE

4

K=4

3

2

K=2

1

0

5

0

5

Fig. 5.

10 15 20 Average SNR per symbol

25

30

Average spectral efficiency for both systems.

74

[6] T. Nechiporenko, P. Kalansuriya, and C. Tellambura, “Performance of optimum switching adaptive mqam for amplify-and-forward relays,” IEEE Transactions on Vehicular Technology, vol. 58, no. 5, pp. 2258– 2268, 2009. [7] V. N. Q. Bao, H. Y. Kong, Asaduzzaman, T. T. Truc, and P. Jihwan, “Optimal switching adaptive m-qam for opportunistic amplify-andforward networks,” in 25th Biennial Symposium on Communications, 2010, Kingston, Ontario, Canada, 2010, pp. 433 – 438. [Online]. Available: http://tinyurl.com/469jorr [8] K.-S. Hwang, Y.-C. Ko, and M.-S. Alouini, “Performance analysis of incremental opportunistic relaying over identically and non-identically distributed cooperative paths,” IEEE Trans. Wirel. Comm., vol. 8, no. 4, pp. 1953–1961, 2009. [9] J.-W. Kwon, K. Young-Chai, and H.-C. Yang, “Maximum spectral efficiency of amplify-and-forward cooperative transmission with multiple relays,” IEEE Transactions on Wireless Communications, vol. 10, no. 1, pp. 49 – 54, 2011. [10] A. Bletsas, A. Khisti, D. P. Reed, and A. Lippman, “A simple cooperative

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Joint Adaptive Modulation and Switching Schemes for ... - IEEE Xplore

Email: [email protected]. Tran Thien Thanh ... Email: thienthanh dv@hcmutrans.edu.vn ... the relaying link even it can provide better spectral efficiency.

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