IEEE COMMUNICATIONS LETTERS, VOL. 14, NO. 2, FEBRUARY 2010 145 Power Allocation for Bidirectional AF Relaying over Rayleigh Fading Channels Yuanyuan Zhang, Yi Ma, Member, IEEE, and Rahim Tafazolli, Senior Member, IEEE AbstractThis letter presents two novel power allocation schemes for bidirectional amplify-and-forward (AF) relaying over Rayleigh fading channels through the exploitation of channel mean strength. The rst scheme aims to maximize the upper bound of average sum rate, and the other aims to achieve the trade-off of outage probability between two terminals. Numerical results show considerable performance improvement in compar- ison with conventional power allocation approaches. Index TermsAmilify-and-forward, average sum-rate, bidirec- tional relaying, power allocation, outage probability. I. I NTRODUCTION S INCE 1960s Shannons ground-breaking work about the two-way channel [1], a lot of research efforts have been paid to nd the fundamental capacity limit of this special com- munication model. However, the capacity for this seemingly simple channel has not been found to this date. Recently, there are increasing research activities towards the combination of two-way channel and relay channel, namely, two-way relay channel (TWRC) or bidirectional relaying [2][3]. In the TWRC system, bidirectional communication between two users can enjoy improved spectral efciency compared with the traditional one-way relay channel [2]. The achievable rate of the system is investigated for relaying protocols including amplify-and-forward (AF), and decode-and-forward (DF) for deterministic channels in [3]. For more efcient use of the power resource, the power allocation has been exploited. In [4][5], the power allocation is to maximize the system capacity and achievable rate for the deterministic channel; while a xed power allocation ratio independent of channel quality is given to improve the upper bound of the average sum rate in [6]. In this letter, we add to this area by investigating power allocation strategies for AF bidirectional relaying system un- der total power constraint 1 . Requiring knowledge of only the channel mean strength, these power allocation strategies are applicable even under rapidly time-varying channels. First, a power allocation strategy is proposed to maximize the upper bound of the average sum rate in high average SNR region. Second, to avoid one of the terminals suffering from severe outage, the outage probability of each individual terminal is Manuscript received November 12, 2009. The associate editor coordinating the review of this letter and approving it for publication was G. Mazzini. This work has been partially supported by the EU-ICT WHERE project and UK MVCE Core 4-Efciency. The authors are with C.C.S.R., University of Surrey, U.K., GU2 7XH (e- mail: y.ma@surrey.ac.uk). Digital Object Identier 10.1109/LCOMM.2010.02.092227 1 The total power constraint is widely considered in relay networks to provide useful insight into the relay optimization [7][8]. Practically, this is motivated by the fact that in networks such as sensor network, where the long-term power consumption is a major concern. derived, which cant be optimized at the same time. Accord- ingly, a power allocation strategy is proposed to make a trade- off between these two terminals. It is noticed in the numerical results that the proposed strategies outperform the traditional equal power allocation in the average sum rate and outage probability. II. SYSTEM MODEL Consider a three-node bidirectional relaying system consist- ing of two terminals, S 1 and S 2 , one relay, R. In Phase I, S 1 and S 2 transmit their signals simultaneously to the relay R and the received signal at R is given by = ℎ 1 1 + ℎ 2 2 + (1) where 1 and 2 are the transmitted signals with transmit power from S 1 and S 2 respectively, ℎ 1 and ℎ 2 are inde- pendent complex Rayleigh fading channel gains of channels from S 1 and S 2 to R, respectively, and is the complex Additive White Gaussian Noise (AWGN) with noise power 0 . The channel mean strengths of these two channels are 1 and 2 , respectively. The channels are assumed to be invariant for the consecutive two phases. At the relay, with amplication factor , the received signal is broadcast to both terminals in Phase II. Then, the received signal at terminal S ,=1,2 is, = ℎ ( )+ (2) With the knowledge of its own signal at each terminal, the self-interference part can be subtracted from resulting ˜ = ℎ 1 ℎ 2 + ℎ + (3) where =2 for =1 and =1 for =2, is chosen subject to the power at relay as [6], = √ ∣ℎ 1 ∣ 2 + ∣ℎ 2 ∣ 2 + 0 (4) Then the received SNR for signals from S1 and S2 are, 1 = ∣ℎ 1 ∣ 2 ∣ℎ 2 ∣ 2 ∣ℎ 1 ∣ 2 + ∣ℎ 2 ∣ 2 ( + )+1 , (5) 2 = ∣ℎ 1 ∣ 2 ∣ℎ 2 ∣ 2 ∣ℎ 2 ∣ 2 + ∣ℎ 1 ∣ 2 ( + )+1 , (6) respectively, where = / 0 and = / 0 . In most early publications, it is assumed all the three nodes transmit with the same power, = , referred as equal power allocation in this paper. However, the performance of this system can be improved by allocating power among these nodes. Next we propose two different power allocation strategies with the total power constraint 2 + = 0 in high average SNR range. 1089-7798/10$25.00 c ⃝ 2010 IEEE www.DownloadPaper.ir www.DownloadPaper.ir