Performance analysis of selective cooperation in amplify‐and‐forward relay networks over identical Nakagami‐m channels

In cooperative communications, multiple relays between a source and a destination can increase the diversity gain. Because all the nodes must use orthogonal channels, multiple‐relay cooperation becomes spectrally inefficient. Therefore, a bestrelay selection scheme was recently proposed. In this paper, we analyzed the performance of this scheme for a system with the relays operating in amplify‐and‐forward mode over identical Nakagami‐m channels using an exact source–relay–destination signal‐to‐noise ratio (SNR).We derived accurate closed‐form expressions for various system parameters including the probability density function of end‐to‐end SNR, the average output SNR, the bit error probability, and the channel capacity. The analytical results were verified through Monte Carlo simulations. Copyright © 2011 John Wiley & Sons, Ltd.     

快衰落信道条件下无线中继系统波束形成方案

随着设备小型化的发展趋势,天线间距较小,信道具有相关性;且假设发射端处于高速移动状态,无法获得完全信道状态信息,只能根据部分信道状态信息设计发射端波束形成方案。针对发射端和接收端配置多天线的固定增益放大转发无线中继系统,以最大化接收端信噪比为准则,设计了基于部分信道状态信息的波束形成方案,推导了系统中断概率和平均误符号率的闭合表达式,通过仿真验证了性能分析的有效性和所设计方案的优越性。在平均误符号率为10-2、相关系数为0.8时,所提方案比反馈信道状态信息的方案节约1.6 dB的信噪比。     

Nelder‐Mead–based power optimization for secrecy enhancement in amplify‐and‐forward cooperative relay networks

Cooperative communication based on relaying nodes has been considered as a promising technique to increase the physical layer security (PLS) performance in wireless communications. In this paper, an optimal power allocation (OPA) scheme based on Nelder‐Mead (NM) algorithm is proposed for improving the secrecy rate of amplify‐and‐forward (AF) cooperative relay networks employing cooperative jamming (CJ) scheme. The proposed hybrid jamming scheme allows the source and selected relay to transmit the jamming signal along with the information to confound the eavesdropper. The path selection probability of ant colony optimization (ACO) algorithm is used for selecting the relay for transmission. The performance based on secrecy rate is evaluated for “n” trusted relays distributed dispersedly between the source and destination. Gradient‐based optimization and three‐dimensional exhaustive search methods are used as benchmark schemes for comparison of the proposed power optimization algorithm. The secrecy performance is also compared with conventional AF scheme and CJ scheme without power optimization (EPA). The impact of single and multiple relays on secrecy performance is also evaluated. Numerical results reveal that, compared with the gradient method and exhaustive search algorithm, the proposed power allocation strategy achieves optimal performance. Also, the derived OPA results show a significantly higher secrecy rate than the EPA strategy for both CJ and AF schemes.     

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.     

Two‐pilot channel estimation scheme for amplify‐and‐forward relay networks

In amplify‐and‐forward relay networks, the equivalent channel to the destination node is not independent of equivalent noise and the equivalent noise does not follow a Gaussian distribution. Therefore, it is difficult to directly estimate the equivalent channel based on traditional optimal rules. In this paper, we propose a two‐pilot estimation (TPE) scheme that decomposes a non‐Gaussian noise channel estimation problem into two channel estimation problems in Gaussian noise. In TPE scheme, the relay‐destination channel is first estimated by one pilot and the other pilot is used to estimate the equivalent channel with the aid of the estimated relay‐destination channel. Simulation results show that the TPE scheme can achieve less estimation error and larger system throughput than other existing channel estimators in slow fading case. Copyright © 2012 John Wiley & Sons, Ltd.     

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.     

Performance analysis of cooperative multi‐carrier relay‐based UAV networks over generalized fading channels

The outage probability in a network of cooperative unmanned airborne vehicles (UAVs) over generalized fading channels is studied analytically using finite mixture with expectation maximization technique. A relay‐based topology with one ground control unit (GCU) is considered, where the cooperative UAVs can communicate with the GCU directly or through relay. The application the UAV is assigned for specifies the minimum required transmission rate the UAV should achieve. The outage probability of the system is defined as the probability that either the transmission rate over any of the links drops below a predefined minimum threshold for that link or the Relay‐GCU link is not able to transmit the aggregate data from all relayed UAVs and the minimum rate required by the relay UAV itself. Throughout the paper, expressions for the outage probability and the average achievable bit rate of a cooperative multi‐carrier system are derived over generalized fading channels. Finite mixture with expectation maximization algorithm is utilized to derive a simple approximate expression for the probability density function (pdf) of the achievable bit rate assuming adaptive M‐ary quadrature amplitude modulation (M‐QAM). This pdf is used to derive closed‐form expressions for the outage probability and the average bit rate. Copyright © 2011 John Wiley & Sons, Ltd.     

An architecture for amplify‐and‐forward cooperative systems with real modulations

This paper proposes a simple architecture for half‐duplex cooperative systems which use amplify‐and‐forward (AF) as a relay strategy and one‐dimensional modulations for source messages. The proposed solution uses the two orthogonal channels of quadrature modulation in order to allow a node to behave simultaneously as a source and a relay. We demonstrate that the new scheme has a similar performance to the conventional orthogonal amplify‐and‐forward protocol without suffering from bandwidth loss, and avoids error propagation problems of previously reported AF superposition schemes. The proposed technique is suitable for applications with low spectral efficiencies and practical adaptive systems where real modulations are implemented based on a quadrature modulation core. Copyright © 2009 John Wiley & Sons, Ltd.     

Iterative receiver for amplify‐and‐forward relay networks with unknown noise correlation

For amplify‐and‐forward relay networks, we propose an iterative scheme to estimate channel and detect information symbols for the multi‐antenna destination in spatially correlated noise. The equivalent channel coefficients and noise covariance are estimated by expectation–maximization algorithm. In addition, we discuss the initialization of iteration and analyze the modified Cramér–Rao bound to show the performance of the proposed iterative estimation. Moreover, on the basis of the structure of the proposed iterative estimator, a joint channel estimation and detection receiver is also provided. Finally, simulation results show that the proposed channel estimator and receiver can achieve the optimal performances in amplify‐and‐forward relay networks with unknown noise correlation. Copyright © 2012 John Wiley & Sons, Ltd.     

Performance analysis of spectrally efficient amplify‐and‐forward opportunistic relaying scheme for adaptive cooperative wireless systems

In this paper, we propose an adaptive amplify‐and‐forward (AF) relaying scheme that selects the best relay among the available relay nodes opportunistically to cooperate with a source node for improvement of the spectral efficiency. This improvement can be achieved by introducing a policy that gives the useful cooperative regions and defines a switching threshold signal‐to‐noise ratio that guarantees the bit error rate (BER) of cooperative transmission is below the target. We model all links as independent non‐identically distributed Rayleigh fading channels. We then derive closed‐form expressions for the average spectral efficiency, average BER, and outage probability when an upper bound for the signal‐to‐noise ratio of the end‐to‐end relay path is applied and adaptive discrete rate is considered. Numerical and simulation results show that the proposed scheme, compared with the outage‐based AF incremental relaying, AF fixed relaying, and the conventional direct transmission, can achieve the maximum average spectral efficiency while maintaining the average BER and outage probability. Copyright © 2013 John Wiley & Sons, Ltd.     

Optimal power‐aware relay placement for cooperative wireless sensor networks

We study the problem of optimizing the symbol error probability (SEP) performance of cluster‐based cooperative wireless sensor networks. Recent studies in literature show that an efficient relay selection protocol based on simple geographical information of the nodes to execute cooperative diversity can significantly improve the SEP performance at the destination of such networks. As well, similar line of research on optimal power allocation (for the source and relay nodes) can be found in literature. However, to achieve the best SEP performance at the destination of a cooperative wireless sensor network, joint optimization of power allocation and relay placement should be accomplished. To this aim, we reformulate the SEP of a multi‐hop cooperative communication in a general form and optimize transmitted power level and relay placement simultaneously. This analysis is developed for both amplify‐and‐forward and decode‐and‐forward relaying protocols. Simulation results demonstrate that the proposed joint optimization can effectively improve the SEP performance of the network. Copyright © 2013 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.     

MMSE‐based transceiver design for distributed MIMO amplify‐and‐forward cooperative networks in correlated channels

In this paper, the source‐precoder, multiple‐relay amplifying matrices, and destination‐equalizer joint optimization is investigated in distributed MIMO amplify‐and‐forward multiple‐relay networks with direct source–destination transmission in correlated fading channels. With the use of taking both the direct link and spatial correlation between antenna elements into account, the cooperative transceiver joint design is developed based on the minimum mean‐squared error criterion under individual power constraints at the source and multiple‐relay nodes. Simulation results demonstrate that the cooperative transceiver joint design architecture for an amplify‐and‐forward MIMO multiple‐relay system outperforms substantially the noncooperative transceiver design techniques on the BER performance under the spatial‐correlation channels.Copyright © 2012 John Wiley & Sons, Ltd.     

Performance and diversity analysis of decode‐and‐forward cooperative system over Nakagami‐m fading channels

In this paper, we derive the upper bound of bit‐error rate (BER) performance and diversity gain for a decode‐and‐forward (DF) cooperative system. Either maximal‐ratio combining (MRC) or cooperative MRC (C‐MRC) is employed at the receiver in the presence of independent, non‐identical Nakagami‐m fading. Both analytical and simulation results show that C‐MRC takes advantage of spatial diversity more efficiently and thus achieves the same or better performance and diversity order as compared to MRC. Copyright © 2009 John Wiley & Sons, Ltd.     

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.     

Cooperative amplify‐and‐forward partial relay selection with outdated channel information in spectrum‐sharing systems

Recently, cooperative relaying techniques have been integrated into spectrum‐sharing systems in an effort to yield higher spectral efficiency. Many investigations on such systems have assumed that the channel state information between the secondary transmitter and primary receiver used to calculate the maximum allowable transmit secondary user transmit power to limit the interference is known to be perfect. However, because of feedback delay from the primary receiver or the time‐varying properties of the channel, the channel information may be outdated, which is an important scenario to cognitive radio systems. In this paper, we investigate the impact of outdated channel state information for relay selection on the performance of partial relay selection with amplify and forward in underlay spectrum‐sharing systems. We begin by deriving a closed‐form expression for the outage probability of the secondary network in a Rayleigh fading channel along with peak received interference power constraint and maximum allowable secondary user transmit power. We also provide a closed‐form expression for the average bit‐error rate of the underlying system. Moreover, we present asymptotic expressions for both the outage probability and average bit‐error rate in the high signal‐to‐noise ratio regime that reveal practical insights on the achievable diversity gain. Finally, we confirm our results through comparisons with computer simulations. Copyright © 2016 John Wiley & Sons, Ltd.     

Performance of joint transmit and receive antenna selection in dual hop amplify‐and‐forward relay network over Nakagami‐m fading channels

In this paper, performance of joint transmit and receive antenna selection in each hop of dual hop amplify‐and‐forward relay network is analyzed over flat and asymmetric Nakagami‐m fading channels. In the network, source, relay, and destination are equipped with multiple antennas. By considering relay location, we derive exact closed‐form cumulative distribution function, moment generating function, moments of end‐to‐end signal‐to‐noise ratio and closed form symbol error probability expressions for fixed and channel state information‐based relay gains. We also derive the asymptotical outage probability and symbol error probability expressions to obtain diversity order and array gain of the network. Analytical results are validated by the Monte Carlo simulations. Copyright © 2012 John Wiley & Sons, Ltd.     

Performance analysis of selective combining decode‐and‐forward relay networks over Nakagami‐n and Nakagami‐q fading channels

In this paper, we present the performance of selective combining decode‐and‐forward relay networks in independent and non‐identically distributed Nakagami‐n and Nakagami‐q fading channels by using the best–worse and the decoding‐set approaches. The outage probability, moment generation function, symbol error probability and average channel capacity are derived in closed‐form using the signal to noise ratio (SNR) statistical characteristics. After that, we analyze the outage probability at high SNRs, and then, we optimize it. Beside the optimum method, we have proposed a sub‐optimum adaptive method. Also, we derive the outage probability for the selection‐combining case with the direct link between the source and the destination. Finally, for comparison with analytical formulas, we perform some Monte‐Carlo simulations. Copyright © 2012 John Wiley & Sons, Ltd.     

Outage probability and channel capacity for the Nth best relay selection AF relaying over INID Rayleigh fading channels

Cooperative diversity systems have recently been proposed as a way to form virtual antenna schemes without utilizing collocated multiple antennas. In this paper, we consider the Nth best opportunistic amplify‐and‐forward (AF) cooperative diversity systems. The AF type can be regarded as one on the basis of modified channel state information. Wireless channels between any pair of nodes (i.e., direct and dual hop links) are assumed quasi‐static independent and nonidentically distributed (INID) Rayleigh fading. The best opportunistic AF (OAF) scheme requires two phases of transmission. During the first phase, the source node transmits a signal to all relays and the destination. In the second phase, the best relay is only selected on the basis of highest signal‐to‐noise ratio (SNR) scheme to forward the source signal to the destination. Therefore, the indirect link (i.e., source‐selected relay destination) can give the highest received SNR. However, the best relay selection cannot be available so that we might choose the second, third, or generally the Nth best relay. In this paper, we derive the approximated outage probability and channel capacity for the Nth best OAF relay systems over INID Rayleigh fading channels. At first, the indirect link's received SNR is approximated as harmonic mean upper bound. With this information, we obtain the given relay's Nth best selection probability as the closed form. Finally, both outage probability and channel capacity are derived as the closed forms. Simulation results are finally presented to validate the analysis. Copyright © 2011 John Wiley & Sons, Ltd.     

An amplify‐and‐forward and decode‐and‐forward mixed relay communication system and its performance analysis

A kind of amplify‐and‐forward (AF) and decode‐and‐forward (DF) mixed relay communication system is proposed in this letter. The source broadcasts the signal to all the relays. Relays that can decode the signal adopt DF scheme to retransmit the signal, while the rest adopt AF scheme for retransmission. The destination employs maximum ratio combining technique to maximize the received signal‐to‐noise ratio. Another situation concerned in this letter is that when the relay cannot decode the source signal, it may retransmit the interference signal with AF scheme. Closed‐form expressions of outage probability are derived. Simulation results show that the analytical curves agree with the simulated ones very well, and the AF‐DF mixed relay system can improve the availability of the relays. Copyright © 2013 John Wiley & Sons, Ltd.