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.     

Performance analysis of dual-hop fixed-gain AF relaying systems with OSTBC over Nakagami-m fading channels

In this paper, we present outage probability and symbol error rate (SER) performance analyses of a dual-hop transmission using fixed-gain amplify-and-forward relaying in flat Nakagami-m fading channels. The system under consideration is equipped with multiple antennas at source and destination adopting orthogonal space-time block coding to provide transmit diversity and maximum ratio combining to provide receive diversity, respectively. For integer and half-integer m values, closed forms of exact outage probability and moment generating function (MGF) expressions are derived through cumulative distribution function (CDF) of the overall system signal-to-noise ratio. Closed-form exact SER expressions based on the overall CDF are obtained for binary phase shift keying, binary frequency shift keying and M-ary pulse amplitude modulation. Exact SER expressions based on the MGF method are also obtained for binary differential phase shift keying, M-ary phase shift keying and M-ary quadrature amplitude modulation. Moreover, the asymptotic diversity order analysis is performed through derivations of asymptotic outage probability and SER. Theoretical analyses are validated by Monte Carlo simulations showing perfect match between each other.     

Robust Transmit Antenna Selection with Phase Feedback Over Correlated Fading Channels

A new transmit antenna selection (TAS) scheme with phase feedback for multiple-input multiple-output systems is proposed in this paper. This scheme allows two or more transmit antennas to simultaneously use one radio frequency chain. By grouping the transmit antennas according to their similarities in instantaneous channel coefficients into two subsets and treating each subset as a single antenna, both hardware complexity reduction and antenna array gain can be achieved. Compared with the transmit antenna selection combined with space-time block code (TAS/STBC) scheme, the proposed TAS scheme provides excellent robustness, in terms of symbol error rate performance, against spatially correlated fading channels. Moreover, the proposed TAS scheme need not use STBC encoder and decoder which used in the TAS/STBC schemes. Therefore, the proposed TAS scheme is simpler than the TAS/STBC schemes in practical hardware implementation.     

Nakagami-m衰落信道下空时分组码的性能估计

基于等效单输入单输出SISO (Single-input Single-output) 模型,利用矩量母函数 (MGF) 分析法,空时分组码STBC (Space-Time Block Coding) 的误符号率是可以得到其准确闭式表达式的.对于独立同分布Nakagami-m衰落信道下的空时分组码的性能进行了研究,给出了采用M-PSK 和M-QAM调制方案的不同空时分组编码矩阵误符号率的闭式解以及基于闭式解的解析性能结果,通过蒙特卡洛仿真验证了闭式解的准确性.还从调制方案的角度对于几种新的空时分组码的性能进行了一些新的讨论.     

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.     

Joint TAS/SC and power allocation for IAF relaying D2D cooperative networks

In this paper, the outage probability (OP) performance of multiple-relay-based incremental amplify-and-forward relaying device-to-device networks with transmit antenna selection (TAS) over N-Nakagami fading channels is investigated. The exact closed-form expressions for OP of the optimal and suboptimal TAS schemes are derived. The power allocation problem is formulated for performance optimization. Then the OP performance under different conditions is evaluated through numerical simulations to verify the analysis. The simulation results showed that optimal TAS scheme has a better OP performance than suboptimal TAS scheme, but the performance gap between the optimal and suboptimal schemes diminishes by increasing the number of antennas at the source; the fading coefficient, the number of cascaded components, the relative geometrical gain, the number of antennas, and the power-allocation parameter have an important influence on the OP performance.     

A Low-BER Clipping Scheme for PAPR Reduction in STBC MIMO-OFDM Systems

Clipping is a simple scheme to reduce the peak-to-average power ratio (PAPR) in orthogonal frequency division multiplexing (OFDM) systems. Further, it can be extended to space-time block coding (STBC) multiple-input multiple-output (MIMO) OFDM systems for the PAPR reduction. In the conventional clipping schemes for STBC MIMO-OFDM systems, the input symbols are first encoded and then clipped. In this paper, a new scheme is proposed, where the clipping operation is performed before space-time block coding. We theoretically prove that the proposed scheme has better bit-error rate (BER) performance while maintaining the same PAPR reduction as the conventional schemes. Additionally, we derive the symbol-error rate (SER) and BER expressions for the new scheme over multipath fading channels. The simulation results show a good match with our analysis.     

Performance of variable-power adaptive MQAM with transmit antenna selection and delayed feedback in Nakagami Fading channel

In this paper, the performance of MIMO systems with variable-power (VP) adaptive MQAM and transmit antenna selection (TAS) over Nakagami-m fading channel is presented. The optimum switching thresholds for attaining maximum spectrum efficiency (SE) subject to a target bit error rate (BER) and an average power constraint are derived. It is shown that the Lagrange multiplier in the constrained SE optimization will be unique if the existence condition for MIMO system with TAS is satisfied. A practical iterative algorithm based on Newton's method for finding the Lagrange multiplier is proposed. By using the switching thresholds, closed-form expressions of the SE and average BER are obtained. Besides, BER expressions with delayed feedback are derived for VP and constant-power (CP) systems, respectively. With these expressions, the impact of feedback delay on the BER performance is effectively assessed. Computer simulation for SE and BER shows that the theoretical analysis and simulation are in good agreement. The results show that the VP adaptive modulation (AM) system with TAS provides better SE than the CP counterpart and VP AM system with space-time coding, and has slight BER performance degradation for the normalized time delay less than 0.01.     

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.     

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.     

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.

     

Performance of Transmit Antenna Selection and Maximal-Ratio Combining in Dual Hop Amplify-and-Forward Relay Network over Nakagami-m Fading Channels

In this paper, we study end-to-end performance of transmit antenna selection (TAS) and maximal ratio combining (MRC) in dual hop amplify-and-forward relay network in flat and asymmetric Nakagami-m fading channels. In the network, source and destination communicate by the help of single relay and source-destination link is not available. Source and destination are equipped with multiple antennas, and relay is equipped with single antenna. TAS and MRC are used for transmission at the source and reception at the destination, respectively. The relay simply amplifies and forwards the signal sent by the source to the destination by using channel state information (CSI) based gain or fixed gain. By considering relay location, for CSI based and fixed relay gains, we derive closed-form cumulative distribution function, moments and moment generating function of end-to-end signal-to-noise ratio, and closed-form symbol error probability expression. Moreover, asymptotical outage probability and symbol error probability expressions are also derived for both CSI based and fixed gains to obtain diversity order of the network. Analytical results are validated by the Monte Carlo simulations. Results show that diversity order is minimum of products of fading parameter and number of antennas at the end in each hop. In addition, for optimum performance the relay must be closer to the source when the diversity order of the first hop is smaller than or equal to that of the second hop.     

Performance analysis of space-time block codes over keyhole Nakagami-m fading channels

In multiple-input-multiple-output (MIMO) fading environments, degenerate channel phenomena, called keyholes or pinholes, may exist under the realistic assumption that the spatial fading is uncorrelated at the transmitter and the receiver, but the channel has a rank-deficient transfer matrix. In this paper, we analyze the exact average symbol error rate (SER) of orthogonal space-time block codes (STBCs) with M-PSK and M-QAM constellations over Nakagami-m fading channels in the presence of the keyhole. We derive the moment generating function (MGF) of instantaneous signal-to-noise ratio (SNR) after space-time block decoding (signal combining) in such channels. Using a well-known MGF-based analysis approach, we express the average SER of the STBC in the form of single finite-range integrals whose integrand contains only the derived MGF. Numerical results show that the keyhole significantly degrades the SER performance of the STBC from idealistic behaviors in independent identically distributed MIMO channels.     

Outage Performance for IDF Relaying Mobile Cooperative Networks

Cooperative communication is a key technique in fifth generation (5G) mobile wireless networks. In this paper, we study the transmit antenna selection (TAS) in mobile cooperative networks. We derive the exact closed-form outage probability (OP) expressions for two TAS schemes. Based on the derived OP expressions, the impact of power allocation on OP performance is evaluated. Then we obtain that the Monte-Carlo simulation results and the analysis results match very well. The OP performance is affected by the power-allocation parameter.     

Transmit selection diversity with maximal-ratio combining for multicarrier DS-CDMA wireless networks over Nakagami-m fading channels

We propose the scheme to integrate transmit selection diversity/maximal-ratio combining (TSD/MRC) with multicarrier (MC) direct-sequence code-division multiple access (DS-CDMA) for various wireless networks. Applying this TSD/MRC-based scheme, the transmitter jointly selects the optimal subcarrier-and-antenna pair to significantly decrease the peak-to-average power ratio (PAPR), which is one of the main problems inherently associated with MC DS-CDMA communications. Over the frequency-selective Nakagami-m fading channels, we develop the unified analytical framework to analyze the symbol-error rate (SER) of the scheme implemented in different types of wireless networks, while dealing with the perfect and imperfect channel state information (CSI) feedbacks, respectively. The imperfect feedbacks we focus on include delayed feedbacks and erroneous feedbacks. Taking the imperfectness of the feedback into account, the resultant SER is compared with that of both conventional selection diversity (SD)/MRC-based and space-time block coding (STBC)/MRC-based schemes. Our analyses show that in a wide variation of the feedback imperfectness, our proposed TSD/MRC-based scheme has significant advantages over the other two schemes for both downlink cellular networks and ad hoc wireless networks. However, our analytical findings indicate that TSD/MRC-based scheme cannot always outperform SD/MRC-based and STBC/MRC-based schemes even when the perfect CSI feedbacks are available.     

Analysis of diversity schemes employing antenna selection in the presence of channel estimation errors and feedback delay

The main objective of this paper is to provide an extensive and complete examination on the effect of practical impairments such as channel estimation errors (CEEs) and feedback delay (FD) on the performance of diversity schemes over Nakagami‐m fading channels. Under erroneous channel estimation and outdated feedback cases, statistical expressions and several performance metrics related to the post‐processing signal‐to‐noise ratio (SNR) are derived for four different diversity schemes: transmit antenna selection (TAS)/orthogonal space–time block coding, TAS/maximal‐ratio transmission (MRT), MRT/receive antenna selection (RAS), and joint transmit and RAS. Exact analytical expressions for outage probability and average error rates of M‐ary modulations are derived in order to provide insightful perspectives on the capacity and error performance of diversity schemes that experience both CEE and FD. The asymptotic diversity order of the investigated diversity schemes are derived via a high‐SNR approximation approach. In order to assess the real‐world performance of the investigated diversity schemes and to observe their robustness or sensitivities in practical imperfections, various configurations are considered together with several performance comparisons. Also, Monte Carlo simulations are performed in order to validate the theoretical results. Copyright © 2014 John Wiley & Sons, Ltd.     

Performance Analysis of Mobile Multiuser Cooperative Networks with TAS Schemes

In this paper, the outage probability (OP) performance of mobile multiuser networks with transmit antenna selection (TAS) and selection combing(SC) is investigated. The exact closed-form OP expressions of the optimal and suboptimal TAS schemes are derived for decode-and-forward (DF) relaying. By using this result,the impact of power allocation on OP performance is evaluated. Then through Monte Carlo simulation,the OP performance under different conditions is evaluated. The simulation results demonstrate that optimal TAS scheme has a better OP performance than suboptimal TAS scheme. Further, the power-allocation parameter has an important influence on the OP performance.

     

Performance Analysis of OSTBC Transmission in Amplify-and-Forward Cooperative Relay Networks

A performance analysis is presented for amplify-and-forward (AF) cooperative relay networks employing transmit antenna diversity with orthogonal space-time block codes (OSTBCs), where multiple antennas are equipped at the transmitter. We develop a symbol-error-rate (SER) and outage performance analysis for OSTBC transmissions with and without cooperative diversity over flat Rayleigh fading channels. We first derive exact probability density functions (pdf's) and cumulative distribution functions (cdf's) for the system SNR without direct transmission with an arbitrary number of transmit antennas and then present the exact closed-form SER and outage probability expressions. Next, we derive the moment-generating function (MGF) for the overall system SNR with direct transmission and present the exact SER and outage probability with joint transmit antenna diversity and cooperative diversity. The theoretical analysis is validated by simulations, which indicate an exact match between them. The results also show how the transmit antenna diversity and the cooperative diversity affect the overall system performance.      

MIMO multichannel beamforming: SER and outage using new eigenvalue distributions of complex noncentral Wishart matrices

This paper analyzes MIMO systems with multichannel beamforming in Ricean fading. Our results apply to a wide class of multichannel systems which transmit on the eigenmodes of the MIMO channel. We first present new closed-form expressions for the marginal ordered eigenvalue distributions of complex noncentral Wishart matrices. These are used to characterize the statistics of the signal to noise ratio (SNR) on each eigenmode. Based on this, we present exact symbol error rate (SER) expressions. We also derive closed-form expressions for the diversity order, array gain, and outage probability. We show that the global SER performance is dominated by the subchannel corresponding to the minimum channel singular value. We also show that, at low outage levels, the outage probability varies inversely with the Ricean A*-factor for cases where transmission is only on the most dominant subchannel (i.e. a singlechannel beamforming system). Numerical results are presented to validate the theoretical analysis.     

Transmit antenna selection for decision feedback detection in MIMO fading channels

In this paper, we investigate a transmit antenna selection (TAS) approach for the decision-feedback detector (DFD) over Rayleigh fading channels. In particular, for a multipleinput multiple-output (MIMO) channel with M transmit and N (N ⩾ M) receive antennas, we derive a lower bound on the outage probability for the TAS approach. The selected transmit antennas are those that maximize the post-processing signalto- noise ratio (SNR) at the receiver end. It is shown that the proposed TAS approach achieves a performance close to optimal selection based on exhaustive search, introduced in the literature, but at a lower complexity. Simulation results are presented to validate and demonstrate the performance gain of the proposed TAS approach.