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.     

Multicellular Alamouti scheme performance in Rayleigh and shadow fading

In this paper, we study the performance of two downlink multicellular systems: a multiple inputs single output (MISO) system using the Alamouti code and a multiple inputs multiple outputs (MIMO) system using the Alamouti code at the transmitter side and a maximum ratio combining (MRC) as a receiver, in terms of outage probability. The channel model includes path-loss, shadowing, and fast fading, and the system is considered interference-limited. Two cases are distinguished: constant shadowing and log-normally distributed shadowing. In the first case, closed form expressions of the outage probability are proposed. For a log-normally distributed shadowing, we derive easily computable expressions of the outage probability. The proposed expressions allow for fast and simple performance evaluation for the two multicellular wireless systems: MISO Alamouti and MIMO Alamouti with MRC receiver. We use a fluid model approach to provide simpler outage probability expressions depending only on the distance between the considered user and its serving base station.     

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.     

Closed-form expressions for the outage and ergodic Shannon capacity of MIMO MRC systems

Transmit-beamforming (TB) over multiple-input multiple-output (MIMO) fading channels steers the transmit power in the receiver's direction, so as to maximize the output signal-to-noise ratio (SNR) after maximal ratio combining (MRC) at the receiver. This letter proposes a simple algorithm that allows evaluating an exact and tractable expression for the probability density function of the SNR at the output of the TB receiver, subject to Rayleigh fading. The latter enables the derivation of closed-form expressions for the outage and ergodic capacity of MIMO MRC systems under Rayleigh fading, thereby avoiding the need for time-consuming numerical integrations or Monte Carlo simulations.     

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.     

Performance Analysis of Multiuser Diversity in MIMO Systems with Antenna Selection

In this paper, a framework is presented to analyze the performance of multiuser diversity (MUD) in multiuser point-to-multipoint (PMP) MIMO systems with antenna selection. Based on this framework, the tight closed-form expressions of outage capacity and average symbol error rate are derived for the multiuser transmit antenna selection with maximal-ratio combining (TAS/MRC) system, by which we show how and with what characteristics antenna selection gains, MIMO antenna configurations and fading gains impact on the system performance, with an emphasis on the study of multiuser diversity influence. From both theoretical and simulation results, our study shows that in multiuser PMP TAS/MRC systems an diversity order equals to the product of the number of transmit antennas, number of receive antennas and number of users can be achieved; what's more, users plays a key role in the system performance and can be viewed as equivalent 'virtual" transmit antennas, which is the source of the multiuser diversity inherent exists in the multiuser system. This kind of diversity can be efficiently extracted in the design of multiantenna systems.     

Performance analysis of MIMO systems with multiuser diversity

In this paper, we present a comprehensive performance analysis for multiple‐input multiple‐output (MIMO) systems with multiuser diversity over Rayleigh fading channels. We derive exact closed‐form expressions of the outage probability and the average bit error rate (BER) for different MIMO schemes, including the selective combining (SC), maximum ratio combining (MRC) and space‐time block codes (STBC). We also provide the explicit upper bounds on the BER performance. Finally, the mathematical formalism is verified by numeric results that study the interaction between the antenna diversity and the multiuser diversity. It is observed that the system performance is deteriorated as the number of transmit antennas increases in multiuser scenario, which is unlike the case in single‐user systems. Copyright © 2007 John Wiley & Sons, Ltd.     

MIMO MRC Systems with and without Multiuser Diversity

In this paper, we consider the multiple-input multiple-output (MIMO) wireless systems employing maximal ratio combining (MRC) in the absence and presence of multiuser diversity. First, using the well-known moment generating function-based analysis approach, we derive the error performance of the MIMO MRC systems without multiuser diversity over spatially correlated fading channels. Second, we present the average capacity of MIMO MRC systems with multiuser diversity. Numerical results demonstrate the accuracy of our analytical expressions.     

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     

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.     

Outage probability analysis of a MIMO relay channel with orthogonal space-time block codes

We investigate the performance of a cooperative multiple-input multiple-output (MIMO) relay channel in which the source and relay use the same orthogonal space-time block code (OSTBC) for transmission whereas the relay and destination use maximum-ratio-combining (MRC) for reception. Considering that perfect channel state information is available at the relay and destination, we derive a closed-form expression for the outage probability of the destination signal-to-noise ratio (SNR) in terms of the confluent hypergeometric function of two variables in a Rayleigh flat-fading environment. The validity of the closed-form expression is confirmed with the numerical results.     

Downlink SINR Distribution of Linearly Precoded Multiuser MIMO Systems

This paper derives mathematical expressions for the SINR distribution in systems with linearly precoded multiuser MIMO and frequency domain packet scheduling. The packet scheduler is able to exploit the available multiuser diversity in both time, frequency and spatial domains. Our analysis model is confined to 3GPP downlink transmission in which we specifically investigate the single user (SU) and multi-user (MU) spatial division multiplexing (SDM) MIMO schemes. From the analytical results we find that the outage probability for systems using the SU-MIMO scheme is larger than the one for the MU-MIMO scheme. Also, in comparison to systems without precoding, linear precoding can improve the outage probability.     

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.     

硬件损伤下能量采集双向中继网络系统中断性能分析

在硬件损伤条件下分析了能量采集双向中继网络的系统中断性能,该网络的终端节点对直达链路信号和中继链路信号分别进行选择合并（Selection Combining, SC）和最大比合并（Maximum Ratio Combining,MRC）。首先,推导了该网络在SC方案下的系统中断概率,并在此基础上得到了由硬件损伤而引起的两种效应,即中继协作效应和系统协作效应。然后,推导了该网络在MRC方案下的系统中断概率。最后,通过仿真分析了硬件损伤及系统参数对系统中断性能的影响,并比较了该网络在SC方案和MRC方案下的系统中断性能。仿真结果表明:在硬件损伤条件下,MRC方案仅引起系统协作效应;相比于MRC方案,SC方案对硬件损伤更加敏感;当数据传输速率低于系统协作门限时,采用MRC能够实现更好的系统中断性能。      

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     

Asymptotic Analysis of Outage Region in CDMA MIMO Systems

Uplink code-division multiple access (CDMA) multiple-input and multiple-output (MIMO) systems are considered in the large system limit within the assumptions of synchrony and frequency flat fading. The outage region maximizing the sum capacity of non-outage users is obtained, which extends the criterion of outage in single-input and single-output (SISO) CDMA systems.      

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。     

Capacity of multiuser diversity systems with adaptive transmission and different MIMO schemes

In this paper, we present a comprehensive capacity analysis of the downlink of multiuser diversity (MD) systems with adaptive transmission over Rayleigh fading channels. First, the exact capacity of the single‐input single‐output (SISO) systems with MD and adaptive transmission technique is derived. The optimal power allocation scheme for such a system is shown to be a water‐filling algorithm. Next, we derive the exact closed‐form capacity expressions for different multiple‐input multiple‐output (MIMO) schemes, including the selective combining (SC), maximum ratio combining (MRC) and space‐time block codes (STBC). In order to avoid the cumbersome numerical root finding techniques in solving the optimal cutoff SNR level below which the channel is not used, we also provide the approximate expressions for the cutoff level. For the MD MIMO systems, it is observed that the optimal power allocation strategy is to focus transmit power on a single transmit antenna (e.g. Tx‐MRC/Rx‐MRC scheme) or selecting the best transmit antennas (e.g. Tx‐SC/Rx‐MRC scheme). Copyright © 2007 John Wiley & Sons, Ltd.     

Error rates of DPSK systems with MIMO EGC diversity reception over Rayleigh fading channels

This paper analyzes the average bit error probability (BEP) of the differential binary and quaternary phase-shift keying (DBPSK and DQPSK respectively) with multiple-input multiple-output (MIMO) systems employing postdetection equal gain combining (MIMO EGC) diversity reception over Rayleigh fading channels. Finite closed-form expressions for the average BEP of DBPSK and DQPSK are presented. Two approaches are introduced to analyze the error rate of DQPSK. The proposed structure for the differential phase-shift keying (DPSK) with MIMO EGC provides a reduced-complexity and low-cost receiver for MIMO systems compared to the coherent phase-shift keying system (PSK) with MIMO employing maximal ratio combining (MIMO MRC) diversity reception. Finally, a useful procedure for computing the associated Legendre functions of the second kind with half-odd-integer order and arbitrarily degree is presented.     

Analysis of macroscopic diversity combining of MIMO signals in mobile communications

In this paper, the system model and performance analysis of macroscopic diversity combining (MDC) multiple-input multiple-output (MIMO) systems are presented for mobile cellular communication applications. The channel capacity of MIMO systems will deteriorate if the dual antenna array (DAA) spacing is insufficient or the scattering environment does not provide completely uncorrelated channels. In addition, the shadowing component of the directional signal is a common factor among the scattered channels, resulting in significant reductions in obtainable channel capacity. Therefore, in this paper, a macroscopic diversity topology is applied to maximize the spatial multiplexing gain while combating the shadowing phenomena. The channel capacity as well as its upper and lower bounds are derived for MIMO-based MDC systems. Additionally, the outage capacity for the proposed MDC system topology has been analyzed. Compared to a single communicating MIMO system pair, the results show that the macroscopic diversity MIMO communication topology enables a larger number of uncorrelated shadowed and scattered channels to exist, and therefore, improvements of enhanced channel capacity and reduced outage is obtained.