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On Relay Selection for Decode-and-Forward Relaying Muhammad Mehboob Fareed, Student Member, IEEE, and Murat Uysal, Senior Member, IEEE Abstract—In this letter, we consider a multi-relay network operating in decode-and-forward mode. We propose a novel relay selection method with a low implementation complexity. Unlike the competing schemes, it requires neither error detection methods at relay nodes nor feedback information at the source. We derive a closed-form symbol error rate (SER) expression for multi-relay network under consideration and demonstrate that the proposed selection method is able to extract the full diversity. Extensive Monte Carlo simulations are also presented to confirm the derived SER expressions and to compare the performance of the proposed scheme with its competitors. Index Terms—Distributed space-time codes, pairwise error probability, power allocation, relay channels. I. INTRODUCTION In contrast to earlier works which assume the participation of all relays, relay selection has emerged as a powerful technique with a higher throughput, because fewer time slots are required to complete transmission of one block. In [6], Bletsas et al. have proposed a simple relay selection criterion for a multi-relay network. Their method first searches the set of relays which are able to decode successfully (i.e., practical implementation requires error detection such as CRC) and then chooses the "best" relay for transmission in relaying phase. Determination of the best relay depends either on the minimum or harmonic mean of source-to-relay and relay-to- destination channel signal-to-noise ratios (SNRs). In [7], Beres and Adve have proposed another selection criterion in which relay-to-destination link with the maximum SNR is chosen. In [8], Ibrahim et al. have introduced a relay selection method based on the scaled harmonic mean of instantaneous source-to-relay and relay-to-destination channel SNRs. This close-loop scheme requires feedback of source-to-relay and relay-to-destination CSIs to the source node so that power can be adjusted before transmission. An error rate performance analysis is further presented in [8] which is mainly restricted for a symmetrical case where relay nodes are located equidistant from the source. A recently proposed scheme by Yi and Kim [9] combines relay selection with C-MRC. They also consider link adaptive regeneration (LAR) [10] where decoded symbols at relay nodes are scaled in power before being forwarded to the destination. LAR method results in reduced signaling overhead as compared to C-MRC. 与早期计划相比，假设所有中继参与，中继选择已成为一种吞吐量较高、功能较强的技术，由于需要在较小的间隙内完成一个块的传输。文献[6]，Bletsas等人对多中继网络提出了简单的中继选择标准。首先，发现一组中继可以成功解码(即实际执行要求的错误检测)CRC），然后在中继传输阶段选择最佳中继。最佳中继的判断取决于从任何对源到中继和中继到目标信道的信号噪声比（SNR）最小或调和平均值。贝雷斯和Adve提出了中继到目的最大信噪比SNR选择链路的另一个选择标准。在文献[8]中，Ibrahim等人已经推出了基于瞬时源到中继和中继的信 道信噪比的比例调和平均值中继选择方法。这种闭环方案需要从中继和中继到目的CSI传输前可调整反馈给源节点。[8]进一步显示了错误率性能分析，主要限制了中继节点在到源等距离的对称性。 由Yi及Kim结合中继选择和等人[9][9]最近提出的计划C-MRC。他们还考虑链路自适应再生（LAR）[10]缩放能力在中继节点解码元转发到目的地之前。LAR与信令开销相比，该方法可以减少信令开销C-MRC。 In this paper, we investigate the performance of a mult- relay network with relay selection avoiding some restrictions and assumptions imposed in previous works. We propose a relay selection criterion based on an open-loop architecture. It does not require any feedback CSI unlike [8] which relies on power allocation by the source node through feedback information. It further does not require any error detection mechanism (e.g., CRC) at relay nodes in contrast to [6], [7]. In our scheme, the destination node chooses the best relay based on the minimum of source-to-relay and relay-to-destination SNRs at the end of broadcasting phase and allows the selected relay to participate only if the minimum of its source-to-relay and relay-to-destination link SNRs is greater than SNR of the direct link. We derive closed-form symbol error rate (SER) performance expressions for the multi-relay network scenario with the proposed relay selection algorithm. In our analysis, we assume arbitrary relay locations, thereby avoiding the symmetrical scenario of [8] which is a simplifying assumption, yet somewhat impractical in real-life situations. Extensive Monte-Carlo simulations are also presented to collaborate on the analytical results. The rest of the paper is organized as follows: In Section II, we describe the multi-relay cooperative network under consideration with DaF relaying and relay selection. In Section III, we derive SER for multi-relays with arbitrary locations. In Section IV, we present simulation results and finally, Section V concludes the paper. Notation: Ey (.) denotes expectation with respect to random 在本文中，我们研究了多中继网络中继选择，以避免对以往作品的一些限制和假设，以加强其性能。我们提出了基于开环架构的中继选择标准。它不需要任何反馈深度。与[8]不同，它依赖于源节点通过反馈信息的功率分配。此外，他不需要任何错误的检测机制（例如，CRC）对比中继节点[6]，[7]。在我们的计划中目的节点选择最佳中继是基于源到中继和中继到目的在广播阶段结束时的最小SNR，允许所选择的中继参加当且仅当最小的源到中继及中继到目标链路信噪比大于直接链路的信噪比。我们推导出闭合形式的符号错误率的多中继网络场景与提出的中继选择算法（SER）性能表达式。在我们的分析中，我们假设任意中继的位置，从而避免[8]它的对称情况是一个简化的假设，但在现实生活中多少有些不切实际。广泛的蒙特卡罗模拟还提出要对分析结果进行协作。本文的其余部分安排如下：在第二部分，我们将描述所考虑的多中继协作网络，德福中继和中继选择。在第三节中，我们得出SER多中继的任意位置。在第四节中，我们提出的模拟结果，最后，第五节总结全文。 注释：Ey (.)表示对于随机变量variable y期望. II. TRANSMISSION MODEL We consider a multi-relay scenario with N relay nodes. Source, relay, and destination nodes operate in half-duplex mode and are equipped with single transmit and receive antennas. All the nodes are assumed to be located in a two dimensional plane where dSD, dSRi, and dRiD, i = 1, 2, ...,N denote the distances of source-to-destination (S→D), source-to-relay (S→Ri), and relay-to-destination (Ri→D) links respectively. We consider an aggregate channel model which takes into account both long-term path loss and short-term Rayleigh fading. The path loss is proportional to d−α where d is the propagation distance and α is path loss coefficient. Normalizing the path loss in S→D to be unity, the relative geometrical gains of S→Ri and Ri→D links are defined as GSRi = (dSD/dSRi )α and GRiD = (dSD/dRiD)α. They can be further related to each other by law of cosines, i.e.,G −2/α Sri + G −2/α RiD − 2G −1/α SRi G −1/α RiD cos θi = 1, where θi is the angle between lines S→Ri and Ri→D [11]. The fading coefficients for S→D, S→Ri, andRi →D links are denoted by hSD, hSRi, and hRiD, respectively and are modeled as zero mean complex Gaussian random variables with unit variance leading to a Rayleigh fading channel model. Let x be a modulation symbol taken from an M-PSK (Phase Shift Keying) constellation. Considering path-loss effects, the received signals in the first time slot at destination and at 1th relay nodes are given by rD1 = _ KSPhSDx + nD1, (1) rRi = _ GSRiKSPhSRix + nRi , (2) where P is the total transmit power shared by the source and relay nodes. KS is an optimization parameter for power allocation and denotes the fraction of power used by the source node in the broadcasting phase. For equal power allocation, KS = 0.5. The remaining power is reserved for relay transmission and power of the selected relay is controlled by another optimization parameter, Ki, i = 1, 2, ...N . Optimized values of KS and Ki, i = 1, 2, ...,N can be found in [1]. In (1)-(2), nRi and nD1 model the additive noise terms and are assumed to be complex Gaussian with zero mean and variance of N0. Let λSD, λSRi, and λRiD denote the instantaneous SNRs in S→D, S→Ri, and Ri →D links respectively. In our scheme, the destination first chooses the best relay based on the following criterion Rsel = argmax Ri {min (λSRi, λRiD)} , (3) where "sel" denotes the index for the selected relay. Then, the destination node instructs the selected relay to participate in cooperation phase only if SNR in direct link is less than the minimum of the SNRs in the selected relaying path, i.e., λSD < λmax ˆ=min(λSRsel, λRselD) . (4) Otherwise, the selected relay node will not participate in cooperation phase. If allowed to cooperate, the relay node performs demodulation1 and transmits re-encoded symbol ˆx in the second time slot. The signal received at destination node is therefore given by rD2 = _ GRselDKselPhRselDˆx + nD2, (5) where nD2 models the additive Gaussian noise term and Ksel = Ki|i=sel. The destination node then combines the received signals given by (1) and (5) using MRC and decodes the symbol transmitted by source. 我们认为，一个多中继情况下用N个中继节点。源，中继，节点和目标节点工作在半双工模式，并配有单发射和接收天线。所有的节点被认为是位于一个二维平面，其中dSD, dSRi, and dRiD, i = 1, 2, ...,N）分别表示源到目的地（S→D），源到中继（S→RI）和中继到目的地（日→D）链路的距离分别。我们认为，总的信道模型，并考虑到双方长期路径损耗和短期瑞利衰落。路径损耗正比于D-α，其中d为传播距离，α是路径损耗系数。正常路径损耗从 被归一化， 和 链路的相对的几何增益被定义为GSRi = (dSD/dSRi )α and GRiD = (dSD/dRiD)α. 他们进而涉及余弦定理，i.e.,G −2/α Sri + G −2/α RiD RID COSθ=1，其中θ是线S→Ri and Ri→D [11].之间的角度。从S→D，S→日的衰减系数，和Ri→d个链接是由HSD，hSRi和hRiD，分别表示和建模为零均值复高斯随机变量与单位方差导致瑞利衰落信道模型。设x是从M-PSK（相移键控）星座采取的调制符号。考虑路径损耗的影响，在到达目的地，并在第1中继节点的第一时隙中接收到的信号由下式给出： （1） （2） 其中P是由源节点和中继节点共享的总发送功率。 KS是用于功率分配的优化参数和表示功率的使用在广播相源节点的分数。对于同等功率分配，KS=0.5。的剩余电力被保留用于所选择的中继的中继传输和功率由另一个优化参数控制Ki, i = 1, 2, ...N . KS和Ki的优化值，I =1，2，...，N，可以在发现[1]。在（1） - （2），NRI和ND1模型的加性噪声的术语和被认为是复杂的高斯均值为零，N0的方差。让λSD，λSRi和λRiD表示S中→D，S→日，和Ri→d个链接分别瞬时信噪比。在我们的方案中，目标首先选择基于以下条件最好的中继{min (λSRi, λRiD)} , (3) 其中“SEL”表示的索引选择的继电器。然后，目的地节点指示所选择的中继参加协作相位仅当信噪比的直接链路小于信噪比的在所选择的中继路径的最小值，即λSD < λmax ˆ=min(λSRsel, λRselD) . (4) 否则，所选择的中继节点将不参与协作阶段。如果允许进行合作，所述中继节点执行解调1与在第二个时隙中发送重新编码的码元x。在目的节点接收到的信号由给出rD2 =（5），其中ND2模型的加性高斯噪声项和KSEL=基| I = SEL。 III. SER DERIVATION In this section, we derive a SER expression for the proposed scheme. Defining λ = [λSD λmax λSRsel λRselD]T, a conditional SER expression can be given as P (e |λ) = Pn−coopPe|direct + PcoopPe|coop , (6) where Pn−coop = P(λSD > λmax) is the probability that the selected relay is not qualified to participate in cooperation phase and Pcoop = 1−Pn−coop is the probability of cooperation. Pe|direct denotes the SER for direct S→D transmission and Pe|coop denotes the SER when the cooperation takes place. If cooperation does not take place, the overall SER is simply equal to the SER of direct link and is given by Pe|direct = β (λSD) where β(.) is given by [12] β (x) = dη, (7) with g = sin2 (π/M). If cooperation takes place, we need to calculate Pe|coop which is given by Pe|coop = Pe_selPe|e_sel + (1 − Pe_sel) Pe|c_sel , (8) where Pe_sel = β (λSRsel ) denotes the probability of the selected relay to make a decoding error. If the selected relay makes an incorrect decision, the corresponding conditional SER is calculated as Pe|e_sel = β _ |λSD + eλRselD|2 _ (λSD + λRselD) _ . In the calculation of Pe|e_sel, we use ˆx = ex to take into account for the error at the relay. We can actually approximate this probability by 1, because, under the assumption that relay is qualified for cooperation (i.e., λmax > λSD), an incorrect decision at destination is much more likely than a correct one. On the other hand, if the selected relay has decoded correctly, the SER is given by Pe|e_sel = β (λSD + λRselD). Replacing all above related definitions in (6), we have P( e| λ) = P (λSD > λmax) β (λSD) _ _ T0 + P (λSD < λmax) β (λSRsel) _ _ T1 + P (λSD < λmax) [1 − β (λSRsel )] β (λRselD + λSD) _ _ T2 . (9) To find the unconditional SER, one needs to take an expectation of (9) with respect to λ. This is quite difficult and would probably not yield closed-form expressions. Therefore, we pursue an alternative approach here reformulating SER in terms of conditional probability density functions (pdfs) of λmax, λSRsel, and λRselD (conditioned on the event that ith relay node is selected). Let ξi, ξC i , μi, and μCi denote the events λmax = λSRi , λmax = λRiD, λSRi < λRiD, and λSRi > λRiD respectively. Further, let Δ denote the set of permutations of 1, 2, ..,N and Pr (σ) denote the probability of one particular permutation σ ∈ Δ. Pe can be then calculated as Pe = P (e |ξi )Pr (ξi) + P _ , (10) which can be further approximated as Pe Pr (σ) Φ0 + Φk Pr (μi) Pr , (11) where we define Φk = Eλ[Tk], k = 0, 1, 2 and ignore the correlation of μi and σ. Calculations of Pr (σ), Pr (μi), and Pr are provided in Appendix A, while calculations of Φ0, Φk, andΦCk , k = 1, 2 are given in Appendix B. Using these results from Appendixes, we obtain the final SER expression given on the top of next page, where ΨSRi (.) and ΨRiD (.) are the MGFs of λSRi and λRiD, respectively and αηk = −g _ sin2 ηk, k = 1, 2, . In the above, operators F1 {.}and F2 {.} are defined by F1 {f (η)} = f (η) dη, (13) (14) We conclude this section by demonstrating the achievable diversity of our scheme. Assuming BPSK, inserting η1 = η2 = π/2 2, the resulting expression can be further approximated as . (15) From (15), it can be readily confirmed that a diversity order of N + 1 is achieved. 在本节中，我们推导出SER表达对该方案。定义λ=[λSD的λmaxλSRselλRselD] T，有条件的SER表达式可以表示为 （6） 其中的Pn-鸡舍= P（λSD>的λmax）是选择的中继是没有资格参加协作阶段，Pcoop=1-PN-鸡舍是合作的概率的概率。 PE|直接表示成Ser的直达S→ð传输和Pe|鸡舍表示SER当协作发生。如果协作不会发生，总体SER就等于直接链接的SER和由下式给出： （8） 如果协作发生，我们需要计算PE|这是由给定的 perl 其中Pe_sel=β（λSRsel）表示所选择的中继的概率，使一个解码错误。如果所选择的中继作出不正确的判定，相应的条件SER被计算为： IV. NUMERICAL RESULTS AND DISCUSSION In this section, we first verify the accuracy of derived SER expression through Monte-Carlo simulation. Then, we present performance comparisons between the proposed scheme and its competitors. We assume α = 2, θi = π, and 4-PSK modulation in our simulation study. In Fig.1, we plot the SER expression given by (12) along with the simulation results. We assume equal power allocation, therefore have KS = K1 = K2 = • • • = KN = 0.5. We consider two, three, and four relays with the following geometrical gains: •Two-relay network with GSRi/GRiD = −30, 0 dB. • Three-relay network with GSRi/GRiD = −30, 0, 30 dB. • Four-relay network with GSRi/GRiD = −30, 0, 30,−10 dB. As observed from Fig.1, our approximate analytical expressions provide an identical match (within the thickness of the line) to the simulation results. It can be also observed that diversity orders of 3, 4, and 5 are extracted indicating the full diversity for the considered number of relays and confirming our earlier observation. In Fig.2, we compare the performance of our proposed DaF multi-relay scheme (using optimum power allocation results from [1]) with other existing DaF schemes (optimized if available) in the literature. We assume two-relay network with both GSR1/GR1D = 0dB and GSR2/GR2D = 0dB. The competing schemes are listed as: Pe ], (12) TABLE I • Relay selection without any error detection or threshold (RS), • Relay selection with 16-bit CRC in a frame length of 1024 bits (RS-CRC) [6], • All relays participating without any error detection or threshold (AP)3, • All relays participating with 16-bit CRC in a frame length of 1024 bits (AP-CRC), • Relay selection with static threshold (RS-STH) [8], • Relay selection with link adaptive relaying (RS-LAR) [9]. The selection method used in RS-STH is based on the modified harmonic mean as described in [8] with optimized values of power allocation parameters. For RS-LAR, the selection criterion used is as described in [9]. In all other selection schemes, the relay selection criteria are based on (3). Table II summarizes implementation aspects of the competing cooperation schemes. Fig.2 illustrates the performance of above cooperation schemes for a channel block length of 512 symbols. AP scheme where both relays participate without any error detection mechanism at relays performs the worst. For the considered relay location, it does not provide any diversity advantage. RS scheme outperforms AP and the later is not able to extract full diversity order. The use of CRC could potentially improve the performance of both AP and RS. As observed from Fig.2, both schemes with CRC (i.e., AP-CRC and RSCRC) take advantage of the full diversity and significantly outperform their counterparts without CRC. It should be noted that the implementation of RS-CRC requires maximum two time slots while AP-CRC might require more time slots (i.e., each relay with correct CRC needs an orthogonal time slot for transmission). RS-LAR performs better than two CRC-based schemes. RS-STH scheme where relay selection is performed with a static threshold is also able to outperform the RSCRC and AP-CRC schemes and avoids the use for CRC in its implementation. Our proposed scheme outperforms all previous schemes. In Fig.3, we repeat our simulation study to demonstrate frame error rate (FER) performance. Similar observations can be made for performance comparisons indicating the superiority of our scheme. Fig.4 illustrates the performance of the above schemes for a channel block length of 128 symbols. The performance of cooperative schemes which rely only on CSI (i.e., AP, RS, RS-STH, RS-LAR as well as the proposed scheme) remain unchanged. On the other hand, performance of schemes which rely also on the accuracy of decoding at relay nodes (i.e., AP CRC, RS-CRC) demonstrates dependency on channel block length. Particularly CRC-assisted schemes suffer a significant degradation if channel varies within CRC frame. Compared to Fig.2, we also observe from Fig.4 that the performance of AP-CRC now becomes better than that of RS-CRC. As earlier mentioned, the proposed relay selection algorithm does not require any feedback information. It, however, requires CSI of S→Ri links at the destination node. This requires transmission of hSRi from each relay to destination. Since the transfer of analog CSI requires to send an infinite number of bits, a control channel with limited number of feedforward bits can be used in practical implementation. To demonstrate the effect of quantization, we provide simulation results in Fig.5 where hSRi is quantized using 2, 3, 4, and 6 bits with a non-uniform quantizer optimized for Rayleigh distributed input [13]. It is observed from Fig. 5 that as low as 6 bits would be enough to obtain a good match to the ideal case. As a final note, we would like to point out that this feedforward channel can be also avoided if one prefers a distributed implementation of relay selection algorithm similar to [6]. The description of such an implementation can be found in [1]. V. CONCLUSION In this letter, we have proposed a simple relay selection method for multi-relay networks with DaF relaying. The proposed method avoids the use of error detection methods at relay nodes and does not require close-loop implementation with feedback information to the source. Its implementation however requires channel state information of source-to-relay channels at the destination. This can be easily done in practice through a feedforward channel from the relay to the destination. Our SER performance analysis has shown that the proposed relay-selection method is able to extract the full diversity. Our simulation results have further demonstrated the superior performance of the proposed scheme over its competitors. VI. APPENDIX A In this appendix, we calculate marginal pdf of λmax and joint pdf of λSRsel and λRselD which are required to take expectation of (9). Let us define λi = min(λSRi, λRiD). Under the Rayleigh fading assumption, both λSRi and λRiD follow exponential distribution. Recall that Δ denotes the set of permutations of 1, 2, ...,N, P(σ) denotes the probability of one particular permutation σ ∈ Δ, and λ(i) denotes the ordered sequence of λis, i.e., λ(1) > λ(2) > λ(3) > ... > λ(N). It can be shown [14] that we can transform λ(i)s into a set of new conditionally independent variables Vn such that λ(i) = n=i AnVn where An = _−1. The joint pdf of Vn is given by where Pr {σ} = and f _ {Vn}N σ∈S Pr {σ} fV|σ _ {Vn}N for [0 < Vn < ∞] with _−1. The above transformation of variables enables us to find the moment generating function (MGF) of variable λmax = λ(1) = For probabilities of event ξi and ξC i , we first define Δi ⊂ Δ as the set of all the permutations for which i is the first element. Then we have Pr (i = sel) = Pr (σ), which denotes the probability of ith relay node being selected. Recall that μi denotes the event of λSRi < λRiD and μCi its complementary event, i.e., λSRi > λRiD. The probabilities of these two events can be approximated4 as Pr (ξi) ∼= Pr (i = sel)Pr (μi), and Pr l)Pr with Pr (μi) = ΛR iD/(ΛSRi +ΛRiD) and Pr ΛSRi/(ΛSRi +ΛRiD). Here, ΛRiD and ΛSRi are the average values of received SNRs and are given by ΛRiD = E[λRiD] = GRiDKi(E/N0) and ΛSRiD = E[λSRi] = GSRiKS(E/N0). Now let us calculate the joint pdf of λSRsel and λRselD conditioned on the respective events ξi and ξC i . For ξi, we have λSRi = λmax, thus conditional statistics of λSRsel and λRselD are given by MGF (λSRsel) = MGF (λmax) and fRselD (λ |ξi) = _ ) exp(− λ 0, otherwise (16) 4Exact value for event ξi can be calculated as Pr(ξi) = Pr(λRiD > λSRi > λk,∀k _= i) ΦC2 = F1 _ ΨSD (αη1 ) _ Ψmax (αη1 ) − Ψmax ΨSD (αη1)ΨSRi (αη2) − Ψmax SD ____ . (23) For event ξC i , we have λRiD = λmax. Thus conditional statistics of λRselD and λSRsel are obtained respectively as MGF (λRselD) = MGF (λmax) and ) exp(− λ ΛSRi ), λ≥ λmax 0, otherwise (17) VII. APPENDIX B In this appendix, we calculate Φ0,Φk and ΦCk , k = 1, 2 which appear in (11). Noting λSD follows an exponential distribution under the considered Rayleigh fading assumption, we have Φ0 = Eλ[T0] = Eλmax [ β (λ) fλSD (λ) dλ]. Using the definition of β (.) from (7), we have Φ0 = F1 _ ΨSD (αη1 )Eλmax _ exp (18) where αη and F1{.} are earlier defined by (13). Averaging over λmax yields Φ0 = F1 _ ΨSD (αη1)Ψmax (19) where ΦSD(.) and Φmax(.) are MGFs of λSD and λmax. For the calculations of Φk and ΦCk , k = 1, 2, we need to consider events ξi and ξC i . A. Case I (Event ξi) From (9), we have T1 = P (λSD < λmax) β (λmax) for this event. Taking expectation with respect to λSD, we have EλSD [T1] = (1− exp (−λmaxΛSD)) β (λmax). Using the definition of β(.) and further taking expectation with respect to λmax, we obtain Φ1 = Eλ [T1] = F1 _ Ψmax (αη1 ) − Ψmax (20) On the other hand, T2 is given as T2 = P (λSD < λmax) [1 − β (λSRsel )] β (λRselD + λSD). First taking expectation with respect to λSD and λRselD using pdf given by (16) and then averaging over λmax, we have Φ2 = F1 ΨSD (αη1)ΨRiD (αη1 ) Ψmax ΨSD (αη1)ΨRiD (αη1 ) Ψmax . (21) B. Case II (Event ξC i ) From (9), we have T1 = P (λSD < λmax) β (λSRsel ) for this event. Averaging over λSD, we obtain EλSD [T1] = (1 − exp (−λmax/ΛSD)) β (λSRsel ). Using the definition of β(.) and taking expectations over λSRsel and λmax, we obtain ΦC1 . (22) On the other hand, we have T2 = P (λSD < λmax) [1 − β (λSRsel )] β (λRselD + λSD). Inserting β(.) in T2, taking expectation of the resulting expression with respect to λSRsel and λmax, we obtain (23). REFERENCES [1] M. M. Fareed and M. Uysal, “A novel relay selection method for decodeand- forward relaying," in IEEE Canadian Conference Electrical Computer Engineering 2008 (CCECE’08), Niagara Falls, Ontario, Canada, May 2008. [2] A. Sendonaris, E. Erkip, and B. Aazhang, “User cooperation diversity Part I: System description," IEEE Trans. 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