Performance Analysis of MIMO-MRC in Double-Correlated Rayleigh Environments

We consider multiple-input multiple-output (MIMO) transmit beamforming systems with maximum ratio combining (MRC) receivers. The operating environment is Rayleigh fading with both transmit and receive spatial correlation. We present exact expressions for the probability density function (pdf) of the output signal-to-noise ratio, as well as the system outage probability. The results are based on explicit closed-form expressions which we derive for the pdf and cumulative distribution function of the maximum eigenvalue of double-correlated complex Wishart matrices. For systems with two antennas at either the transmitter or the receiver, we also derive exact closed-form expressions for the symbol-error rate. The new expressions are used to prove that MIMO-MRC achieves the maximum available spatial diversity order, and to demonstrate the effect of spatial correlation. The analysis is validated through comparison with Monte Carlo simulations     

Largest eigenvalue of complex Wishart matrices and performance analysis of MIMO MRC systems

This paper extends Khatri (1964, 1969) distribution of the largest eigenvalue of central complex Wishart matrices to the noncentral case. It then applies the resulting new statistical results to obtain closed-form expressions for the outage probability of multiple-input-multiple-output (MIMO) systems employing maximal ratio combining (known also as "beamforming" systems) and operating over Rician-fading channels. When applicable these expressions are compared with special cases previously reported in the literature dealing with the performance of (1) MIMO systems over Rayleigh-fading channels and (2) single-input-multiple-output (SIMO) systems over Rician-fading channels. As a double check these analytical results are validated by Monte Carlo simulations and as an illustration of the mathematical formalism some numerical examples for particular cases of interest are plotted and discussed. These results show that, given a fixed number of total antenna elements and under the same scattering condition (1) SIMO systems are equivalent to multiple-input-single-output systems and (2) it is preferable to distribute the number of antenna elements evenly between the transmitter and the receiver for a minimum outage probability performance.     

基于机会中继和最大比合并下的协作通信系统

分析了机会中继和最大比合并下的协作通信系统性能.首次给出了Nakagami衰落信道下的符号错误率和中断概率的精确闭式结果.通过对中断概率的近似结果分析发现对于任意一条源节点-中继-目的节点链路,分集增益均由源节点-中继链路和中继-目的节点链路中的深衰落链路决定.     

MIMO解码转发双向中继系统中的传输策略与中断概率分析

在多输入多输出(MIMO)解码转发(DF)双向中继系统中,分别设计了两种信道状态信息(CSI)情况下的系统传输策略,并推导了系统中断概率的闭合表达式.当已知完全CSI时,采用(最大比发送-最大比接收)MRT-MRC技术设计波束形成和合并向量;当未知完全CSI时,设计了基于有限反馈的传输策略,并采用随机向量量化和Grassmann两种码本进行数值仿真验证.仿真结论显示,所设计的双向中继传输策略的中断概率性能明显优于其他策略,所推导的闭合表达式能准确地表征系统中断概率性能.     

有信道估计误差MIMO MRC系统性能研究

利用维希特随机矩阵理论和矩生成函数方法,推导了有信道估计误差的独立瑞利衰落信道上采用多输入多输出（MIMO）最大比合并（MRC）天线分集方案的矩形M进制正交幅度调制（MQAM）的平均误符号率（SER）解析表达式。数值计算结果阐明了信道估计误差和收发天线数对矩形MQAM调制MIMO MRC系统误码性能的影响。     

Outage probability of multi-hop MIMO relaying with transmit antenna selection and ideal relay gain over rayleigh fading channels

We present a study on the outage probability of multi-hop wireless communication systems with multiple-input multiple-output (MIMO) link based on the transmit antenna selection and the maximal-ratio combining (MRC) at the receiver. A nonregenerative system (NS) is investigated with an ideal amplifying gain. MIMO channels are assumed in uncorrelated Rayleigh fading.We derive a moment generating function (MGF) of the reciprocal of the end-to-end signal-to-noise ratio (SNR) and obtain a closed-form approximation on the outage probability through the numerical inversion of a Laplace transform. Numerical results show that the presented outage is exactly matched with the outage probability when assuming the ideal relay gain. For more practical gains, the result is shown to be a lowerbound that gets tight at high average SNR as well as for a small number of hops and/or of antennas. We also compare the outage probabilities of nonregenerative MIMO relaying with a regenerative counterpart for multiple hops.     

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.      

基于卫星移动MIMO系统的天线相关性性能分析

研究了卫星移动MIMO系统中,上、下行信道存在阴影衰落和空间相关条件下的系统性能,利用围线积分、留数定理及特殊函数积分等方法推导了系统中断概率(OP),平均符号错误概率(SER)的闭合表达式。利用Monte-Carlo仿真分析了系统在不同相关系数、天线数目及调制方式下的性能表现。仿真结果表明,尽管阴影衰落和空间相关性降低了系统性能,但与单天线系统相比,卫星移动MIMO系统的OP及SER改善明显。     

Approximate closed-form expression for the ergodic capacity of polarisation-diversity MIMO systems

MIMO systems using single dual-polarised antennas at transmitter and receiver can be a simple, cheap and compact alternative to conventional multi-antenna MIMO configurations. Recently, approximate expressions and bounds for the ergodic capacity of such systems have been proposed assuming Rayleigh or Ricean channel models. A tight closed-form approximation for the ergodic capacity of such systems in arbitrary multipath fading channels is derived.     

Outage Probabilities of Wireless Systems with LCMV Beamforming

This paper investigates the outage probability of a wireless system with linear constrained minimum variance (LCMV) beamforming using a uniform linear array beamformer. LCMV beamforming is able to perfectly cancel a number of dominant interferers while other interferers remain. A simplified beamforming model is used to derive closed-form outage probability expressions considering the impact of LCMV beam patterns on various interferers. Fading statistics of Rayleigh, Rician, and Nakagami are used to characterize the desired signal, whereas interferers are assumed to be subject to Rayleigh fading. One important aspect of this paper is the consideration of the directions of arrivals (DOA) of the dominant interferers and the exact beam patterns in the outage performance evaluations of LCMV beamforming systems. Numerical results of the outage probability are presented to illustrate the impact of DOA's of the dominant interferers and the impact of different fading scenarios. The paper also presents performance comparison between LCMV beamforming and conventional beamforming considering different interference scenarios (DOA's of dominant interferers).     

Performance Analysis of Quantized Beamforming MIMO Systems

Multiple-input multiple-output (MIMO) wireless systems can achieve significant diversity and array gain by using single-stream transmit beamforming and receive combining. A MIMO beamforming system with feedback using a codebook based quantization of the beamforming vector allows practical implementation of such a strategy in a single-user scenario. The performance of this system in uncorrelated Rayleigh flat fading channels is studied from the point-of-view of signal-to-noise ratio (SNR) and outage probability. In this paper, lower bounds are derived on the expected SNR loss and the outage probability of systems that have a single receive antenna or two transmit antennas. For arbitrary transmit and receive antennas, approximations for the SNR loss and outage are derived. In particular, the SNR loss in a quantized MIMO beamforming system is characterized as a function of the number of quantization bits and the number of transmit and receive antennas. The analytical expressions are proved to be tight with asymptotically large feedback rate. Simulations show that the bounds and approximations are tight even at low feedback rates, thereby providing a benchmark for feedback system design     

Training-based and semiblind channel estimation for MIMO systems with maximum ratio transmission

This paper is a comparative study of training-based and semiblind multiple-input multiple-output (MIMO) flat-fading channel estimation schemes when the transmitter employs maximum ratio transmission (MRT). We present two competing schemes for estimating the transmit and receive beamforming vectors of the channel matrix: a training-based conventional least-squares estimation (CLSE) scheme and a closed-form semiblind (CFSB) scheme that employs training followed by information-bearing spectrally white data symbols. Employing matrix perturbation theory, we develop expressions for the mean-square error (MSE) in the beamforming vector, the average received signal-to-noise ratio (SNR) and the symbol error rate (SER) performance of both the semiblind and the conventional schemes. Finally, we describe a weighted linear combiner of the CFSB and CLSE estimates for additional improvement in performance. The analytical results are verified through Monte Carlo simulations.     

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.     

On the information throughput and optimized power allocation for MIMO wireless systems with imperfect channel estimation

In this paper, we focus on the throughput analysis, outage evaluation and optimized power allocation for Multiple-Input Multiple-Output (MIMO) pilot-based wireless systems subject to short-term constraints on the radiated power and equipped with a feedback-path for communicating back to the transmitter the imperfect MIMO channel estimates available at the receiver. The case of the ergodic throughput for Gaussian distributed input signals is analyzed, and the conditions for the (asymptotical) achievement of the Shannon capacity are pointed out. The main contributions of this work may be so summarized. First, we develop closed-form analytical expressions for the computation of the ergodic information throughput conveyed by the considered MIMO system for the case of ideal feedback link. Second, we present an iterative algorithm for the optimized power allocation over the transmit antennas that explicitly accounts for the imperfect MIMO channel estimates available at the receiver. Third, after relaxing the assumption of ideal feedback link, we test the sensitivity of the proposed power allocation algorithm on errors possibly introduced by the feedback channel, and then, we numerically evaluate the resulting throughput loss. Finally, we develop closed-form upper and lower bounds on the outage probability that are asymptotically tight.     

基于发射分集的多点中继合作通信系统性能研究

为了降低合作通信系统中的误码率和中断概率,本文研究了多点中继合作通信系统.采用矩母函数(Moment Generating Function)分析方法,通过引入超几何函数,详尽推导出Rayleigh衰落信道下的平均符号错误率和中断率的精确表达式.通过蒙特卡洛仿真,验证了表达式的正确性,其性能优于单点中继合作通信系统.     

Performance of cross-layer design for orthogonal space-time block coded MIMO systems with imperfect CSI in Ricean fading channels

A cross-layer design (CLD) scheme for orthogonal space-time block coded MIMO systems with imperfect channel state information is presented by combining adaptive modulation and automatic repeat request, and the corresponding system performance is investigated over Ricean fading channel. The fading gain value is partitioned into a number of regions by which the modulation is adapted in terms of the region the fading gain falls in. The fading gain switching thresholds subject to a target packet error rate (PER) constraint are derived. According to these results, and using the generalized Marcum Q-function, we derive the theoretical formulae of average PER and spectrum efficiency (SE) of the system with CLD for both perfect and imperfect estimation in detail. As a result, closed-form expressions for average PER and SE are obtained. These expressions include some existing expressions in Rayleigh channel as special cases. With these expressions, the system performance in Ricean channel with perfect and imperfect estimation information can be evaluated effectively. Computer simulation for average PER and SE show that the theoretical analysis and simulation are consistent. The results show that the system performance will be effectively improved as Ricean factor increases, but it will be degraded as estimation errors increases.     

Performance analysis of TAS/MRC-based scheme in time-varying Rayleigh fading channels

This paper investigates a Multiple-Input Multiple-Output (MIMO) scheme combining Transmit Antenna Selection and receive Maximal-Ratio Combining (TAS/MRC) in time-varying Rayleigh fading channels. We first present new closed-form expressions for optimal received Signal-to-Noise Ratio (SNR), which is expressed in polynomial form. These are used to analyze ergodic capacity, outage probability and Bit Error Rate (BER) of TAS/MRC systems. Numerical results are presented to validate the theoretical analysis.     

Quadratic forms in complex Gaussian matrices and performance analysis of MIMO systems with cochannel interference

This paper establishes an analytical framework for the performance analysis of multiple-input/multiple output (MIMO) systems subject to cochannel interference and operating over fading channels. First, we present some new statistical results dealing with the distribution of the largest eigenvalue of certain quadratic forms in complex Gaussian matrices and establish the connection between these results and the performance analysis of MIMO systems subject to cochannel interference. We consider interference limited systems in which the number of cochannel interferers exceeds or is equal to the number of receiving antenna elements. We then derive new "closed-form" expressions of the probability density function of the outage signal-to-interference ratio and the system outage probability for MIMO systems in Rician-Rayleigh (i.e., the desired user is subject to Rician fading while cochannel interferers are subject to Rayleigh fading) and Rayleigh-Rayleigh fading environments. When applicable, these expressions are compared to special cases previously reported in the literature dealing with the performance of single-input/multiple-output (SIMO) systems. As a double check, these analytical results and assumptions are validated by Monte Carlo simulations and as an illustration of the mathematical formalism some numerical examples for particular cases of interests are plotted and discussed. These results show that under the same the scattering and interfering conditions and given a fixed number of total antenna elements and cochannel interferers: 1) SIMO systems will always outperform multiple-input/single-output systems and 2) it is preferable to distribute the number of antenna elements evenly between the transmitter and the receiver for an optimum performance.     

Level Crossing Rates of Ricean MIMO Channel Eigenvalues for Imperfect and Outdated CSI

In this paper, the exact closed-form expressions for the level crossing rates of the multiple-input multiple output (MIMO) channel ordered eigenvalues are derived for the Ricean propagation and arbitrary channel matrix dimensions. The novel expressions can be applied for the imperfect channel state information (CSI) and feedback delay, with or without prediction. The analytical results are validated by simulation.     

The Performance of Space-Time Block Codes from Coordinate Interleaved Orthogonal Designs over Nakagami-m Fading Channels

Space-time block codes (STBCs) from coordinate interleaved orthogonal designs (CIODs) offer several advantages including full-diversity and single-symbol decodability. In an effort to assess their performance in quasi-static frequencynonselective i.i.d. Nakagami-m fading channels, we analyze the error rate, outage capacity, and information outage probability. First, based on an accurate closed-form formula for the average symbol pairwise error rate (SPER), we derive tight union upper and lower bounds on the symbol-error rate (SER). Second, we apply Gaussian and Gamma approximations to provide closedform expressions for the outage capacity. Third, using high signal-to-noise ratio (SNR) and moment-matching approximation techniques, we also derive accurate closed-form approximations for the information outage probability (IOP). Finally, we show that STBCs from CIODs provide full-diversity by deriving SERbased and IOP-based asymptotic and instantaneous diversity orders. Monte-Carlo simulations show that the analytical results agree with simulation experiments.