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.     

Spatial multiplexing with transmit antenna and constellation selection for correlated MIMO fading channels

We consider spatial multiplexing systems in correlated multiple-input multiple-output (MIMO) fading channels with equal power allocated to each transmit antenna. Under this constraint, the number and subset of transmit antennas together with the transmit symbol constellations are determined assuming knowledge of the channel correlation matrices. We first consider a fixed data rate system and vary the number of transmit antennas and constellation such that the minimum margin in the signal-to-noise ratio (SNR) is maximized for linear and Vertical Bell Laboratories Layered Space-Time (V-BLAST) receivers. We also derive transmit antenna and constellation selection criteria for a successive interference cancellation receiver (SCR) with a fixed detection order and a variable number of bits transmitted on each substream. Compared with a system using all available antennas, performance results show significant gains using a subset of transmit antennas, even for independent fading channels. Finally, we select a subset of transmit antennas to maximize data rate given a minimum SNR margin. A lower bound on the maximum outage data rate is derived. The maximum outage data rate of the SCR receiver is seen to be close to the outage channel capacity.     

Approximate capacity of OSTBC-OFDM in spatially correlated MIMO Nakagami-m fading channels

Orthogonal space-time block coding in combination with orthogonal frequency-division multiplexing converts frequency-selective multiple-input-multiple-output (MIMO) channels into a set of equivalent scalar Gaussian channels. For MIMO Nakagami-m fading channels in the presence of spatial correlation, a simple and closed-form approximation for the capacity of the equivalent channels is derived with good accuracy.     

Performance analysis of orthogonal space-time block codes in spatially correlated MIMO Nakagami fading channels

Orthogonal space-time block coding (STBC) is an open-loop transmit diversity scheme that decouples the multiple-input multiple-output (MIMO) channel, thereby reducing the space-time decoding into a scalar detection process. This characteristic of STBC makes it a powerful tool, achieving full diversity over MIMO fading channels, and requiring little computational cost for both the encoding and decoding processes. In this paper, we exploit the single-input single-output equivalency of STBC in order to analyze its performance over nonselective Nakagami fading channels in the presence of spatial fading correlation. More specifically, we derive exact closed-form expressions for the outage probability and ergodic capacity of STBC, when the latter is employed over spatially correlated MIMO Nakagami fading channels. Moreover, we derive the exact symbol error probability of coherent M-PSK and M-QAM, when these modulation schemes are used along with STBC over such fading channels. The derived formulae are then used to assess the robustness of STBC to spatial correlation by considering general MIMO correlation models and analyzing their effects on the outage probability, ergodic capacity, and symbol error probability achieved by STBC.     

MIMO Diversity in the Presence of Double Scattering

The potential benefits of multiple-antenna systems may be limited by two types of channel degradations-rank deficiency and spatial fading correlation of the channel. In this paper, we assess the effects of these degradations on the diversity performance of multiple-input multiple-output (MIMO) systems, with an emphasis on orthogonal space-time block codes (OSTBC), in terms of the symbol error probability (SEP), the effective fading figure (EFF), and the capacity at low signal-to-noise ratio (SNR). In particular, we consider a general family of MIMO channels known as double-scattering channels-i.e., Rayleigh product MIMO channels-which encompasses a variety of propagation environments from independent and identically distributed (i.i.d.) Rayleigh to degenerate keyhole or pinhole cases by embracing both rank-deficient and spatial correlation effects. It is shown that a MIMO system with transmit and receive antennas achieves the diversity of order in a double-scattering channel with effective scatterers. We also quantify the combined effect of the spatial correlation and the lack of scattering richness on the EFF and the low-SNR capacity in terms of the correlation figures of transmit, receive, and scatterer correlation matrices. We further show the monotonicity properties of these performance measures with respect to the strength of spatial correlation, characterized by the eigenvalue majorization relations of the correlation matrices.     

Spatial multiplexing in correlated fading via the virtual channel representation

Spatial multiplexing techniques send independent data streams on different transmit antennas to maximally exploit the capacity of multiple-input multiple-output (MIMO) fading channels. Most existing multiplexing techniques are based on an idealized MIMO channel model representing a rich scattering environment. Realistic channels corresponding to scattering clusters exhibit correlated fading and can significantly compromise the performance of such techniques. In this paper, we study the design and performance of spatial multiplexing techniques based on a virtual representation of realistic MIMO fading channels. Since the nonvanishing elements of the virtual channel matrix are uncorrelated, they capture the essential degrees of freedom in the channel and provide a simple characterization of channel statistics. In particular, the pairwise-error probability (PEP) analysis for correlated channels is greatly simplified in the virtual representation. Using the PEP analysis, various precoding schemes are introduced to improve performance in virtual channels. Unitary precoding is proposed to provide robustness to unknown channel statistics. Nonunitary precoding techniques are proposed to exploit channel structure when channel statistics are known at the transmitter. Numerical results are presented to illustrate the attractive performance of the precoding techniques.     

On the capacity of OFDM-based spatial multiplexing systems

This paper deals with the capacity behavior of wireless orthogonal frequency-division multiplexing (OFDM)-based spatial multiplexing systems in broad-band fading environments for the case where the channel is unknown at the transmitter and perfectly known at the receiver. Introducing a physically motivated multiple-input multiple-output (MIMO) broad-band fading channel model, we study the influence of physical parameters such as the amount of delay spread, cluster angle spread, and total angle spread, and system parameters such as the number of antennas and antenna spacing on ergodic capacity and outage capacity. We find that, in the MIMO case, unlike the single-input single-output (SISO) case, delay spread channels may provide advantages over flat fading channels not only in terms of outage capacity but also in terms of ergodic capacity. Therefore, MIMO delay spread channels will in general provide both higher diversity gain and higher multiplexing gain than MIMO flat fading channels     

Outdoor MIMO wireless channels: models and performance prediction

We present a new model for multiple-input-multiple-output (MIMO) outdoor wireless fading channels and their capacity performance. The proposed model is more general and realistic than the usual independent and identically distributed (i.i.d.) model, and allows us to investigate the behavior of channel capacity as a function of the scattering radii at transmitter and receiver, distance between the transmit and receive arrays, and antenna beamwidths and spacing. We show how the MIMO capacity is governed by spatial fading correlation and the condition number of the channel matrix through specific sets of propagation parameters. The proposed model explains the existence of "pinhole" channels which exhibit low spatial fading correlation at both ends of the link but still have poor rank properties, and hence, low ergodic capacity. In fact, the model suggests the existence of a more general family of channels spanning continuously from full rank i.i.d. to low-rank pinhole cases. We suggest guidelines for predicting high rank (and hence, high ergodic capacity) in MIMO channels, and show that even at long ranges, high channel rank can easily be sustained under mild scattering conditions. Finally, we validate our results by simulations using ray tracing techniques. Connections with basic antenna theory are made.     

MIMO Precoder Designs for Frequency-Selective Fading Channels Using Spatial and Path Correlation

Multiple-input–multiple-output (MIMO) precoder design for frequency-selective fading channels using partial channel information based on the spatial and path correlation matrices is presented. By representing a frequency-selective fading channel as a multipath model with $L$ effective paths, a general precoding structure is proposed and used to derive optimum precoding designs that maximize Jensen's upper bound on the channel ergodic capacity under the transmitted power constraint for two cases, i.e., uncorrelated and correlated channel paths. Analytical results show that, in the uncorrelated case, the precoder structure consists of a number of parallel precoders for frequency-flat fading channels. The power assignment to each precoder and the power allocation over the eigenmodes of each precoder are calculated based on the power of channel paths and the eigenvalues of the transmit correlation matrix. In the correlated case, the precoder structure is an eigenbeamformer with the beams referred to a function of eigenvectors of the Kronecker product of path and transmit correlation matrices. Furthermore, the power allocated to each eigenmode can be obtained from a statistical water-pouring policy that is specified by the product of eigenvalues of the transmit antenna and path correlation matrices. Simulation results for different scenarios indicate that the proposed precoder can increase the ergodic capacity of MIMO systems in a frequency-selective fading environment with spatial and path correlations, and its offered capacity gain is increased with the level of correlation and numbers of antennas and channel paths.      

Spatially and temporally correlated MIMO channels: modeling and capacity analysis

Wireless communication systems employing multiple antennas at both the transmitter and receiver have been shown to offer significant gains over single-antenna systems. Recent studies on the capacity of multiple-input-multiple-output (MIMO) channels have focused on the effect of spatial correlation. The joint effect of spatial and temporal correlation has not been well studied. In this paper, a geometric MIMO channel model is presented, which considers motion of the receiver and nonisotropic scattering at both ends of the radio link. A joint space-time cross-correlation function is derived from this model and variates with this joint correlation are generated by using the vector autoregressive stochastic model. The outage capacity of this channel is considered where the effects of antenna spacing, antenna array angle, degree of nonisotropic scattering, and receiver motion are investigated. When n transmit and n receive antennas are employed, it is shown that the outage capacity still increases linearly with respect to n, despite the presence of spatial and temporal correlation. Furthermore, analytical expressions are derived for the ergodic capacity of a MIMO channel for the cases of spatial correlation at one end and at both ends of the radio link. The latter case does not lend itself to numerical evaluation, but the former case is shown to be accurate by comparison with simulation results. The proposed analysis is very general, as it is based on the transmit and receive antenna correlations matrices.     

Mutual Information of Multiple-Input Multiple-Output (MIMO) Transmission Schemes

We analyze the mutual information of some common multiple-input multiple-output (MIMO) transmission schemes. Whereas most capacity evaluations are done under the assumption of Gaussian transmit symbols, we take into account restrictions on the transmit symbol alphabet and analyze real world signal constellations. Moreover, we include suboptimum detectors which might be applied in practical systems in the capacity evaluation. Furthermore, we consider not only spatially uncorrelated full rank channels but also channel degradations such as spatial correlation and keyhole effects. The results show that in many practical relevant cases, simple space-time block codes are a robust solution which achieves similar, sometimes even better capacities than spatial multiplexing even though they do not exploit all available MIMO dimensions.     

同信道干扰下相关多输入多输出信道容量分析

在Rayleigh衰落环境下,研究了具有同信道干扰的多输入多输出(MIMO)信道容量问题,分析了通信用户发送端带有空间相关性的情况。假设接收端完美地知道信道状态信息而发送端不知道,基于矩阵变量分布理论,推导出MIMO信道互信息之矩生成函数的精确闭式表达式。利用该表达式进一步推导出MIMO遍历信道容量的精确表达式。用数值结果验证了分析结果的正确性,并给出各种参数对遍历信道容量的影响。     

Introducing Space into MIMO Capacity Calculations

The large spectral efficiencies promised for multiple-input multiple-output (MIMO) wireless fading channels are derived under certain conditions which do not fully take into account the spatial aspects of the channel. Spatial correlation, due to limited angular spread or insufficient antenna spacing, significantly reduces the performance of MIMO systems. In this paper we explore the effects of spatially selective channels on the capacity of MIMO systems via a new capacity expression which is more general and realistic than previous expressions. By including spatial information we derive a closed-form expression for ergodic capacity which uses the physics of signal propagation combined with the statistics of the scattering environment. This expression gives the capacity of a MIMO system in terms of antenna placement and scattering environment and leads to valuable insights into the factors determining capacity for a wide range of scattering models.     

Degrees of freedom in some underspread MIMO fading channels

Consider a multiple-input multiple-output (MIMO) fading channel in which the fading process varies slowly over time. Assuming that neither the transmitter nor the receiver have knowledge of the fading process, do multiple transmit and receive antennas provide significant capacity improvements at high signal-to-noise ratio (SNR)? For regular fading processes, recent results show that capacity ultimately grows doubly logarithmically with the SNR independently of the number of transmit and receive antennas used. We show that for the Gauss-Markov fading process in all regimes of practical interest the use of multiple antennas provides large capacity improvements. Nonregular fading processes show completely different high-SNR behaviors due to the perfect predictability of the process from noiseless observations. We analyze the capacity of MIMO channels with nonregular fading by presenting a lower bound, which we specialize to the case of band-limited slowly varying fading processes to show that the use of multiple antennas is still highly beneficial. In both cases, regular and nonregular fading, this capacity improvement can be seen as the benefit of having multiple spatial degrees of freedom. For the Gauss-Markov fading model and all regimes of practical interest, we present a communication scheme that achieves the full number of degrees of freedom of the channel with tractable complexity. Our results for underspread Gauss-Markov and band-limited nonregular fading channels suggest that multiple antennas are useful at high SNR.     

Adaptive MIMO Transmission for Exploiting the Capacity of Spatially Correlated Channels

We consider a novel low-complexity adaptive multiple-input multiple-output (MIMO) transmission technique. The approach is based on switching between low-complexity transmission schemes, including statistical beamforming, double space-time transmit diversity, and spatial multiplexing, depending on the changing channel statistics, as a practical means of approaching the spatially correlated MIMO channel capacity. We first derive new ergodic capacity expressions for each MIMO transmission scheme in spatially correlated channels. Based on these results, we demonstrate that adaptive switching between MIMO schemes yields significant capacity gains over fixed transmission schemes. We also derive accurate analytical approximations for the optimal signal-to-noise-ratio switching thresholds, which correspond to the crossing-points of the capacity curves. These thresholds are shown to vary, depending on the spatial correlation, and are used to identify key switching parameters. Finally, we propose a practical switching algorithm that is shown to yield significant spectral efficiency improvements over nonadaptive schemes for typical channel scenarios     

On spectral efficiency of low-complexity adaptive MIMO systems in Rayleigh fading channel

Adaptive MQAM modulation is used to maximize spectral efficiency of Multiple-Input Multiple-Output (MIMO) systems while keeping bit error rate (BER) under a target level. Closed-form expressions of the average spectral efficiency, coined as discrete-rate spectral efficiency (DRSE), are derived for adaptive modulation MIMO systems using different algorithms. To further enhance the spectral efficiency, a low complexity adaptation scheme is suggested to switch across different algorithms based on the DRSE. In the current letter, we investigate the adaptation scheme that switches between Orthogonal Space-Time Block Codes (OSTBC) and spatial multiplexing with zero-forcing (ZF) detection for MIMO systems with two transmit antennas. Two types of operating environment are considered: flat Rayleigh fading channel without spatial correlation and spatially correlated Rayleigh fading channel with transmit correlation.     

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.     

The impact of fading correlation on the error performance of MIMO systems over Rayleigh fading channels

This paper analyzes the impact of receive fading correlation on the error performance of a multiple-input multiple-output (MIMO) system that employs a zero-forcing detection scheme over frequency-nonselective Rayleigh fading channels. Error rate expressions as a function of the eigenvalues of the fading correlation matrix and the number of transmit and receive antennas are derived. Numerical results indicate that MIMO systems are resistant to receive fading correlation.     

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     

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.