Performance analysis of hybrid transmit antenna selection/maximal‐ratio transmission in Nakagami‐m fading channels

Hybrid diversity systems have been of great importance because they provide better diversity orders and robustness to the fading effects of wireless communication systems. This paper focuses on the performance analysis of multiple‐input gle‐output systems that employ combined transmit antenna selection (TAS)/maximal‐ratio transmission (MRT) techniques (i.e., hybrid TAS/MRT). The probability density function, the moment generating function and the n ^th order moments of the output signal‐to‐noise ratio of the investigated diversity scheme are derived for independent identically distributed flat Nakagami‐m fading channels. The system capacity of the hybrid TAS/MRT scheme is examined from the outage probability perspective. Exact bit/symbol error rate (BER/SER) expressions for binary frequency shift keying, M‐ary phase shift keying and square M‐ary quadrature amplitude modulation signals are derived by using the moment generating function‐based analysis method. By deriving the upper bounds for BER/SER expressions, it is also shown that the investigated systems achieve full diversity orders at high signal‐to‐noise ratios. Also, by Monte Carlo simulations, analytical performance results are validated and the effect of feedback delay, channel estimation error and feedback quantization error on BER/SER performances are examined. Copyright © 2011 John Wiley & Sons, Ltd.     

Analysis of transmit antenna selection/orthogonal space‐time block coding with receive selection and combining in the presence of feedback errors

Examining the effect of imperfect transmit antenna selection (TAS) caused by the feedback link errors on the performance of hybrid TAS/orthogonal space‐time block coding (OSTBC) with single receive antenna selection (i.e., joint transmit and receive antenna selection (JTRAS)/OSTBC) and TAS/OSTBC (with receive maximal‐ratio combining‐like combining structure) over slow and frequency‐flat Nakagami‐m fading channels is the main objective of this paper. Under ideal channel estimation and delay‐free feedback assumptions, statistical expressions and several performance metrics related to the post‐processing signal‐to‐noise ratio are derived by defining a unified system model concerning both JTRAS/OSTBC and TAS/OSTBC schemes. Exact analytical expressions for outage probability (OP) and bit/symbol error rates of M‐ary modulations are presented in order to provide a detailed examination on the OP and error performances of the unified system that experiences feedback errors. Also, the asymptotic diversity order analysis, which shows that the diversity order of the investigated schemes is equal to the diversity order provided by OSTBC transmission itself, is included in the paper. Moreover, we have validated the theoretical results via Monte Carlo simulations. Copyright © 2014 John Wiley & Sons, Ltd.     

最大比发射/选择接收技术的性能研究

为了提高系统性能并降低接收端(移动台)的硬件复杂度,提出一种新的MIMO传输技术。即在发射端(基站)按最大比发射(MRT,maximal-ratio transmit)技术,接收端则基于信噪比最大的原则仅选择一根接收天线来处理信号,记作MRT/RAS(maximal-ratio transmit/receiver antenna selection)。根据随机矩阵和排序统计的最新理论,推导出瑞利衰落信道下MRT/RAS系统的中断概率、误码率(BER)等性能指标的确切表达式。仿真结果表明MRT/RAS系统可以取得很好的阵列增益及满分集增益。相同频谱条件下,性能超过某些复杂的空时编码系统。而且在准静态衰落信道下,信道估计错误对取得的分集阶数并没有影响。仿真试验也证明了分析结果的正确性。     

Diversity order of decode-and-forward MIMO relaying with transmit antenna selection

This article analyzes the diversity order of several proposed schemes, where the transmit antenna selection (TAS) strategies are combined with low-complexity decode-and-forward (DF) protocols in the multiple-input multiple-output (MIMO) relaying scenario. Although antenna selection is a suboptimal form of beamforming, it enjoys the advantages of tractable optimization and low feedback overhead. Specifically, this article proposes schemes that combine TAS strategies with fixed decode-and-forward (FDF) and selection decode-and-forward (SDF) protocols. Following that, the asymptotic expressions of outage probabilities are derived and the diversity order of the proposed schemes analyzed. These kinds of combination of transmit antenna selection strategies and low-complexity decode-and-forward protocols can achieve partial diversity order in the MIMO relaying scenario. The numerical simulations verify the analysis.     

Analysis of cooperative MIMO transmission system with transmit antenna selection and selection combining

Error performance of a cooperative system can be enhanced by using transmit and receive diversity techniques at transmission links. The number of transmit/receive RF chain pairs required to achieve full diversity can be decreased to one for each link by using transmit antenna selection (TAS) method at the transmitter and selection combining (SC) method at the receiver. Thus, hardware complexity of a multiple input multiple output (MIMO) cooperative scheme can be significantly reduced when compared to systems that use TAS and maximum ratio combining (MRC). In this paper, we investigate the performance of an amplify‐and‐forward cooperative system where TAS/SC is utilized. We derive the probability density function (pdf) of end‐to‐end SNR of the system for Rayleigh fading channels. By using this pdf, we obtain the exact symbol error rate expressions for M‐PSK and M‐QAM modulations and the exact outage probability expression. We also obtain the asymptotical diversity order using upper and lower bounds of the outage probability expression and show that our system provides the same diversity order as the cooperative system where TAS/MRC is utilized. We verify our results via computer simulations. Copyright © 2010 John Wiley & Sons, Ltd.     

Conventional and modified TAS/OSTBC schemes in dual‐hop fixed‐gain amplify‐and‐forward relaying systems with imperfect feedback

Modified transmit antenna selection (TAS)/orthogonal space‐time block coding (OSTBC) (M‐TAS/OSTBC) schemes have been shown to achieve superior error performance together with a reduced‐rate feedback channel in the presence of feedback errors (FEs) when compared with the conventional TAS/OSTBC (C‐TAS/OSTBC) schemes. This paper focuses on the bringing of fixed‐gain amplify‐and‐forward (FGAF) relaying schemes that employ M‐TAS/OSTBC schemes at both hops that provides reduced feedback‐rate and robust error performance in the presence of erroneous‐feedback channels. The exact expressions of the outage and error probabilities for both dual‐hop FGAF relaying schemes in Nakagami‐m fading channels have been derived and validated via Monte Carlo simulations. Additionally, with the help of high signal‐to‐noise ratio (SNR) (i.e., asymptotic) approaches and some analytical approximations, the asymptotic diversity order analysis has been carried out. Besides, by providing a simulation‐based examination on the inclusion of power allocation within the modified scheme, the additional advantages on the performance have been exhibited. The extensive investigation and comparisons to the conventional schemes have shown that M‐TAS/OSTBC schemes employed at each transmission link provide full diversity order and considerable error performance as the C‐TAS/OSTBC scheme in ideal feedback cases and also achieve more robust error performance in the presence of FEs. Thus, by using M‐TAS/OSTBC schemes, the overall performances of the dual‐hop FGAF relaying schemes have been enhanced, which would result in reductions on the average SNR requirements to achieve a specified error rate constraint. Copyright © 2015 John Wiley & Sons, Ltd.     

Performance analysis of Alamouti scheme with transmit antenna selection in non‐identical Nakagami‐m fading channels

In this paper, error performances of multiple‐input multiple‐output systems that employ Alamouti‐coded transmission with transmit antenna selection are examined for binary phase‐shift keying, binary frequency‐shift keying, M‐ary phase‐shift keying, and M‐ary quadrature amplitude‐modulation signals in independent but non‐identically distributed flat Nakagami‐m fading channels. Exact symbol error rate expressions are derived by using the moment‐generating function‐based analysis method. Upper bound expressions have been obtained in order to examine the asymptotic diversity order of transmit antenna selection/Alamouti scheme. Also, outage probability analysis of investigated systems has been given in order to examine the system capacity. Monte Carlo simulations have validated the analytical symbol error rate performance results. Copyright © 2011 John Wiley & Sons, Ltd.     

Joint TAS and power allocation for DF relaying M2M cooperative system

The outage probability (OP) performance of transmit antenna selection (TAS) in a decode-and-forward relaying mobile-to-mobile system with relay selection over N-Nakagami fading channels is investigated. Exact closed-form expressions for the OP of two TAS schemes are derived, and the optimal power allocation optimisation problem is formulated. The OP performance is evaluated via Monte Carlo simulation to verify the analysis. The results obtained show that the optimal TAS scheme has better performance than the suboptimal TAS scheme, but the performance gap between these techniques decreases as the number of source antennas increases.     

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.     

MF中继选择系统的物理层安全性能

针对合谋窃听场景下单天线多中继修改转发（MF）协作无线系统的安全性能较差问题,提出一种合谋窃听场景下联合源节点发送天线选择（TAS）和多中继选择的MF协作物理层安全系统,考虑最优的最大化主信道信噪比（SNR）和次优的最大化源节点-中继节点链路 SNR 两种中继选择方案,推导其安全中断概率（SOP）和遍历安全容量（ESC）的解析表达式。最优或次优中继选择的MF安全中继系统的SOP和ESC的数值计算结果与仿真结果相吻合,验证了上述理论分析的正确性;同时也表明源节点发射天线数和中继节点数越多、窃听节点数越少,最优或次优中继选择的MF安全中继系统的物理层安全性能越好。     

Outage and ergodic sum‐rate performance of cooperative MIMO‐NOMA with imperfect CSI and SIC

In this paper, we examine a half‐duplex cooperative multiple‐input multiple‐output non‐orthogonal multiple access system with imperfect channel state information (CSI) and successive interference cancelation. The base station (BS) and mobile users with multi‐antenna communicate by the assistance of a CSI based or fixed gain amplify‐and‐forward (AF) relay with a single antenna. The diversity schemes, transmit antenna selection, and maximal ratio combining are applied at the BS and mobile users, respectively. We study the system performance in terms of outage probability (OP) and ergodic sum‐rate. Accordingly, the exact OP expressions are first derived jointly for the CSI based and fixed gain AF relay cases in Nakagami‐m fading channels. Next, the corresponding lower and upper bound expressions of the OP are obtained. The high signal‐to‐noise ratio analyses are also carried out to demonstrate the error floor value resulted in the practical case and achievable diversity order and array gain in the ideal case. Moreover, the lower and upper bounds of the ergodic sum‐rate expressions are derived together for the CSI based and fixed gain AF relay cases. Finally, the Monte‐Carlo simulations are used to verify the correctness of the analytical results.     

非理想反馈链路下的发送天线选择系统性能分析

该文提出了一种近似分析的方法,得到了非理想反馈链路下的发送天线选择(Transmit Antenna Selection, TAS)系统的符号差错概率(Symbol Error Probability,SEP)。这种近似的方法适用于采用任意正交空时分组码的TAS系统,并且对于发送端选择两天线的系统还给出了SEP的显式表达式。该文研究表明TAS系统的发送分集度由所选天线子集中最大的矩幅序号决定。蒙特卡罗仿真验证了当信噪比较高时,由该文近似方法得到的系统SEP和理论上的SEP非常吻合。     

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.     

Security enhancement with joint transmit antenna selection and transmit beamforming under energy harvesting constraints

This paper considers a multiuser multiple‐input single‐output (MISO) broadcasting system with simultaneous wireless information and power transfer (SWIPT), which consists of one information receiver (IR) and several energy harvesting receivers (ERs) which are capable of eavesdropping the legitimate signals. For reducing cost and hardware complexity, transmit antenna selection (TAS) is applied in the transmitter. We aim to maximize the achievable secrecy rate under the individual energy harvesting constraint at the ERs and the transmit power constraint at the transmitter by jointly optimizing TAS, transmit beamforming, and artificial noise (AN). The joint optimization problem is a non‐convex mixed integer programming problem. We apply variable replacements to decouple the variable couplings and relax and approach the binary constraint by the difference of two convex constraints. Afterwards, penalty method and constrained concave convex procedure (CCCP) are applied to transform the relaxed problem into a sequence of semi‐definiteness programming (SDP) problems. Simulation results shows that our proposed joint optimization scheme is superior over existing non‐joint optimization schemes. This paper studies the joint transmit antenna selection (TAS), transmit beamforming, and artificial noise (AN) optimization in a multiple‐input multiple‐output (MISO) wiretap system with simultaneous wireless information and power transfer (SWIPT). The joint optimization problem is nonconvex and we propose a penalty method based scheme to solve it. The simulation results show that our joint optimization scheme is superior to other non‐joint optimization schemes.     

Unified analysis of transmit,receive and hybrid diversity techniques over generalized‐K channels

In this work, unified performance analysis of various transmit, receive and hybrid diversity techniques are studied over generalised‐K composite fading channels. Of transmit diversity techniques, orthogonal space‐time block coding, maximal‐ratio transmission and transmit antenna selection techniques are investigated. On the other hand, maximal‐ratio combining and selection combining are examined as receive antenna diversity techniques. In this paper, 10 different multi‐antenna techniques have been analyzed. Exact outage probability, symbol error probability, moment generating function, moments and ergodic capacity expressions are derived in closed‐form. Asymptotic expressions are also derived in order to provide deeper insight by obtaining array and diversity gains of the studied multi‐antenna scenarios. Simulations verify theoretical results. We show that the diversity orders of the investigated scenarios are the minimum of the diversity orders of the system for only small‐scale fading channel case and the shadowing parameter, and limited by the shadowing effect especially in heavy shadowing case. Copyright © 2015 John Wiley & Sons, Ltd.     

Outage analysis of TAS/MRC in dual hop full-duplex MIMO relay networks with co-channel interferences

In this paper, we investigate the outage performance of transmit antenna selection (TAS) and maximal-ratio combining (MRC) in dual hop full-duplex (FD) amplify-and-forward (AF) relay network over Rayleigh fading channels. In the analysis, Rayleigh faded multiple co-channel interferers (CCIs) are also taken into account at the relay. In the network, source and destination are equipped with multiple antennas, and relay is equipped with one receive and one transmit antennas, respectively and source-destination link is not available. While the TAS is applied at the source without considering residual self-interference (RSI) effect, received signals at the destination are combined based on the MRC technique. For the analysis, we consider three approaches at the relay. In the first, we consider the received signal at the relay is corrupted by faded RSI and noise, in the second one, the RSI is considered as non-fading. In the last one, the noise is neglected. In all cases, the relay suffers from multiple Rayleigh faded CCIs. Outage probability (OP) expression related to all the cases is derived and obtained in single integral forms in case of the faded/non-fading RSI and in closed form in case of the noise neglected approach. Moreover, we also find asymptotic OPs and conduct effective diversity order analysis. The analytical results are verified by the Monte Carlo simulations. Results show that TAS decreases error floor at high signal-to-noise ratio (SNR) region and MRC provides diversity gain at low SNR region. In addition, approaches II and III are good approximations to approach I at low and high SNR regions, respectively.     

Performance Analysis of Multiuser Diversity on OSTBC MIMO Systems with Antenna Selection in the Presence of Feedback Delay CSI

In this paper, we studied a comprehensive analytical symbol error probability (SEP) performance analysis of downlink multiuser diversity (MUD) on orthogonal space–time block code (OSTBC) system with transmit antenna selection (TAS) in the presence of imperfect channel state information (CSI) due to feedback delay over Rayleigh fading channels. The novel analytical approach is suitable for MUD with TAS/OSTBC systems in which effective receiver signal-to-noise ratio (SNR) is described as highest order statistic of Chi square distribution. Based on this framework, the closed-form SEP expressions are evaluated for the MUD exploiting TAS/OSTBC with normalized SNR based scheduling in heterogeneous wireless networks. Further, we derive approximate SEP; upper bound and lower bound SEP at high SNR under delayed feedback CSI. Thereafter the impact of feedback delay and antenna structures with significance on the consideration of MUD on the performance of the system has been analyzed.

     

Analysis of Transmit Antenna Selection/Maximal-Ratio Combining in Rayleigh Fading Channels

In this paper, we investigate a multiple-input-multiple-output (MIMO) scheme combining transmit antenna selection and receiver maximal-ratio combining (the TAS/MRC scheme). In this scheme, a single transmit antenna, which maximizes the total received signal power at the receiver, is selected for uncoded transmission. The closed-form outage probability of the system with transmit antenna selection is presented. The bit error rate (BER) of the TAS/MRC scheme is derived for binary phase-shift keying (BPSK) in flat Rayleigh fading channels. The BER analysis demonstrates that the TAS/MRC scheme can achieve a full diversity order at high signal-to-noise ratios (SNRs), as if all the transmit antennas were used. The average SNR gain of the TAS/MRC is quantified and compared with those of uncoded receiver MRC and space-time block codes (STBCs). The analytical results are verified by simulation. It is shown that the TAS/MRC scheme outperforms some more complex space-time codes of the same spectral efficiency. The cost of the improved performance is a low-rate feedback channel. We also show that channel estimation errors based on pilot symbols have no impact on the diversity order over quasi-static fading channels.     

Transmit antenna selection of correlated MIMO multiuser cognitive radio networks in Nakagami‐m fading channels

In this paper, we examine the impact of antenna correlation on transmit antenna selection with receive maximal ratio combining (TAS/MRC) in multiple‐input multiple‐output multiuser underlay cognitive radio network (MIMO‐MCN) over a Nakagami‐m fading environment. The secondary network under consideration consists of a single source and M destinations equipped with multiple correlated antennas at each node. The primary network composed of L primary users, each of which is equipped with multiple correlated antennas. For the considered underlay spectrum sharing paradigm, the transmission power of the proposed secondary system is limited by the peak interference limit on the primary network and the maximum transmission power at the secondary network. In particular, we derive exact closed‐form expressions for the outage probability and average symbol error rate of the proposed secondary system. To gain further insights, simple asymptotic closed‐form expressions for the outage probability and symbol error rate are provided to obtain the achievable diversity order and coding gain of the system. In addition, the impact of antenna correlation on the secondary user ergodic capacity has been investigated by deriving closed‐form expressions for the secondary user capacity. The derived analytical formulas herein are supported by numerical and simulation results to clarify the main contributions. Copyright © 2016 John Wiley & Sons, Ltd.     

Analytical modelling of multiservice switching networks with multiservice sources and resource management mechanisms

In this paper, we presents an analytical link capacity and outage performance analysis of downlink multiuser diversity (MUD) in multiple-input multiple-output (MIMO) system employing maximal-ratio combining (MRC) with transmit antenna selection (TAS) in the presence of imperfect channel state information (CSI) due to feedback delay over Rayleigh fading channels. The unified achievable analysis is appropriate for MUD–MIMO with TAS/MRC systems in which effective output signal-to-noise ratio (SNR) is specified as highest order statistic of chi-square distribution. Based on this framework, the closed-form channel capacity and outage probability expressions are examined for the MUD–MIMO exploiting TAS/MRC with normalized SNR based scheduling in heterogeneous wireless networks. Further, we derive approximate upper bound capacity as well as capacity at high SNR and low SNR region under delayed feedback CSI. The upper and lower bound of outage probability under delayed feedback CSI is also evaluated. Thereafter the impact of feedback delay and antenna structures with significance on the consideration of MUD on the performance of the system has been analyzed.