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.     

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.     

Capacity scaling and spectral efficiency in wide-band correlated MIMO channels

The dramatic linear increase in ergodic capacity with the number of antennas promised by multiple-input multiple-output (MIMO) wireless communication systems is based on idealized channel models representing a rich scattering environment. Is such scaling sustainable in realistic scattering scenarios? Existing physical models, although realistic, are intractable for addressing this problem analytically due to their complicated nonlinear dependence on propagation path parameters, such as the angles of arrival and delays. In this paper, we leverage a recently introduced virtual representation of physical models that is essentially a Fourier series representation of wide-band MIMO channels in terms of fixed virtual angles and delays. Motivated by physical considerations, we propose a D-connected model for correlated channels defined by a virtual spatial channel matrix consisting of D nonvanishing diagonals with independent and identically distributed (i.i.d.) Gaussian entries. The parameter D provides a meaningful and tractable measure of the richness of scattering. We derive general bounds for the coherent ergodic capacity and investigate capacity scaling with the number of antennas and bandwidth. In the large antenna regime, we show that linear capacity scaling is possible if D scales linearly with the number of antennas. This, in turn, is possible if the number of resolvable paths grows quadratically with the number of antennas. The capacity saturates for linear growth in the number of paths (fixed D). The ergodic capacity does not depend on frequency selectivity of the channel in the wide-band case. Increasing bandwidth tightens the bounds and hastens the convergence of scaling behavior. For large bandwidth, the capacity scales linearly with the signal-to-noise ratio (SNR) as well. We also provide an explicit characterization of the wide-band slope recently proposed by Verdu. Numerical results are presented to illustrate the key theoretical results.     

平坦衰落环境中多输入多输出系统衰落相关与信道容量研究

为分析模型物理参数和天线排列方式对多输入多输出系统信道容量的影响,提出了一种平坦衰落环境中信道容量的研究方法。该方法基于接收均匀圆阵和均匀线阵分别构建了蕴含模型物理参数的相关矩阵,并利用Wishart分布的性质推导了信道容量上下限。该方法回避了求取衰落相关矩阵特征值的概率密度函数,降低了运算量;可被推广到多天线-频分复用系统。仿真结果表明,天线间距较小时,采用均匀圆阵比均匀线阵的系统信道容量要高;天线间距增大到一定程度后,系统信道容量达到饱和。散射角越大,信道容量的增长速率越快且采用均匀线阵比均匀圆阵系统的信道容量高。接收信噪比较大时,平均信道容量上下限基本接近其实际值。     

On the Ergodic Capacity of Rank-1 Ricean-Fading MIMO Channels

This paper investigates the ergodic capacity of Ricean-fading multiple-input-multiple-output (MIMO) channels with rank-1 mean matrices under the assumption that the channel is unknown at the transmitter and perfectly known at the receiver. After introducing the system model and the concept of ergodic capacity of MIMO channels, we derive the explicit expressions for the expected values of the determinant and log-determinant of complex noncentral Wishart matrices. Subsequently, we obtain new upper and lower bounds on the ergodic capacity of rank-1 Ricean-fading MIMO channels at any signal-to-noise ratio (SNR). We show that our bounds are tighter than previously reported analytical bounds, and discuss the impact of spatial fading correlation and Ricean K-factor with the help of these bounds. Furthermore, we extend the analysis of ergodic capacity to frequency selective spatially correlated Ricean-fading MIMO channels. We demonstrate that the calculation of ergodic capacity of frequency selective fading MIMO channels can be converted to the calculation of the one of equivalent frequency flat-fading MIMO channels. Finally, we present numerical results that confirm the theoretical analysis     

室内MIMO系统采用极化分集时的信道容量

典型的室内传播信道为莱斯衰落信道,可将其分解为LOS传播信道和散射信道.本文假设散射信道为瑞利衰落信道,并根据天线的极化特性,给出了存在极化分集时的LOS传播信道.基于此,本文提出了室内MIMO系统采用极化分集时的信道模型.研究表明:极化分集可以有效提高MIMO信道容量.     

基于双端莱斯相关几何信道模型的MIMO系统容量界研究

MIMO system can provide higher capacity in independent conditions. When the spatial-temporal fading correlation exists, the capacity may decrease. In this paper, the geometrical MIMO channel model is presented with Rician factor. Based on the MIMO ergodic capacity, the capacity bounds are derived with arbitrary finite number of antennas.The bounds are derived in the exact expressions in doubly correlated MIMO Rician channel. Then a simple expression for the capacity bounds is attained for the high SNR. Finally, the tightness of derived bounds is verified by Monte Carlo simulation.     

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。     

Exact capacity distribution for dual MIMO systems in Ricean fading

It is well known that multiple input multiple output (MIMO) systems offer the promise of achieving very high spectrum efficiencies (many tens of bit/s/Hz) in a mobile environment. The gains in MIMO capacity are sensitive to the type of channel encountered in the radio environment. To date most analytical work has concentrated on Rayleigh fading channels. Hence, in this letter we consider the capacity outage performance of MIMO systems in Ricean channels. Due to analytical complexity we concentrate on dual antenna systems (either two transmit or two receive antennas) and derive exact densities and distribution functions for the capacity.     

On the bounds of frequency-selective channel capacity with doubly correlated geometrical MIMO channel model

The multi-input multi-output (MIMO) technology plays an important role in link transmissions. This article considers the general case for the ergodic capacity in doubly correlated frequency-selective MIMO channel. In the study, the geometrical MIMO channel model is presented. Based on the formula of MIMO ergodic capacity, the capacity limits are studied with arbitrary finite number of antennas in the frequency-selective MIMO channel. It first derives the exact expressions for the upper bound and lower bound in doubly correlated MIMO channel. The results for the single-ended correlation and independent identically distributed (i.i.d.) MIMO channel are also obtained as special cases. Then the simple expressions of the capacity bounds are attained at high SNR. Finally, results are provided by Monte Carlo simulations to verify the tightness of the derived bounds.     

An Investigation of MIMO Performance in the Indoor Ricean Environment

In this paper, we investigate the Multiple-Input Multiple-Output (MIMO) channel capacity in indoor Ricean channels based on MIMO channel measurements at 2.45 GHz. The measured data is analysed using a super resolution parameter estimation algorithm. Our results demonstrate that the line-of-sight (LOS) component in a Ricean scenario influences indoor MIMO performance through increased spatial correlation between array elements. We found that indoor channels with higher values of Ricean K factor have smaller numbers of effective multipath components and increased spatial correlation. Measurement results also showed that, the effect of varying antenna height on indoor MIMO capacity is also due to the spatial correlation of multipath propagation and has a close relationship with the separation between the transmitter and receiver. Zhongwei Tang is currently with the Wireless Technologies Laboratory at CSIRO. He was with Microwave and Wireless Technology Research Laboratory (MWTRL), Information and Communication Group, Faculty of Engineering of the University of Technology Sydney, Australia, where he pursued his Ph.D. Degree. His current research interests include RF propagation, MIMO Space-Time channel measurements, characterization and channel modelling, smart antennas, MIMO systems and array signal processing. Ananda S. Mohan is currently a member of the Faculty of Engineering, University of Technology, Sydney (UTS), Australia where he leads research on antennas, microwaves, wave propagation, and wireless technology. He received a Ph.D. degree in electrical communication engineering from the Indian Institute of Technology, Kharagpur, India and was a Scientist and Senior Scientist at the Research and Training Unit for Navigational Electronics, Hyderabad, India. At UTS, he directed the Sydney microwave design resource centre and was the associate program leader of the co-operative research centre for satellite systems. He currently directs the microwave and wireless technology research laboratory and a core member of the university research centre on health technologies. His current teaching and research interests include wireless mobile communications, microwaves and antennas, smart antennas and applications of microwave and wireless technology in medicine and has obtained many competitive research grants in these areas. Dr. Mohan was a co-recipient of the Priestly memorial award from the Institute of Radio and Electronic Engineers (IREE), Australia. He was a member of the organizing and technical Program Committees of the IEEE Globecom'98, APMC 2000, and International Symposium on Wireless Systems and Networks, 2003 and IASTED International Conference on Antennas, Radar, and Wave Propagation, for 2004 and 2005.     

On the capacity of MIMO relay channels

We study the capacity of multiple-input multiple- output (MIMO) relay channels. We first consider the Gaussian MIMO relay channel with fixed channel conditions, and derive upper bounds and lower bounds that can be obtained numerically by convex programming. We present algorithms to compute the bounds. Next, we generalize the study to the Rayleigh fading case. We find an upper bound and a lower bound on the ergodic capacity. It is somewhat surprising that the upper bound can meet the lower bound under certain regularity conditions (not necessarily degradedness), and therefore the capacity can be characterized exactly; previously this has been proven only for the degraded Gaussian relay channel. We investigate sufficient conditions for achieving the ergodic capacity; and in particular, for the case where all nodes have the same number of antennas, the capacity can be achieved under certain signal-to-noise ratio (SNR) conditions. Numerical results are also provided to illustrate the bounds on the ergodic capacity of the MIMO relay channel over Rayleigh fading. Finally, we present a potential application of the MIMO relay channel for cooperative communications in ad hoc networks.     

28 GHz MIMO无线信道特性分析与研究

基于室内视距(Line-of-Sight,LOS)和非视距(Non-Line-of-Sight,NLOS)无线信道测量数据,研究了28 GHz多输入多输出(Multiple-Input Multiple-Output,MIMO)信道参数和容量特性.具体地说,分析了莱斯K因子、时延扩展、出发角和到达角的角度扩展等信道参数,研究了MIMO信道容量及空间相关性对容量的影响.结果表明:莱斯K因子、时延扩展以及角度扩展值取决于测量环境及场景;LOS条件下时延扩展的累积分布函数(Cumulative Distribution Function,CDF)曲线与正态分布拟合优于NLOS条件下的数据;MIMO天线空间相关性越大信道容量越小.本文结果可为28 GHz无线通信系统设计提供有用信息.     

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.     

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.     

Multiple-antenna channel hardening and its implications for rate feedback and scheduling

Wireless data traffic is expected to grow over the next few years and the technologies that will provide data services are still being debated. One possibility is to use multiple antennas at base stations and terminals to get very high spectral efficiencies in rich scattering environments. Such multiple-input/multiple-output (MIMO) channels can then be used in conjunction with scheduling and rate-feedback algorithms to further increase channel throughput. This paper provides an analysis of the expected gains due to scheduling and bits needed for rate feedback. Our analysis requires an accurate approximation of the distribution of the MIMO channel mutual information. Because the exact distribution of the mutual information in a Rayleigh-fading environment is difficult to analyze, we prove a central limit theorem for MIMO channels with a large number of antennas. While the growth in average mutual information (capacity) of a MIMO channel with the number of antennas is well understood, it turns out that the variance of the mutual information can grow very slowly or even shrink as the number of antennas grows. We discuss implications of this "channel-hardening" result for data and voice services, scheduling, and rate feedback. We also briefly discuss the implications when shadow fading effects are included.     

General Capacity Bounds for Spatially Correlated Rician MIMO Channels

This paper considers the capacity of spatially correlated Rician multiple-input multiple-output (MIMO) channels. We consider the general case with double-sided correlation and arbitrary rank channel means. We derive tight upper and lower bounds on the ergodic capacity. In the particular cases when the numbers of transmit and receive antennas are equal, or when the correlation is single sided, we derive more specific bounds which are computationally efficient. The bounds are shown to reduce to known results in cases of independent and identically distributed (i.i.d.) and correlated Rayleigh MIMO channels. We also analyze the outage characteristics of the correlated Rician MIMO channels at high signal-to-noise ratio (SNR). We derive the mean and variance of the mutual information and show that it is well approximated by a Gaussian distribution. Finally, we present numerical results which show the effect of the antenna configuration, correlation level (angle spreads), Rician$K$-factor, and the geometry of the dominant Rician paths.     

On the capacity formula for multiple input-multiple output wirelesschannels: a geometric interpretation

The capacity of multiple input, multiple output (MIMO) wireless channels is computed for Ricean channels. The novelty is a geometrical (ray-tracing) interpretation of the MIMO channel capacity formula to find array geometries which greatly enhance channel capacity compared to single input-single output (SISO) systems     

动态MIMO散射无线信道模型及性能分析

基于多入多出(MIMO)散射无线信道模型,提出一种动态MIMO散射无线信道模型,分析散射体及其收发多天线的运动对MIMO无线信道空域相关性及其容量的影响,得出这种影响是由收发天线的初始位置、运动速度及其传播环境决定的.数值模拟验证了这种影响,并指出空域相关性随天线单元间距增大而减小,随散射信号角度扩展增大不是一致减小,存在使相关性达最小的角度扩展值.     

Characterizing the statistical properties of mutual information in MIMO channels

We consider Gaussian multiple-input multiple-output (MIMO) frequency-selective spatially correlated fading channels, assuming that the channel is unknown at the transmitter and perfectly known at the receiver. For Gaussian codebooks, using results from multivariate statistics, we derive an analytical expression for a tight lower bound on the ergodic capacity of such channels at any signal-to-noise ratio (SNR). We show that our bound is tighter than previously reported analytical lower bounds, and we proceed to analytically quantify the impact of spatial fading correlation on ergodic capacity. Based on a closed-form approximation of the variance of mutual information in correlated flat-fading MIMO channels, we provide insights into the multiplexing-diversity tradeoff for Gaussian code books. Furthermore, for a given total number of antennas, we consider the problem of finding the optimal (ergodic capacity maximizing) number of transmit and receive antennas, and we reveal the SNR-dependent nature of the maximization strategy. Finally, we present numerical results and comparisons between our capacity bounds and previously reported bounds.