2011 International Conference on Advanced echnologies for Communications (AC 2011 Joint Adaptive Modulation and Switching Schemes for Opportunistic Cooperative Networs Vo Nguyen Quoc Bao elecom. Dept. Posts and elecom. Inst. of ech., Vietnam Email: baovnq@ptithcm.edu.vn Bui Pham Lan Phuong School of EE Ho Chi Minh Internaltional Uni. Email: bplphuong@hcmiu.edu.vn ran hien hanh Faculty of EE Ho Chi Minh City Uni. of ransport. Email: thienthanh dv@hcmutrans.edu.vn Abstract In this paper, we propose a novel scheme, which combines both advantages of adaptive modulation and the concept of distributed switching. Unlie previous incremental relaying protocols under adaptive modulation, we consider a more realistic scenario where the lin 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 networ enhances the system performance in terms of spectral efficiency by around 3 db, compared to the conventional incremental relaying networs. Finally, the derivation is validated through Monte Carlo simulations. Index erms amplify-and-forward, Rayleigh fading, outage probability, spectral efficiency, bit error rate, adaptive transmission, incremental relaying. I. INRODUCION 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]. he 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 LE, IEEE 802.11 and WiMax [3], [4], [5]. Motivated by studies on incremental relaying first introduced by Laneman [2], there have been wors concerning the multi-node relay networ that combines the cooperative diversity and adaptive modulation together to improve the system spectral efficiency even further. he 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 networs 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 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 networs 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 networs 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 networ is not the optimal one in terms of spectral efficiency because it does not fully use the relaying lin even it can provide better spectral efficiency than the direct lin. Very recently, to address this concern, in [9], a switched cooperative networ 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. o the best of the authors nowledge, there is no published wor concerning the performance of switched cooperative networs in conjunction with selection relay schemes. In this paper, for the first time, we propose a novel switched relaying networ in conjunction with relay selection under adaptive modulation. By choosing either the relaying lin via the best relay or the direct lin for data transmission, the proposed networ 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. he 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. 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. II. SYSEM MODEL Consider an opportunistic cooperative system having a source (S, N relay denoted as R 1,...,R N and a destination (D operating over Rayleigh fading channels. he channel gain is assumed to remain constant during the entire time of a pacet transmission (frame, but independently change over frame intervals. We further assume that all nodes in the networ employ only one antenna each. he 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. he 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 γ R = max γ n (1,...,N where γ n is the end-to-end instantaneous SNR of the dual AF lin (S R n D, given by [2] γ SRn γ RnD γ n = (2 γ SRn + γ RnD + N 0 where γ SRn = P s h SRn 2/ N 0 and γ RnD = P r h 2/ RnD N 0 are the instantaneous SNRs for the S R n and R n D lin, respectively. h RnD and h RnD denote the corresponding channel coefficients. Under the assumption of independent and identical distributed Rayleigh fading channels, h SRn 2 and h RnD 2 are exponentially distributed with parameters λ 1 and λ 2, respectively. P s and P r are the transmit powers for the source and the selected node with N 0 denoting the additive noise terms at the relays and the destination. From (2, it is obvious that γ n follows MacDonald distribution with parameters γ 1 = P s λ 1 /N 0 and γ 2 = P r λ 2 /N 0 [12]. However, it seems to be impossible to further analytical study the proposed scheme with the exact form of the PDF and CDF for γ n provided in [12, eq. (2-3]. o circumvent the difficulty in the exact analysis, the noise figure in (2 is usually ignored along with using the well-nown relationship of SNRs in dual-hop lin at high SNRs rendering γ n in an analytically more tractable form, namely [2] γ n γ SR n γ RnD min(γ SRn,γ RnD. (3 γ SRn + γ RnD Combining (1 and (3 yields γ R = max min(γ SR n,γ,...,n RnD (4 Maing use the fact that the minimum of two exponentially distributed random variables is again an exponentially distributed variable, thans to [13], we have the probability density function (PDF of γ R as follows: N ( f γr (γ = ( 1 n 1 N 1 e γ γ R (5 n γ R γ 1 γ 2 where γ R = 1 n ( γ 1+ γ 2. he cumulative distribution function (CDF associated to γ R can be obtained by integrating f γr (γ between 0 and γ as N ( F γr (γ = ( 1 n 1 N ( 1 e γ γ R. (6 n With the direct lin from the source to the destination, the PDF and CDF of the instantaneous SNR, γ D, can be expressed as f γd (γ = 1 e γ D γ γ D, F γd (γ =1 e γ γ D (7 where γ D = P s /N 0 E{ h SD } 2 = P s /N 0 λ 0 with E{.} denoting expectation. Different from the incremental relaying scheme in conjunction with adaptive modulation [8] where the relaying lin will be active when the direct lin 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 lins. he lin with higher instantaneous spectral efficiency will be chosen to convey the source data to the destination. Stated another way, the relaying lin will be employed whenever it can provide better spectral efficiency as compared to the direct lin. o that effect, the destination needs to monitor the instantaneous channel conditions of both the direct lin and relaying lin. his 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 lin as well as the chosen transmission mode will be fed bac to the source node. We further assume that there exists an error-free feedbac 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, BER. If the system supports K discrete adaptive modulation modes, there should be K +1 values of the switching threshold, {γ }K+1 =0 with γ0 =0and γ K+1 =+. Denoting γ Σ as the end-to-end received SNR of the system, modulation mode is used if γ Σ [γ,γ +1. 71
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] ( BER(, γ Σ α Q β γ Σ (8 { 1, =1, 2 where α = and β = 4/, 3 { 2/, =1, 2 3 / 1 (2. Having the BER expression 1, 3 in hand, ones can obtain the switching threshold for = 1,...,K by solving the inverse approximate BER expression as follows: γ = 1 [ ( ] 2 Q 1 BER. (9 β α III. PERFORMANCE ANALYSIS Here we present the asymptotic analysis, which provides an insight to the performance of the proposed system under adaptive modulation. A. Occurrence Probability We first consider the concurrence probability defined as the probability or the percentage of time that mode is used. In steady-state, according to the operation of the proposed scheme, adaptive modulation mode is selected with probability as shown at the top of the next page where Pr(γ Z x =F γz (x with Z {D, R}. Furthermore, x and x denote the floor and ceiling function, respectively. Assuming the independence of γ D and γ R, π can be rewritten as follows: π (1, =0 π = π (2, =1,..., K/2 (11 π (3, = K/2 +1,...,K with π (1 = Pr(γ D γ 1 Pr(γ R γ 1, π (2 = Pr(γ <γ D γ +1 Pr(γ γr γ 2+1 +Pr(γ <γ R γ +1 Pr(γ D γ /2, π (3 = Pr(γ <γ D γ +1 Pr(γ γr γ K+1 B. Outage Probability +Pr(γ <γ R γ +1 Pr(γ D γ /2. 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 that here BPSK is considered as a special case of M-QAM (M =2. guarantee the target BER, i.e. γ Σ γ 1. As such, the system outage probability is written as OP = Pr(γ D γ 1 Pr(γ R γ 1 (12 = (1 [ e γ1 N ( γ D ( 1 n 1 N (1 ] e γ1 γ R. n BER = =1 C. Average Spectral Efficiency Recalling that due to the constraint of half-duplex transmission, the spectral efficiency of the direct lin and relaying lin of mode are log 2 (M and log 2 (M /2, respectively. herefore, the total average spectral efficiency of the proposed system can be calculated as ASE = K log 2 (M Pr(γ <γ Σ γ +1 =1 [ K/2 m Pr(γ R γ 2+1 Pr(γ = <γ ] D γ +1 =1 +m [ /2 Pr(γ D γ /2 Pr(γ <γ Σ γ +1 K m Pr(γ R γ K+1 Pr(γ + <γ ] D γ +1 = K/2 +1 +m /2 Pr(γ D γ /2 Pr(γ <γ. R γ +1 D. Bit Error Rate he average BER for the proposed networs can be calculated, as in [15], as [ ] K/2 Pr(γR γ 2+1 BER D, m + K = K/2 +1 +Pr(γ [ D γ /2 BER R, ] Pr(γR γ K+1 BER D, m +Pr(γ D γ /2 BER R, K =1 m (14 π in which BER Z, denotes the average BER of lin Z in a specific region of [γ γ+1, given by BER Z, = = γ +1 γ N BER(, γf Z (γdγ I ( γ D, Z = D I ( γ R, Z = R.(15 ( 1 n 1( N n Furthermore, I ( γ is defined as shown in the next page with Γ(a, x = t a 1 e t dt [16]. x IV. NUMERICAL RESULS AND DISCUSSION 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 BER =10 3. We consider flat Rayleigh fading in two relaying scenarios: balanced networs (λ 0 = λ 1 = λ 2 =1 and unbalanced networs (λ 0 = λ 1 /5=λ 2 /5=1. For simplicity, the equal transmit power profile is employed at the source and the relay, i.e., P s = P r. 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 (13 72
π = Pr(γ <γ Σ γ +1 Pr(γ D γ 1 Pr(γ R γ 1, =0 [ Pr(γR γ 2+1 Pr(γ <γ ] D γ +1 γ γr γ 2+1 = +Pr(γ D γ /2 Pr(γ <γ R γ +1 γ D γ /2, =1,..., K/2 [ Pr(γR γ K+1 Pr(γ <γ ] D γ +1 γ γr γ K+1 +Pr(γ D γ /2 Pr(γ <γ R γ +1 γ D γ /2, = K/2 +1,...,K Pr(γ D γ 1 Pr(γ R γ 1, =0 [ ] Pr(γ <γ D γ +1,γ γr γ 2+1 = +Pr(γ <γ R γ +1,γ D γ /2, =1,..., K/2 [ ] Pr(γ <γ D γ +1,γ γr γ K+1 +Pr(γ <γ R γ +1,γ D γ /2, = K/2 +1,...,K (10 I (x = γ +1 γ ( α Q β γ e γ γ 1 γ ( ( = α {Q β γ 1 e γ γ 1 2 [ ( 1 1 π Γ 2, β γ 2 ( β β 2π 2 + 1 γ 1 ( ( 2 1 Γ 2, β 2 + 1 γ ]} γ +1 γ γ +1 (16 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 networ 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. he 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 lins. he 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. his can be explained by the fact that at high SNR regime, the highest modulation level is used on the direct lin level most of the time. Finally, we compare the average spectral efficiency from (13 with that of the conventional incremental opportunistic cooperative networs. In incremental opportunistic cooperative networs, the relaying lin is demanded since the direct lin is in outage. Note that both networs 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 networs 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 networs increases from 2 to 3 db as K increases from 6to8. V. CONCLUSION In this paper, we propose a joint adaptive modulation and lin switching scheme for opportunistic cooperative networs. he performance of the proposed networs in flat Rayleigh fading has been presented. From the analysis, we demonstrate that overall system spectral efficiency can be maximized by choosing the lin having higher spectral efficiency for data transmission and the proposed scheme outperforms the opportunistic incremental relaying networs in terms of spectral efficiency. his feature maes this scheme an attractive candidate from practical point of view for cooperative networs under adaptive modulation. ACKNOWLEDGMEN his research was supported by the Vietnam s National Foundation for Science and echnology Development (NAFOSED (No. 102.99-2010.10. 73
10 3 iid channels ind channels simulation 1 0.9 0.8 BER 10 4 10 5 Occurence Probability 0.7 0.6 0.5 0.4 0.3 0.2 0.1 10 6 0 5 10 15 20 25 30 35 40 45 50 0 0 5 10 15 20 25 30 35 40 Fig. 3. Average bit error rate versus average SNR per symbol. Fig. 1. Occurrence probability versus average SNR per symbol. 4.5 4 3.5 N=1 N=2 N=3 N=4 N=5 10 0 10 2 iid channels ind channels simulation ASE 3 2.5 2 N increasing OP 10 4 1.5 10 6 1 0.5 10 8 0 0 2 4 6 8 10 12 14 16 18 20 0 5 10 15 20 25 30 35 Fig. 4. Average spectral efficiency versus average SNR per symbol. Fig. 2. Outage probability versus average SNR per symbol. ASE 7 6 5 4 3 2 1 MSE IR K = 8 K = 6 K = 4 K = 2 REFERENCES [1] A. Nosratinia,. E. Hunter, and A. Hedayat, Cooperative communication in wireless networs, Communications Magazine, IEEE, vol. 42, no. 10, pp. 74 80, 2004. [2] J. N. Laneman, D. N. C. se, and G. W. Wornell, Cooperative diversity in wireless networs: Efficient protocols and outage behavior, IEEE ransactions on Information heory, 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-song, 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. 0 0 5 10 15 20 25 30 Fig. 5. Average spectral efficiency for both systems. 74
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