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.     

SER Performance of Amplify-and-Forward Cooperative Diversity Over Asymmetric Fading Channels

In this paper, the performance of amplify-and-forward (AF) cooperative diversity is analyzed over asymmetric fading channels. The source–relay and the relay–destination links experience Rayleigh fading while the source–destination link is subject to generalized Gamma fading. First, the probability density function (PDF) and the moment generating function (MGF) of the source–relay–destination link and the MGF of the source–destination link are derived. Then, the symbol error rate (SER) is determined based on the MGF of the total end-to-end signal-to-noise ratio (SNR). Moreover, the SER performance of N-relay assisted AF cooperative diversity is illustrated for M-ary phase shift keying (M-PSK) and M-ary quadrature amplitude modulation (M-QAM). Based on the derived MGF expressions, the numerical results are obtained by varying the modulation types and channel parameters for different scenarios.     

Performance Analysis and Optimal Power Allocation for Space–Time and Amplify-and-Forward Cooperative System

In this paper, we consider a space?Ctime and amplify-and-forward (ST-AF) cooperative system which consists of two-antenna source, single-antenna relay and destination. Source transmits Alamouti space?Ctime coding symbols to destination with cooperation of relay which adopts AF strategy. Closed-form symbol error rate (SER) is derived for the ST-AF system with PSK signals. Moreover, a SER approximation is developed to show the asymptotic performance of the ST-AF cooperative system in medium and high SNR regimes. For comparison, the SER approximation of another cooperative space?Ctime coding (C-STC) scheme is also derived. Theoretical analysis shows that the ST-AF can obtain more diversity gain and achieve higher diversity order than C-STC. Statistical optimal power allocation (OPA) algorithm for the ST-AF cooperative system is presented based on the SER performance. It turns out the OPA only depends on the channel links related to the relay, not depend on the direct link between source and destination. Finally, numerical simulations validate the theoretical analysis.     

Performance analysis and power allocation for decode‐and‐forward cooperative communications over Rician fading channel

This paper derives the asymptotic symbol error rate (SER) and outage probability of decode‐and‐forward (DF) cooperative communications over Rician fading channels. How to optimally allocate the total power is also addressed when the performance metric in terms of SER or outage probability is taken into consideration. Analysis reveals the insights that Rician factor has a great impact on the system performance as compared with the channel variance, and the relay–destination channel quality is of importance. In addition, the source–relay channel condition is irrelevant to the optimal power allocation design. Simulation and numerical evaluation substantiate the tightness of the asymptotic expressions in the high‐SNR regions and demonstrate the accuracy of our theoretical analysis. Copyright © 2011 John Wiley & Sons, Ltd.     

Optimal power allocation to minimize SER for multinode amplify-and-forward cooperative communication systems

An optimal power allocation （OPA） method with mean channel gains is proposed for a multinode amplify-and-forward cooperative communication system. By making use of M-PSK modulation, a closed-form symbol-error-rate （SER） formulation and corresponding upper bound are first derived. Subsequently the OPA method is utilized to minimize the SER. Comparison of the SER of the proposed OPA method with that of the equal power allocation （EPA） method, shows that the SER of both methods, which is approximately optimal performance, is almost the same when relays are near the source. OPA outperforms the EPA when the relays are near the middle between the source and destination or near the destination. The proposed OPA method depends only on the ratio of mean channel gains of the source-to-relay to those of the relay-to-destination. Extensive simulations are performed to validate the theoretical results.     

Performance Analysis of Generic Amplify-and-Forward Cooperative Networks over Asymmetric Fading Channels

In this paper, we analyze the performance of multi-hop multi-branch amplify-and-forward (AF) networks over generalized fading channels. Using the moment generating function (MGF)-based approach, we develop general expressions for the outage probability and symbol-error rate (SER) performance of the system with maximal ratio combining (MRC) receiver. The MGF-based approach relies on numerical integration. To gain insights into system performance, we therefore investigate the asymptotic outage and SER performance of the system with MRC and selection combining (SC) receiver at the destination. In particular, we develop the asymptotic statistics of the end-to-end signal-to-noise ratio (SNR) of an AF multi-hop link. We further derive the cumulative density function of the sum of the individual end-to-end SNRs, received from different diversity paths for MRC receiver. We also study the power allocation problem in a multi-hop multi-branch system with MRC receiver. In generalized Gamma fading environments, we seek to find the power allocation strategy that maximizes the SNR at the destination subject to a total power constraint. By means of simulations, we validate our theoretical developments and verify the efficiency of our proposed power allocation in improving the received SNR compared to a generic cooperative system with no power allocation. We also conclude that our asymptotic expressions for the outage probability and SER match the simulations very well in medium-to-high-SNR regime.     

Minimized SER and QOS Based Power Allocation Strategies for Multi HDAF Relay Cooperative Network

In this paper, a multi hybrid decode-amplify-forward relay cooperative network with perfect CSI in flat Rayleigh fading channel is considered. Using moment generating function based approach, the closed form of symbol error rate (SER) with asymptotic approximation is derived. Based on the lower bound of SER (Olfat and Olfat in IET Commun 5(4):2018–2027, 2011), Lagrange multiplier method and differential evolution (DE) algorithm based power allocation schemes are proposed. With fixed source power, the relay powers are optimized with the proposed schemes by the power allocation factor. Further the SER performance of proposed power allocation schemes is investigated by varying the location of the relays. The performance gain of proposed power allocation schemes depends on the channel quality of source to relay and relay to destination links. It is observed that the proposed power allocation schemes outperform the equal power allocation scheme and DE based power allocation provides SER response close to power allocation with Lagrange multiplier method. In order to achieve the target SER (quality of service) minimum power allocation is introduced as minimum relay power allocation and minimum source and relay power allocation.

     

Cognitive amplify‐and‐forward relay networks with beamforming under primary user power constraint over Nakagami‐m fading channels

In this paper, we analyze the performance of cognitive amplify‐and‐forward (AF) relay networks with beamforming under the peak interference power constraint of the primary user (PU). We focus on the scenario that beamforming is applied at the multi‐antenna secondary transmitter and receiver. Also, the secondary relay network operates in channel state information‐assisted AF mode, and the signals undergo independent Nakagami‐m fading. In particular, closed‐form expressions for the outage probability and symbol error rate (SER) of the considered network over Nakagami‐m fading are presented. More importantly, asymptotic closed‐form expressions for the outage probability and SER are derived. These tractable closed‐form expressions for the network performance readily enable us to evaluate and examine the impact of network parameters on the system performance. Specifically, the impact of the number of antennas, the fading severity parameters, the channel mean powers, and the peak interference power is addressed. The asymptotic analysis manifests that the peak interference power constraint imposed on the secondary relay network has no effect on the diversity gain. However, the coding gain is affected by the fading parameters of the links from the primary receiver to the secondary relay network. Copyright © 2012 John Wiley & Sons, Ltd.     

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.     

Power allocation of cooperative amplify-and-forward communications with multiple relays

Cooperative diversity is one of the most effective ways to mitigate the fading effect of wireless channels and obtain the spatial gain in wireless networks.In this paper,an optimal power allocation(OPA)scheme for a cooperative communication system using the amplify-and-forward(AF)transmit strategy with multiple relay users is proposed by minimizing the bit-error-rate(BER)at the destination under the constraint of the total transmit power of both the source user and the relay users.Simulation results indicate that the proposed power allocation method can achieve significant BER performance improvement than using the equal power allocation(EPA)scheme,while still attains low complexity.The system performance is improved significantly with the increasing of the number of relay users at high signal-noise ratio(SNR).However,at low SNR,the system performance decreases when the relay number increases.Thus,an adaptive relay selection scheme may be used to choose the appropriate relay numbers in different transmission scenarios to provide system performance improvement and keep the power allocation scheme with low complexity.     

基于矩生成函数的协同中继传输误符号率性能分析

多中继协同分集技术在慢衰落无线环境下可以提供巨大的性能增益。该文从接收端平均误符号率的角度,分析了独立的瑞利衰落信道下,采用放大转发的多中继协同最大比合并检测方案和多节点侦听,单中继转发的机会中继方案的性能;并基于矩生成函数推导出两种方案下M-PSK和M-QAM调制信号平均误符号率的闭合表达式。经蒙特卡罗仿真验证,该表达式在中高信噪比下与仿真的实际结果非常吻合。同时也可以看出机会中继的分集增益与协同侦听的节点数成正比,误符号率性能优于使用最大比合并检测的多中继协同方案。     

Exact SEP and performance bounds for orthogonal space‐time block codes in cooperative multiantenna AF relaying networks

In this paper, we derive a moment generating function (MGF) for dual‐hop (DH) amplify‐and‐forward (AF) relaying networks, in which all nodes have an arbitrary number of antennas, with orthogonal space‐time block code (OSTBC) transmissions over Rayleigh fading channels. We present an exact error rate expression based on the derived MGF and another analytical approach to derive achievable performance bounds as closed‐forms of symbol error rate, outage probability, and normalized channel capacity. Furthermore, we derive the asymptotic behavior of symbol error rate and outage probability. From this asymptotic behavior, it is shown that the diversity order and its dependence on antenna configurations can be explicitly determined. Simulation results are also presented to verify their accuracy by comparing with numerical results and to provide an insight to the relationship between relaying networks' antenna configuration and diversity order. It is confirmed that the transmit antenna gain of the source node and the receive antenna gain of the relay node can be obtained only when the relay is close to the destination, and then, the transmit antenna gain of the relay node and the receive antenna gain of the destination node can be obtained only when the relay is close to the source.     

Quasi‐optimal power allocation based on ergodic capacity for wireless relay networks

Half‐duplex amplify‐and‐forward (AF) transmissions may result in insufficient use of degrees of freedom if they always use the cooperative mode regardless of the fading states. In this paper, we investigate the conditions under which cooperation offers better performance and the corresponding optimal power allocation during cooperation. Specifically, we first derive an expression of ergodic capacity and its upper bound for an AF cooperative communication system with n relay nodes. Secondly, we propose a novel quasi‐optimal power allocation (QOPA) scheme to maximize the upper bound of the derived ergodic capacity. For the QOPA scheme, the cooperative mode is only adopted when the channel gain of source‐to‐destination is worse than that of relay‐to‐destination. Moreover, we analyze the performance of the system with QOPA scheme when the relay moves, which is based on the random direction model, in a single‐relay wireless network. For a multi‐relay AF network, we compare the ergodic capacity and symbol error rate, corresponding to the proposed QOPA and equal power allocation schemes, respectively. Extensive simulations were conducted to validate analytical results, showing that both ergodic capacity and symbol error rate of the system with QOPA scheme are better than those of the system with equal power allocation scheme in a multi‐relay AF network. Copyright © 2011 John Wiley & Sons, Ltd.     

Distributed Adaptive Power Allocation for Wireless Relay Networks

In this paper, we consider a 2-hop wireless diversity relay network. We explore transmit power allocation among the source and relays to maximize the received signal to noise ratio (SNR) at the destination. We consider two relay protocols, "amplify and forward" (AAF) and "decode and forward" (DAF) and design the respective power allocations for both uneeded and coded systems. For a 2-hop relay system with one relay node, we derive a closed-form power allocation solution and, based on it, we propose a relay activation condition. If and only if the fading channel coefficients satisfy this condition, the relay transmits the signals to the destination; otherwise, the relay will stay in the idle state. For a system with more than one relay node, general closed-form power allocation solutions based on an exact SNR expression are difficult to derive; we hence, calculate a SNR upper bound and derive a sub-optimum power allocation solution based on this bound. The simulation results show that for a 2-hop diversity relay channel with one relay node the proposed adaptive power allocation (APA) scheme yields about 1- 2 dB SNR gains compared to the equal power allocation. This SNR gain increases monotonically as the number of relays increases     

Statistical channel knowledge-based optimum power allocation for relaying protocols in the high SNR regime

We are concerned with transmit power optimization in a wireless relay network with various cooperation protocols. With statistical channel knowledge (in the form of knowledge of the fading distribution and the path loss information across all the nodes) at the transmitters and perfect channel state information at the receivers, we derive the optimal power allocation that minimizes high signal-to-noise ratio (SNR) approximations of the outage probability of the mutual information (MI) with amplify-and-forward (AF), decode-and-forward (DF) and distributed space-time coded (DSTC) relaying protocols operating over Rayleigh fading channels. We demonstrate that the high SNR approximation-based outage probability expressions are convex functions of the transmit power vector, and the nature of the optimal power allocation depends on whether or not a direct link between the source and the destination exists. Interestingly, for AF and DF protocols, this allocation depends only on the ratio of mean channel power gains (i.e., the ratio of the source-relay gain to the relay-destination gain), whereas with a DSTC protocol this allocation also depends on the transmission rate when a direct link exists. In addition to the immediate benefits of improved outage behavior, our results show that optimal power allocation brings impressive coding gains over equal power allocation. Furthermore, our analysis reveals that the coding gain gap between the AF and DF protocols can also be reduced by the optimal power allocation     

Error rate and outage of dual‐hop DF relay system with selection combining over Rice fading

Performance of dual‐hop decode‐and‐forward relay system with selection‐combining receiver is analyzed over Rice fading channels. The following closed‐form expressions of performance metrics are derived: moment generating function for selection‐combining receiver output signal‐to‐noise ratio, exact average bit error rate of noncoherent modulations, approximate average symbol error rate for coherent modulations, and outage probability. We also obtain simple asymptotic expressions for moment generating function, exact average bit error rate, average symbol error rate, and outage probability, which are useful to characterize the diversity order and the coding gain. The optimal power allocation analysis suggests that the optimal power allocation factor is independent of total signal‐to‐noise ratio and source‐to‐destination link fading parameters. The accuracy of the obtained analytical expressions are supported by computer simulation results.     

End‐to‐end performance of transmit antenna selection and generalized selection combining in dual‐hop amplify‐and‐forward relay network in the presence of feedback errors

In this paper, end‐to‐end performance of transmit antenna selection (TAS) and generalized selection combining (GSC) is studied in a dual‐hop amplify‐and‐forward relay network over flat Rayleigh fading channels. In the system, source and destination equipped with multiple antennas, communicate by the help of single relay equipped with single antenna. Source‐destination link is not available. TAS is used for transmission at the source, and GSC is used for reception at the destination. By considering the relay location and the presence of error in feedback channel from the relay to the source, we derive closed‐form outage probability, moment generating function and moments of end‐to‐end signal‐to‐noise ratio, and closed‐form symbol error probability (SEP) expressions for channel state information (CSI)‐based and fixed relay gains. The diversity order and array gain of the network are obtained for both CSI‐based and fixed relay gains by deriving asymptotical outage probability and SEP expressions. The analytical results are validated by the Monte Carlo simulations. Copyright © 2012 John Wiley & Sons, Ltd.     

Performance analysis of cooperative network over Nakagami and Rician fading channels

This paper presents an analysis on the performance of single‐relay and multiple fixed‐relay cooperative network. The relay nodes operate in amplify‐and‐forward (AF) mode and transmit the signal through orthogonal channels. We consider maximal‐ratio combining at the destination to get the spatial diversity by adding the received signals coherently. The closed‐form moment‐generating function (MGF) for the total equivalent signal‐to‐noise ratio (SNR) is derived. The exact expressions of symbol‐error rate, outage capacity, and outage probability are obtained using the closed‐form MGF for single‐relay and multiple‐relay cooperative network with M‐ary phase shift keying (M‐PSK) and M‐ary quadrature amplitude modulation (M‐QAM) over independent and non‐identical Nakagami‐m channels and Rician fading channels. The approximated closed‐form expression of ergodic capacity is derived for both Nakagami‐m and Rician fading channels. The performance of the system is analyzed at various relay locations. The theoretical results are then compared with the simulation results obtained for binary PSK, quadrature PSK, and 16‐QAM modulation schemes to verify the analysis. Here, the expressions derived can be easily and more efficiently used to compute the performance parameters than doing Monte Carlo simulations. It is shown that cooperation is significant only for low K values for Rician by plotting cooperation gain versus K. The results show that the cooperative network performs best when the relay is located in the middle of source to destination link, at lower SNR values, and the performance of the system is worst if the relay is located closer to the source than to the destination. Copyright © 2013 John Wiley & Sons, Ltd.     

BER analysis and power allocation for cooperative diversity networks with distributed Alamouti code

In this paper, we consider the distributed Alamouti code for a cooperative diversity network consisting of a source, a non‐regenerative relay, and a destination. While in the first time phase, the source radiates signals to both relay and destination; in the second time phase, the source and the relay cooperatively send signals to the destination by using an Alamouti code. Considering the amplify‐and‐forward protocol and independent Rayleigh fading, we first derive the exact average bit error rate performance in a single integral expression so that the system performance can be numerically evaluated. Then, based on a new approximation method of the Marcum Q‐function, we also give a tight upper bound for the system performance with a summation of a number of series components. We demonstrate through simulation that, in various operation scenarios with different channel quality and types of modulation, the results of the exact bit error rate expression accurately matches the simulation results, and the bound is tighter and more robust than existing approximation methods. Finally, we show that the analytic work also provides a method for the optimal allocation of power between the source and the relay in the second time phase. Copyright © 2013 John Wiley & Sons, Ltd.     

双向协作系统的中继选择和功率分配策略

针对瑞利衰落信道下双向多中继协作通信系统,为了降低中断概率,提出了一种基于最小化中断概率的中继选择策略和功率分配方案。首先联合考虑两条链路的中继节点处信噪比和信道增益实现双链路中继选择,然后推导出一种新的最优中继下双向放大转发协作中断概率的近似表达式上界,并利用凸优化求解得到使中断概率最小的最优功率分配解。仿真结果表明,与现有策略相比,提出的策略能够明显降低系统中断概率和误码率,显著提高系统性能。