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.     

Capacity of multiple-antenna fading channels: spatial fading correlation, double scattering, and keyhole

The capacity of multiple-input multiple-output (MIMO) wireless channels is limited by both the spatial fading correlation and rank deficiency of the channel. While spatial fading correlation reduces the diversity gains, rank deficiency due to double scattering or keyhole effects decreases the spatial multiplexing gains of multiple-antenna channels. In this paper, taking into account realistic propagation environments in the presence of spatial fading correlation, double scattering, and keyhole effects, we analyze the ergodic (or mean) MIMO capacity for an arbitrary finite number of transmit and receive antennas. We assume that the channel is unknown at the transmitter and perfectly known at the receiver so that equal power is allocated to each of the transmit antennas. Using some statistical properties of complex random matrices such as Gaussian matrices, Wishart (1928) matrices, and quadratic forms in the Gaussian matrix, we present a closed-form expression for the ergodic capacity of independent Rayleigh-fading MIMO channels and a tight upper bound for spatially correlated/double scattering MIMO channels. We also derive a closed-form capacity formula for keyhole MIMO channels. This analytic formula explicitly shows that the use of multiple antennas in keyhole channels only offers the diversity advantage, but provides no spatial multiplexing gains. Numerical results demonstrate the accuracy of our analytical expressions and the tightness of upper bounds.     

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.     

Exact bit error probabilities and packet error statistics for SVD transmission over time-varying dual-branch MIMO systems obtained by a Markov model

Using a finite state Markov channel model, we develop an analytical method for evaluation of the packet error structure in multiple-input multiple-output (MIMO) systems based on singular value decomposition (SVD). We consider dual-branch MIMO systems, with either two transmit and arbitrary number of receive antennas, or arbitrary number of transmit and two receive antennas. The corresponding Markov model parameters are obtained using a novel closed-form expressions for probability density function and level crossing rate of the signal-to-noise ratio at the output of eigenchannels in a MIMO system, derived for a case of Rayleigh propagation, imperfect channel state information and any fixed power allocation. The exact bit error rate for the transmission of quadrature amplitude modulated (QAM) symbols through the eigenchannels is derived in polynomial closed form. Furthermore, by using the developed Markov model, the packet error statistics in the corresponding eigenchannels are determined, and the closed-form analytical expression for the system throughput is derived when ‘go-back-N’ automatic repeat request procedure is applied in time-varying eigenchannels. The analytical results are validated by using Monte Carlo simulations.     

空间相关MIMO信道天线选择系统闭合容量式

在空间瑞利相关信道下,笔者推导了混合选择/多输入多输出系统(H-S/MIMO)信道容量的精确表达式。以2发送天线和2/3接收天线的MIMO系统为模型,使用MATLAB对该系统进行了仿真。结果表明,理论分析与仿真曲线相吻合,进一步说明文中理论分析的正确性。     

A study of opportunism for multiple-antenna systems

Recently proposed opportunistic beamforming exploits the multiuser diversity to reduce the feedback by not requiring the precoding information used for closed-loop schemes to be known at the transmitter. Opportunism could also be beneficially employed for other multiple-antenna transmission techniques like cophasing and antenna selection. For opportunistic beamforming and antenna selection, we give closed-form expressions for throughput that closely approximate the performance of these schemes with a Proportionally Fair scheduler (PFS) at low signal-to-noise ratios (SNRs). For large number of transmit antennas, opportunistic cophasing has similar performance as opportunistic beamforming. Asymptotic dependence of the required number of users to achieve the gains of opportunism on the number of transmit antennas is exponential for opportunistic beamforming (and cophasing for large numbers of transmit antennas), and at best linear for opportunistic antenna selection. For multiple-antenna receivers, we additionally examine an opportunistic multiple-input multiple-output (MIMO) scheme that transmits multiple data streams simultaneously to the same user.     

多输入多输出系统信道容量研究

该文研究接收端采用均圆阵天线阵放置空间有限的条件下,存在相关衰落时MIMO系统的信道容量。建立了衰落相关模型,分析了散射角大小及天线数对信道容量的影响,采用随机理论推导了MN的MIMO系统信道容量的闭式解。分析结果表明,MIMO系统信道容量主要由衰落相关矩阵的特征值决定。仿真结果表明,在接收端空间有限的情况下,天线数增大到一定程度时,信道容量达到饱和,再增加天线数,对信道容量的影响很小。     

On the capacity of spatially correlated MIMO Rayleigh-fading channels

In this paper, we investigate the capacity distribution of spatially correlated, multiple-input-multiple-output (MIMO) channels. In particular, we derive a concise closed-form expression for the characteristic function (c.f.) of MIMO system capacity with arbitrary correlation among the transmitting antennas or among the receiving antennas in frequency-flat Rayleigh-fading environments. Using the exact expression of the c.f., the probability density function (pdf) and the cumulative distribution function (CDF) can be easily obtained, thus enabling the exact evaluation of the outage and mean capacity of spatially correlated MIMO channels. Our results are valid for scenarios with the number of transmitting antennas greater than or equal to that of receiving antennas with arbitrary correlation among them. Moreover, the results are valid for an arbitrary number of transmitting and receiving antennas in uncorrelated MIMO channels. It is shown that the capacity loss is negligible even with a correlation coefficient between two adjacent antennas as large as 0.5 for exponential correlation model. Finally, we derive an exact expression for the mean value of the capacity for arbitrary correlation matrices.     

Performance Evaluation of Generalized Selection Combiners Over Slow Fading with Estimation Errors

In this paper we derive closed-form expressions for the single-user adaptive capacity of generalized selection combining (GSC) system, taking into account the effect of imperfect channel estimation at the receiver. The channel considered is a slowly varying spatially independent flat Rayleigh fading channel. The complex channel estimate and the actual channel are modelled as jointly Gaussian random variables with a correlation that depends on the estimation quality. Three adaptive transmission schemes are analyzed: (1) optimal power and rate adaptation; and (2) constant power with optimal rate adaptation, and (3) channel inversion with fixed rate. In addition to deriving an exact expression for the capacity of the aforementioned adaptive schemes, we analyze the impact of channel estimation error on the capacity statistics and the symbol error rate for GSC systems. The capacity statistics derived in this paper are the moment generating function, complementary cumulative distribution function and probability density function for arbitrary number of receive antennas. Moreover, exact closed-form expressions for M-PAM/PSK/QAM employing GSC are derived. As expected, the channel estimation error has a significant impact on the system performance.     

Closed-Form Exact BER and Optimization of Generalized Orthogonal STBCs

The closed-form exact bit error rate (BER) expressions of generalized orthogonal space-time block codes (OSTBCs) are first derived for quadrature amplitude modulation (QAM) and phase shift keying (PSK) constellations in spatially white Rayleigh multiple input multiple output (MIMO) channels. Then this analysis is generalized to arbitrarily spatially correlated MIMO channels. Based on the BER analysis, the transmission power of the generalized OSTBCs is optimized such that the average BER is minimized. Furthermore, the optimum transmit power which maximizes the upper-bound of the capacity is derived in closed-form.     

The Downlink Capacity of Single-User SA-MIMO System

In this paper, a novel multiple antenna system framework, which combines smart antennas (SA) with multiple-input-multiple-output (MIMO) at the transmitter, is proposed. The downlink capacity of the single-user SA-MIMO wireless systems is investigated. The joint optimization problem corresponding to the capacity is deduced. After that, upper bounds of the capacity are given in general case and in the case of equal power allocation, respectively. Furthermore, in the case of equal power allocation and the same direction of departure from one transmit smart antenna to all antenna arrays at the receiver the closed-form expression of the capacity is obtained. Some numerical results are given to show that smart antennas can bring significant capacity gain for the MIMO systems due to the smart antennas gain, without additional spatial degrees of freedom, especially at high SNR with strong correlation among the MIMO channel links or at low SNR.     

瑞利衰落信道下最大比发射联合选择接收技术的性能分析

本文设计了一种新的MIMO传输技术,它在发射端(基站)按最大比发射(MRT),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MRT/RAS.其目标就是为了提高系统性能并降低接收端(移动台)的硬件复杂度.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.仿真试验也证明了分析结果的正确性.     

BER analysis using zero-forcing linear precoding scheme for massive MIMO under imperfect channel state information

ABSTRACT

In massive MIMO systems, inter-user interference has effect on the transmitted signals, so linear precoding techniques are employed for multiuser transmission channels to remove this inter-user interference. It is very complicated to design a suitable linear precoding technique having low computational complexity, which will give an excellent Bit Error Rate (BER) performance. In this paper, we analyse BER under imperfect Channel-State-Information (CSI) using Zero-Forcing (ZF) linear precoding scheme in the downlink, massive MIMO in Time-Division-Duplex (TDD) mode. We derive the closed-form expressions for BER that are obtained from the new expressions derived for Signal-Interference-Noise Ratio (SINR), and then analysis with different parameters using numerical and Monte Carlo simulated results is carried out in MATLAB under imperfect CSI. It was found that our theoretical analysis agrees well with the simulated results. In our analysis, BER was observed in most cases to be good when the number of Base Station (BS) antennas is large enough to accommodate the served users, but when the number of users grows up, the BER performance degrades depending on how many BS antennas are capable of handling the additional users. Also, increasing the downlink transmit power was found to improve the performance, but it is not an energy-efficient way for massive MIMO.     

Performance analysis of large-scale MIMO system for wireless backhaul network

In this paper, we present a performance analysis of large-scale multi-input multi-output (MIMO) systems for wireless backhaul networks. We focus on fully connected N nodes in a wireless meshed and multi-hop network topology. We also consider a large number of antennas at both the receiver and transmitter. We investigate the transmission schemes to support fully connected N nodes for half-duplex and full-duplex transmission, analyze the achievable ergodic sum rate among N nodes, and propose a closed-form expression of the achievable ergodic sum rate for each scheme. Furthermore, we present numerical evaluation results and compare the resuts with closed-form expressions.     

Mutual information statistics for dual MIMO systems in correlated Rayleigh fading

In this letter, we derive very simple and exact expressions for the mutual information (MI) distributions under isotropic Gaussian input of dual multiple-input multiple-output (MIMO) systems, where the minimum number of antennas at either side of the wireless link is two, in a semicorrelated Rayleigh fading environment with correlation at the dual-antenna side only. Furthermore, exact closed-form expressions for the MI moments (mean, variance), and other higher order statistics, such as the skewness and kurtosis, are derived. The proposed methodology for evaluating the MI statistics, is easily extendable to other multielement antenna settings such as single-input multiple-output (SIMO), multiple-input single-output (MISO) and dual MIMO systems for both uncorrelated and semicorrelated Rayleigh fading, where correlation can be assumed at the side with the largest number of antennas.     

Bit error rate in eigenchannels of SVD-based MIMO system

In this paper, we derive the exact closed-form expressions on the bit error rate (BER) in the individual eigenchannels of the singular value decomposition (SVD)-based multiple-input multiple-output (MIMO) system with the perfect channel state information (CSI) at both the transmitter and receiver. It is assumed that a MIMO system operates in uncorrelated Rayleigh fading environment and uses M-ary quadrature amplitude modulation (BPSK, QPSK, 16-QAM and 64-QAM). The obtained results are applicable for the systems with two eigenchannels, i.e. with M transmit and 2 receive antennas or with 2 transmit and N receive antennas. Besides the exact expressions, the corresponding high signal-to-noise ratio (SNR) approximations are also presented.     

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.     

Peroformance analysis of decode-and-forward MIMO relay channels with OSTBCs

Performance analysis is presented for multiple-input multiple-output(MIMO) relay channels employing transmit antenna diversity with orthogonal space-time block codes(OSTBCs),where the source and the destination are equipped with Ns and Nd antennas,and communicate with each other with the help of a multiple-antenna relay operating in decode-and-forward(DF) mode.Over independent,not necessarily identical Rayleigh fading channels,exact closed-form symbol error rate(SER) expressions are derived for various digi...     

Optimal antenna selection based on capacity maximization for MIMO systems in correlated channels

Recent work has shown that multiple-input multiple-output (MIMO) systems with multiple antennas at both the transmitter and receiver are able to achieve great capacity improvement. In such systems, it is desirable to select a subset of the available antennas so as to reduce the number of radio frequency (RF) chains. This paper addresses the problem of antenna selection in correlated channels. We consider a narrowband communication system with M transmit and N receive antennas. We present the criterion for selecting the optimal L/sub t/ out of M transmit and L/sub r/ out of N receive antennas in terms of capacity maximization, assuming that only the long-term channel statistics, instead of the instantaneous channel-state information, are known. Simulations will be used to validate our theoretical analysis and demonstrate that the number of required RF chains can be significantly decreased using our proposed selection strategy, while achieving even better performance than the conventional MIMO system without antenna selection.     

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