Optimal Diversity‐Multiplexing Tradeoff of MIMO Multi‐way Relay Channel

A MIMO multi‐way relay channel with full data exchange in which K users exchange messages with each other via the help of a single relay is considered. For the case in which each link is quasi‐static Rayleigh fading and the relay is full‐duplex, the fundamental diversity‐multiplexing tradeoff (DMT) is investigated, and we show that a compress‐and‐forward relay protocol can achieve the optimal DMT.     

On the Diversity Gain of AF and DF Relaying With Noisy CSI at the Source Transmitter

The problem of optimizing resource allocation over a half-duplex relay channel with noisy channel state information at the source transmitter (CSIT) is studied, with a focus on the asymptotically high signal-to-noise ratio (SNR) regime. A novel upper bound on the diversity-multiplexing tradeoff (DMT) is derived, taking into account the quality of the CSIT. It is shown that from a DMT perspective, the decode-and-forward (DF) protocol is strictly optimal over a certain range of the multiplexing gains. When the quality of the CSIT is sufficiently high, the DMT performance of the DF protocol with noisy CSIT equals that of the dynamic DF protocol shifted above by a constant diversity gain, which depends only on the quality of the CSIT about the source-destination link. When the quality of the CSIT reduces, DF relaying is still DMT-optimal, but only over a smaller range of the multiplexing gains. In an intermediate range of the multiplexing gains, nonorthogonal schemes provide some additional gains when the CSIT quality is sufficiently low. It is also shown that the DMT of the amplify-and-forward (AF) protocol is offset by a constant term depending on the quality of the CSIT of the source-destination link only.     

Multiple-Antenna Cooperative Wireless Systems: A Diversity–Multiplexing Tradeoff Perspective

We consider a general multiple-antenna network with multiple sources, multiple destinations, and multiple relays in terms of the diversity-multiplexing tradeoff (DMT). We examine several subcases of this most general problem taking into account the processing capability of the relays (half-duplex or full-duplex), and the network geometry (clustered or nonclustered). We first study the multiple-antenna relay channel with a full-duplex relay to understand the effect of increased degrees of freedom in the direct link. We find DMT upper bounds and investigate the achievable performance of decode-and-forward (DF), and compress-and-forward (CF) protocols. Our results suggest that while DF is DMT optimal when all terminals have one antenna each, it may not maintain its good performance when the degrees of freedom in the direct link are increased, whereas CF continues to perform optimally. We also study the multiple-antenna relay channel with a half-duplex relay. We show that the half-duplex DMT behavior can significantly be different from the full-duplex case. We find that CF is DMT optimal for half-duplex relaying as well, and is the first protocol known to achieve the half-duplex relay DMT. We next study the multiple-access relay channel (MARC) DMT. Finally, we investigate a system with a single source-destination pair and multiple relays, each node with a single antenna, and show that even under the ideal assumption of full-duplex relays and a clustered network, this virtual multiple-input multiple-output (MIMO) system can never fully mimic a real MIMO DMT. For cooperative systems with multiple sources and multiple destinations the same limitation remains in effect.     

On the Diversity–Multiplexing Tradeoff in Multiple-Relay Network

This paper studies the setup of a multiple-relay network in which $K$ half-duplex multiple-antenna relays assist in the transmission between either one or several multiple-antenna transmitter(s) and a multiple-antenna receiver. Each two nodes are assumed to be either connected through a quasi-static Rayleigh-fading channel, or disconnected. We propose a new scheme, which we call random sequential (RS), based on the amplify-and-forward relaying. We prove that for general multiple-antenna multiple-relay networks, the proposed scheme achieves the maximum diversity gain. Furthermore, we derive diversity–multiplexing tradeoff (DMT) of the proposed RS scheme for general single-antenna multiple-relay networks. It is shown that for single-antenna two-hop multiple-access multiple-relay $(K > 1)$ networks (without direct link between the transmitter(s) and the receiver), the proposed RS scheme achieves the optimum DMT. However, for the case of multiple-access single-relay setup, we show that the RS scheme reduces to the naive amplify-and-forward (AF) relaying and is not optimum in terms of DMT, while the dynamic decode-and-forward (DF) scheme is shown to be optimum for this scenario.      

On the diversity gain region of the dynamic decode-and-forward relay-assisted Z-channel

In an interference-limited system, the interference forwarding by a relay enhances the interference level and thereby enables the cancellation of the interference. In this work, interference forwarding by a half-duplex dynamic decode-and-forward (HD DDF) relay in a two-user Z-channel is considered. In the two-user Z-channel, one user is interference-limited while the other user is interference-free. The diversity gain region (DGR), which characterizes the tradeoff between the achievable diversity orders between the two users, is an appropriate performance metric for the Z-channel. Closed-form expression for the achievable DGR with the interference forwarding by the HD DDF relay is presented. The multiplexing gain regions (MGRs) where the HD DDF protocol achieves better DGR over the direct transmission scheme, full-duplex decode-and-forward (FD DF) and FD partial DF relay assisted Z- channel are identified. The HD DDF protocol is shown to achieve better DGR than the FD DF and FD PDF relay for a large range of MGR. The achievable DGRs for the HD DDF, FD DF, and FD PDF relay-assisted Z-channel and direct transmission scheme are presented for various interference levels and multiplexing gain pairs.     

Quantifying the Loss of Compress–Forward Relaying Without Wyner–Ziv Coding

The compress-and-forward (CF) strategy achieves the optimal diversity–multiplexing tradeoff (DMT) of a three-node half-duplex relay network in slow fading, under the assumption that the relay has perfect knowledge of all three channel coefficients and that the relay makes use of Wyner–Ziv (WZ) source coding with side information. This paper studies the achievable DMT of the same network when the relay is constrained to make use of standard (non-WZ) source coding. Under a short-term power constraint at the relay, using source coding without side information results in a significant loss in terms of the DMT. For multiplexing gains $r leq {2over 3}$, this loss can be fully compensated for by using power control at the relay. On the contrary, for $r in ({2over 3},1)$, the loss with respect to WZ coding remains significant.      

Average BER Analysis for Binary Signallings in Decode-and-Forward Dissimilar Cooperative Diversity Networks

In this letter, the average bit-error rate (BER) performance is analyzed for uncoded decode-and-forward (DF) cooperative diversity networks. We consider two typical networks: a single-relay cooperative network with the direct sourcedestination link and a two-relay cooperative network with the direct source-destination link, under dissimilar network settings, i.e., the fading channels of different relay branches may have different variances. We first derive a closed-form approximate average BER expression of binary signallings including noncoherent binary frequency shift keying (BFSK), coherent BFSK, and coherent binary phase shift keying (BPSK), for the singlerelay network. We then generalize our analysis to the two-relay network, and a closed-form approximate average BER expression for binary signallings is derived. We also show that our BER expressions can be considered as generalizations of previously reported results in the literature. Throughout our analysis, only one approximation, so-called the piecewise-linear approximation, is made. Simulation results are in excellent agreement with the theoretical analysis, which validates our proposed BER expressions.     

Subcarrier pairing for amplify-and-forward and decode-and-forward OFDM relay links

We consider a two-hop relay link in which orthogonal frequency division multiplexing (OFDM) is used on both hops. Under a joint sum-power constraint, our aim is to allocate power over subcarriers on the two hops such that the instantaneous rate of the relay link is maximized. Ordered subcarrier pairing (OSP) has been proposed in the literature to further improve the relay link rate; however, the optimality of OSP has been proven only for equal power allocation and the proof of its optimality under optimal power allocation has not been available yet. In this letter, we will provide our proof which verifies that OSP is optimal for both amplify-and-forward (AF) and decode-and-forward (DF) relay links when optimal power allocation is applied.     

基于能效的解码转发中继OFDM链路自适应功率分配方案研究

在能效问题中,设备本身的电路功耗已成为不可忽略的一部分,故将中继引入无线网络之后势必会带来更严重的电路功耗.该文基于解码转发(DF)中继OFDM频率选择性链路,结合电路所耗功率,提出一种最优能效功率分配方法,求得DF中继链路能效上界,同时分析了速率和功率限制对能效的影响.仿真结果表明,该文所提基于能效的功率分配算法可求出最大化能效的最优功率解,并能在保证较高速率的同时获得最好的系统能效.     

Decode-to-cooperate: a sequential alamouti-coded cooperation strategy in dual-hop wireless relay networks

An optimal cooperation strategy, decode-to-cooperate, is proposed and investigated for performance improvements in dual-hop wireless relay networks. Based on decode-and-forward (DF) strategy with multiple relay selection, we design a novel scheme such that the source node keeps transmitting sequentially and the selected relays cooperate by transmitting the decoded signal using distributed Alamouti coding. We exploit the multipath propagation effect of the wireless channel to achieve lower probability of error and introduce optimum power allocation and relay positioning. We analyze the scenario when the source to destination direct link is not available and derive a closed form expression for symbol error rate (SER), its upper bound and an asymptotically tight approximation to exploit the performance gain by selecting the optimum relays in a multiple-relay cooperation scheme. Moreover, asymptotic optimum power allocation (based on the SER approximation) and optimal relay positioning are also considered to further improve the SER. The proposed relay selection scheme outperforms cooperative (DF) and non-cooperative schemes by more than 2 dB.     

认知中继网络中的信道分配方法研究

认知中继网络中,对信道进行分配可以有效地提高端到端吞吐量。对三节点认知中继网络下的信道分配进行了研究。中继节点采用解码转发协议时,提出了一种次优的分配方法,将信道按信道增益排序,然后逐个地分配中继信道。中继节点采用放大转发协议时,给出了最优的信道分配方法,提出了一种次优的信道分配方法。次优方法逐个地比较中继信道采用传统协作方式传输时的端到端吞吐量、分配为双跳信道S-R和R-D链路时的端到端吞吐量完成分配。和最优方法相比,两种次优方法以较小的性能损失换取了计算复杂度的降低。给出了数值仿真,比较了两种传输方式下的端到端吞吐量性能,验证了以上方法的有效性。通过对比仿真时间,比较了最优方法和次优方法的计算复杂度。给定信道总数,对次优方法下信道分配后的比例进行了仿真,发现待分配中继信道以1/3的比例分配为直传信道;而在放大转发下,待分配中继信道几乎不被分配为双跳信道。      

Cooperative Transmission Using Quasi-Orthogonal Space-Time Block Codes with Adaptive Decode-and-Forward Relaying Protocol

In this paper, we propose a cooperative transmission scheme using quasi-orthogonal space-time block codes (QOSTBCs) for multiple-input multiple-output (MIMO) relay networks. Comparing with the conventional cooperative transmission scheme using orthogonal space-time block codes (OSTBCs), the proposed scheme can achieve higher bandwidth efficiency with the same decoding complexity. Moreover, an adaptive decode-and-forward (ADF) relaying protocol is proposed based on one-bit channel state information (CSI) feedback. According to the CSI feedback, a better transmission mode can be selected between the direct transmission and decode-and-forward (DF) cooperative transmission. In addition, the outage performance of the proposed scheme is investigated and a closed-form upper bound on the outage probability is derived. The performance analysis shows that the proposed scheme can achieve a full diversity order, which is higher than that of the direct and DF cooperative transmissions.     

Performance analysis of multiuser diversity in cooperative multi-relay networks under rayleigh-fading channels

In multiuser cooperative relay networks, cooperative diversity can be obtained with the help of relays, while multiuser diversity is an inherent diversity in multiuser systems. In this letter, the performance analysis of multiuser diversity in cooperative multi-relay networks is presented. Both the case of all relay participating and the case of relay selection are considered. We first derive asymptotic expressions of outage probability and symbol error probability for amplify-and-forward (AF) and decode-and-forward (DF) protocols with joint multiuser and cooperative diversity. Then, the theoretical analysis are validated by Monte Carlo simulations. Both the theoretical analysis and simulations show that a multiuser diversity order of K and a cooperative diversity order of M+ 1 can be achieved simultaneously for both AF and DF protocols (where K is the number of accessing users and M is the number of available relays). These demonstrate that the multiuser diversity can be readily combined with the cooperative diversity in multiuser cooperative relay networks.     

A novel cooperative transmission scheme based on superposition coding and partial relaying

This paper considered the single relay system and proposed a novel repetition coding decode‐and‐forward (DF) cooperative transmission scheme on the basis of superposition coding and partial relaying. In the proposed scheme, the link disparity due to the geometry of the relay network is emphasized, and only a fraction of the information is transmitted in relay mode with the rest being transmitted directly, which benefits from the utility of superposition coding (SC) in broadcast situation. The proposed scheme is analyzed in two cases, one assumes full channel state information at the source (full CSIS), the other with only mean gain of each link known by the source (partial CSIS). For both cases, the optimal design of system parameters is considered. We investigate the achievable rate and expected rate performance for these two cases, respectively. The proposed schemed is well compared with conventional repetition coding DF, parallel coding DF, as well as another promising superposition coding relaying. It is concluded that, by designing protocols that orients to certain network geometry, better trade‐off between performance and complexity can be obtained. The analysis reveals that the gap between conventional repetition and parallel coding is largely mitigated by the proposed scheme, quite for the scenario that the relay locates relatively but not extremely closer to the source, at moderate SNR regime for both partial and full CSIS cases. The proposed scheme becomes more beneficial in severe path loss attenuation scenario. Copyright © 2013 John Wiley & Sons, Ltd.     

Network Beamforming Using Relays With Perfect Channel Information

This paper deals with beamforming in wireless relay networks with perfect channel information at the relays, receiver, and transmitter if there is a direct link between the transmitter and receiver. It is assumed that every node in the network has its own power constraint. A two-step amplify-and-forward protocol is used, in which the transmitter and relays not only use match filters to form a beam at the receiver but also adaptively adjust their transmit powers according to the channel strength information. For networks with no direct link, an algorithm is proposed to analytically find the exact solution with linear (in network size) complexity. It is shown that the transmitter should always use its maximal power while the optimal power of a relay can take any value between zero and its maxima. Also, this value depends on the quality of all other channels in addition to the relay's own. Despite this coupling fact, distributive strategies are proposed in which, with the aid of a low-rate receiver broadcast, a relay needs only its own channel information to implement the optimal power control. Then, beamforming in networks with a direct link is considered. When the direct link exists during the first step only, the optimal power control is the same as that of networks with no direct link. For networks with a direct link during the second step only and both steps, recursive numerical algorithms are proposed. Simulation shows that network beamforming achieves the maximal diversity order and outperforms other existing schemes.      

Coding and Decoding for the Dynamic Decode and Forward Relay Protocol

We study the Dynamic Decode-and-Forward (DDF) protocol for a single half-duplex relay, single-antenna channel with quasi-static fading. The DDF protocol is well known and has been analyzed in terms of the diversity–multiplexing tradeoff (DMT) in the infinite block length limit. We characterize the finite block length DMT and give new explicit code constructions. The finite block length analysis illuminates a few key aspects that have been neglected in the previous literature: 1) we show that one dominating cause of degradation with respect to the infinite block length regime is the event of decoding error at the relay; 2) we explicitly take into account the fact that the destination does not generally know a priori the relay decision time at which the relay switches from listening to transmit mode. Both of the above problems can be tackled by a careful design of the decoding algorithm. In particular, we introduce a decision rejection criterion at the relay based on Forney's decision rule (a variant of the Neyman–Pearson rule), such that the relay triggers transmission only when its decision is reliable. Also, we show that a receiver based on the generalized likelihood ratio test (GLRT) rule that jointly decodes the relay decision time and the information message achieves the optimal DMT. Our results show that no cyclic redundancy check (CRC) for error detection or additional protocol overhead to communicate the decision time are needed for DDF. Finally, we investigate the use of minimum mean-squared error generalized decision feedback equalizer (MMSE-GDFE) lattice decoding at both the relay and the destination, and show that it provides near-optimal performance at moderate complexity.      

OFDM中继系统中减少反馈的节能方法研究

针对正交频分复用（OFDM）中继系统中上行反馈负荷过多和两跳链路能量消耗过大的问题,提出了一种减少系统上行反馈的节能方案（RFSE）。首先,根据用户的反馈中断概率,分别为中继和基站设置反馈门限;然后,通过信道的状态变化动态调整反馈门限,以达到减少系统反馈量的同时保证系统反馈量的稳定。最后,根据中继系统两跳链路中速率不匹配的规律,调整基站和中继处的发射功率,以达到减少系统能耗的目的。仿真结果表明,与减少信道反馈信息的分布式调度（RRFD）方案相比较,RFSE方案在减少系统反馈的同时,不仅保证了系统反馈量的稳定性,而且能够极大程度地减少系统能耗。      

Cooperative Communication Protocols in Wireless Networks: Performance Analysis and Optimum Power Allocation

In this paper, symbol-error-rate (SER) performance analysis and optimum power allocation are provided for uncoded cooperative communications in wireless networks with either decode-and-forward (DF) or amplify-and-forward (AF) cooperation protocol, in which source and relay send information to destination through orthogonal channels. In case of the DF cooperation systems, closed-form SER formulation is provided for uncoded cooperation systems with PSK and QAM signals. Moreover, an SER upper bound as well as an approximation are established to show the asymptotic performance of the DF cooperation systems, where the SER approximation is asymptotically tight at high signal-to-noise ratio (SNR). Based on the asymptotically tight SER approximation, an optimum power allocation is determined for the DF cooperation systems. In case of the AF cooperation systems, we obtain at first a simple closed-form moment generating function (MGF) expression for the harmonic mean to avoid the hypergeometric functions as commonly used in the literature. By taking advantage of the simple MGF expression, we obtain a closed-form SER performance analysis for the AF cooperation systems with PSK and QAM signals. Moreover, an SER approximation is also established which is asymptotically tight at high SNR. Based on the asymptotically tight SER approximation, an optimum power allocation is determined for the AF cooperation systems. In both the DF and AF cooperation systems, it turns out that an equal power strategy is good, but in general not optimum in cooperative communications. The optimum power allocation depends on the channel link quality. An interesting result is that in case that all channel links are available, the optimum power allocation does not depend on the direct link between source and destination, it depends only on the channel links related to the relay. Finally, we compare the performance of the cooperation systems with either DF or AF protocol. It is shown that the performance of a systems with the DF cooperation protocol is better than that with the AF protocol. However, the performance gain varies with different modulation types and channel conditions, and the gain is limited. For example, in case of BPSK modulation, the performance gain cannot be larger than 2.4 dB; and for QPSK modulation, it cannot be larger than 1.2 dB. Extensive simulation results are provided to validate the theoretical analysis.     

Cross-layer resource allocation over wireless relay networks for quality of service provisioning

The authors propose a physical-datalink cross-layer resource allocation scheme over wireless relay networks for quality-of-service (QoS) guarantees. By integrating information theory with the concept of effective capacity, the proposed scheme aims at maximizing the relay network throughput subject to a given delay QoS constraint. This delay constraint is characterized by the so-called QoS exponent thetas, which is the only requested information exchanged between the physical layer and the datalink layer in our cross-layer design based scheme. Over both amplify-and-forwards (AF) and decode-and-forward (DF) relay networks; the authors develop the associated dynamic resource allocation algorithms for wireless multimedia communications. Over DF relay network, the authors also study a fixed power allocation scheme to provide QoS guarantees. The simulations and numerical results verify that our proposed cross-layer resource allocation can efficiently support diverse QoS requirements over wireless relay networks. Both AF and DF relays show significant superiorities over direct transmissions when the delay QoS constraints are stringent. On the other hand, the results demonstrate the importance of deploying the dynamic resource allocation for stringent delay QoS guarantees.     

A distributed selection cooperation protocol with feedback and its DMT in nakagami-m fading channels

Selection cooperation is a simple and effective method proposed for cooperative diversity systems. We develop a distributed cooperative protocol with feedback based on selection cooperation. The best relay is selected in a fully decentralized manner and the protocol can be easily integrated with existing wireless networks. The diversity-multiplexing tradeoff (DMT) of the proposed protocol as well as common selection cooperation with feedback is derived over Nakagami-m fading channels. The result shows the protocol has significant increase of the spectral efficiency compared with the one without feedback. We also show that the selection cooperation has the same DMT as opportunistic relaying in general fading channels with or without feedback.