Performance analysis of switch‐and‐examine diversity systems with interference and Rayleigh fading channels

This paper studies the behavior of the low‐complexity switch‐and‐examine diversity combining (SEC) and switch‐and‐examine diversity combining with post‐examine selection (SECps) antenna selection schemes with interference. In this paper, we first derive the cumulative distribution function (CDF) of the end‐to‐end (e2e) signal‐to‐interference plus noise ratio at the selection scheme combiner output. This CDF is then used to derive closed‐form expressions for the e2e outage and symbol error probabilities for the independent nonidentically distributed and independent identically distributed cases of diversity branches. In the analysis, the channels of the desired user and the interferers are assumed to follow Rayleigh distribution. Furthermore, to have more details about the system insights, the performance is evaluated at the high signal‐to‐noise ratio (SNR) values where the diversity order and coding gain are derived and analyzed. The derived analytical and asymptotic results are validated via a comparison with Monte‐Carlo simulations. Main findings show that with interference power does not scale with average SNR; the system can still achieve performance gain when more receive antennas are used. This happens at the values of switching threshold that are close to average SNR. Also, results illustrate that the interference is noticeably affecting the gain achieved in system performance when more antennas are used. Furthermore, findings show that the SECps selection scheme outperforms the conventional SEC scheme when more antennas are added with the switching threshold is much larger than the average SNR. Finally, findings show that the SEC and SECps antenna selection schemes are efficient for systems which operate at the range of low SNR values and this makes them attractive candidates to be implemented in the emerging mobile broadband communication systems. Copyright © 2015 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.     

Switch‐and‐examine combining with different new switch statistics for diversity over Rayleigh fading channels

Three schemes of multibranch switch‐and‐examine combining (MSEC) with switch statistics different from the signal‐to‐noise ratio used in the traditional MSEC are analyzed. For each diversity branch, with its fading factor a and low‐passed received signal r, the switch statistics for the three MSEC schemes considered in the paper are | r | , | ar | , and a linear combination of a and | r | , respectively. To illustrate the performances of the MSEC schemes, the average BER of each MSEC scheme with BPSK signaling is evaluated for independent and identically distributed Rayleigh fading channels. For performance optimization, the optimal switch thresholds of the MSEC schemes are obtained. Numerical results based on the analysis and simulations are presented for performance illustrations. Copyright © 2012 John Wiley & Sons, Ltd.     

Decode‐and‐forward with full‐duplex relaying

This paper addresses the full‐duplex relaying. Some expressions for outage and average capacity of a two‐hop cooperative system with a full‐duplex relay are derived under an independent but not identically distributed Rayleigh fading environment. Using these expressions, we provide the performance analysis without Monte Carlo simulations. The impact of interference between the relay output and input is investigated. Copyright © 2011 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.     

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.     

Novel noncoherent detection for multi‐hop amplify‐and‐forward relaying systems

Because of the multiplication of fading gains and noise, the actual distributions of the received signals in multi‐hop amplify‐and‐forward relaying systems are no longer Gaussian. In this work, they are fitted with the t location‐scale distribution and the logistic distribution. Using these distributions, two novel noncoherent detectors are proposed based on the maximum likelihood method. Numerical results show that both new detectors outperform the conventional energy detector. The performance gain increases when the signal‐to‐noise ratio increases or when the hop number decreases. Importantly, the bit error rate of the conventional energy detector reaches an error floor while the bit error rates of the new detectors do not. Copyright © 2015 John Wiley & Sons, Ltd.     

Error performance for relaying protocols with multiple decode‐and‐forward relays

This paper investigates the error performance of three relaying protocols with multiple decode‐and‐forward relays. In the first protocol, relays that can decode correctly will forward the signals from source. Nevertheless, selection cooperation (SC) and opportunistic relaying (OR) are adopted to select only a single relay to forward in the other two protocols, respectively. At sufficiently high signal‐to‐noise ratio, the upper bounds on bit error probability are derived for three protocols, where the developments apply for various channel fading models. Simulation results are provided to verify the tightness of the analytical bounds, and the performance comparisons among different relaying protocols are presented. Copyright © 2010 John Wiley & Sons, Ltd.     

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.     

Performance of fixed‐gain amplify‐and‐forward nonlinear relaying with hardware impairments

In this paper, a fixed‐gain amplify‐and‐forward relaying under non‐ideal hardware is analyzed. The relaying system is impaired because of relay's power amplifier (PA) nonlinearity and in‐phase and quadrature‐phase (IQ) imbalance at a destination. Closed‐form expressions for outage probability as well as ergodic capacity approximation and its upper bound are derived. Also, the outage probability and the ergodic capacity asymptotic expressions in the high signal‐to‐noise ratio are deduced. For the first time, the joint influence of PA nonlinearity and IQ imbalance on the system in terms of outage probability, symbol error rate, and ergodic capacity is investigated. The results are compared with the respect to soft envelope limiter and traveling‐wave tube amplifier at the relay. Based on the analytical and the numerical results, important insights into the impact of IQ imbalance and nonlinearity of the aforementioned PA models on the system performance are gained as well as valuable information on the performance of practically deployed fixed‐gain amplify‐and‐forward relaying system. Copyright © 2015 John Wiley & Sons, Ltd.     

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.     

Amplify‐and‐forward‐based cooperative jamming strategy with power allocation for secure communication

This paper deals with the use of jamming transmission for secure amplify‐and‐forward‐based relay networks with total power constraints. An approach that the source and the relay use some of their available power to transmit jamming signals in order to create interference at the eavesdropper is investigated. Assume that the relay and destination have an a priori knowledge of the jamming signals. A power allocation policy that defines how the available power is distributed between the message signal and that of the jamming signal is presented. The results show that the proposed approach can increase the secrecy level and that a positive secrecy rate can be achieved even when the eavesdropper may be near the source. Copyright © 2014 John Wiley & Sons, Ltd.     

Packet splitting and adaptive modulation based on CSI of time domain for decode‐and‐forward cooperative OFDM systems in different channel model

Cooperative communications obtain the transmission and channel diversity gains by using the relay node. However, since cooperative communications transmit the redundancy signal to obtain the transmission diversity gain, the transmission rate is degraded. Moreover, since cooperative communications add the interference in the relay node, the diversity gain is also degraded. The packet splitting has been proposed based on the channel state information of the time domain to obtain the good system performance without the redundancy signal. Moreover, the adaptive modulation has been proposed to improve the transmission rate. In this paper, we propose the combination method with the packet splitting and the adaptive modulation based on the channel state information of the time domain to improve the bit error rate and throughput performances for decode‐and‐forward cooperative orthogonal frequency division multiplexing systems in the different channel model. From the computer simulation results, we determine the optimum weight and threshold for the proposed method. Moreover, the proposed method shows the good bit error rate and throughput performances.     

Channel estimation algorithms for cooperative spectrum sensing in amplify‐and‐forward cooperative system

In amplify‐and‐forward (AF)‐based cooperative spectrum sensing system, the bit‐error‐rate (BER) performance and detection probability will decrease because of the existence of channel estimation error. In this paper, the influence of channel estimation error on system performance is firstly deduced, and then, linear minimum mean‐square error (LMMSE) channel estimation algorithm with filtering delay time‐domain windowing (LMMSE‐filtering‐DTW) technique and modified singular value decomposition‐based LMMSE algorithm are proposed to improve the channel estimation performance for code division multiple access system and orthogonal frequency division multiplexing system in AF cooperative scenario, respectively. Simulation results verify the effectiveness of the two proposed channel estimation algorithms in cooperative spectrum sensing, and when E_b/ N₀ is bigger than 20 dB, given the required false alarm probability smaller than 15%, the difference of detection probability between the channel obtained using the proposed channel estimation algorithms and the ideal channel is less than 2.5%, respectively. Copyright © 2012 John Wiley & Sons, Ltd.     

System performance analysis of cooperative multihop relaying network applying approximation to dual‐hop relaying network

In this paper, the closed‐form expressions for outage probability, channel capacity, and average symbol error probability are derived for amplify‐and‐forward multihop relay network. Based on approximation of multihop relay by dual‐hop relay systems, the analytical expressions are obtained for the case when maximal ratio combining technique is employed at each relay while destination node uses selection combining technique. The impact of system and channel parameters on the system performances is investigated, and numerical results are graphically presented. The derived analytical expressions are verified by numerical simulation.     

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.     

Outage performance of orthogonal space–time block code transmission in opportunistic decode‐and‐forward cooperative networks

Outage performance is analyzed for opportunistic decode‐and‐forward cooperative networks employing orthogonal space–time block codes. The closed‐form expressions of diversity order and the end‐to‐end outage probability at high signal‐to‐noise ratio regime are derived for arbitrary relay number (K) and antenna configuration (N antennas at the source and each relay, N_D antennas at the destination) under independent but not necessarily identical Rayleigh fading channels. The analysis is carried out in terms of the availability of the direct link between the source and the destination. It is demonstrated that the diversity order is min{N, N_D} ⋅ KN if the direct link is blocked, and if the direct link is available, the diversity order becomes min{N, N_D} ⋅ KN + NN_D. Simulation and numerical results verify the analysis well. Copyright © 2011 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.     

Comparison of average symbol error rate and optimal power allocation for two‐way opportunistic relaying with amplify‐and‐forward protocol

In this paper, we investigate the statistical characteristics of the equivalent end‐to‐end signal‐to‐noise ratios (SNRs), the average symbol error ratios (SERs), and the optimal power allocation (OPA) for two‐way amplify‐and‐forward opportunistic relaying (TWOR‐AF) systems. First, with strict mathematic manipulation, we obtain the closed‐form solutions to the PDF, CDF, and moment generating function of the end‐to‐end SNRs. Then, based on the obtained statistical results, we present the total average SER of the Non‐OPA TWOR‐AF systems by using the appropriate approximation, in which only the greater segment of the two terminal SERs is considered. Finally, by aiming at minimizing the total average SER and using the SNRs balancing condition at both transceivers, we study the OPA problem subject to a total transmission power constraint. The comparison analysis shows that, for the Non‐OPA TWOR‐AF systems, we can only evaluate exactly the greater segment of the two SERs of the received signals at two transceivers by using the derivations. However, for the OPA TWOR‐AF systems, with our derivations we can evaluate exactly not only each segment of the two terminal SERs but also the sum SER (exact total SER). Moreover, the simulations show the OPA TWOR‐AF systems outperform the Non‐OPA TWOR‐AF systems. Copyright © 2012 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.