Previous studies have shown that single-user systems employing-element antenna arrays at both the transmitter and the receiver can achieve a capacity proportional to , assuming independent Rayleigh fading between antenna pairs. In this paper, we explore the capacity of dual-antenna-array systems under correlated fading via theoretical analysis and ray-tracing simulations. We derive and compare expressions for the asymptotic growth rate of capacity with antennas for both independent and correlated fading cases; the latter is derived under some assumptions about the scaling of the fading correlation structure. In both cases, the theoretic capacity growth is linear in but the growth rate is 10--20% smaller in the presence of correlated fading. We analyze our assumption of separable transmit/receive correlations via simulations based on a ray-tracing propagation model. Results show that empirical capacities converge to the limit capacity predicted from our asymptotic theory even at moderate n=16. We present results for both the cases when the transmitter does and does not know the channel realization.

This paper presents an overview of recent progress in the area of multiple-input–multiple-output (MIMO) space–time coded wireless systems. After some background on the research leading to the discovery of the enormous potential of MIMO wireless links, we highlight the different classes of techniques and algorithms proposed which attempt to realize the various benefits of MIMO including spatial multiplexing and space–time coding schemes. These algorithms are often derived and analyzed under ideal independent fading conditions. We present the state of the art in channel modeling and measurements, leading to a better understanding of actual MIMO gains. Finally, the paper addresses current questions regarding the integration of MIMO links in practical wireless systems and standards.

We provide an overview of the extensive recent results on the Shannon capacity of single-user and multiuser multiple-input multiple-output (MIMO) channels. Although enormous capacity gains have been predicted for such channels, these predictions are based on somewhat unrealistic assumptions about the underlying time-varying channel model and how well it can be tracked at the receiver, as well as at the transmitter. More realistic assumptions can dramatically impact the potential capacity gains of MIMO techniques. For time-varying MIMO channels there are multiple Shannon theoretic capacity definitions and, for each definition, different correlation models and channel information assumptions that we consider. We first provide a comprehensive summary of ergodic and capacity versus outage results for single-user MIMO channels. These results indicate that the capacity gain obtained from multiple antennas heavily depends

Abstract—This paper deals with the capacity behavior of wireless Orthogonal Frequency Division Multiplexing (OFDM)-based spatial multiplexing systems in broadband fading environments for the case where the channel is unknown at the transmitter and perfectly known at the receiver. Intro-ducing a physically motivated multiple-input multiple-output (MIMO) broadband 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 advantage 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.

We present a new model for multiple-input multiple-output (MIMO) outdoor wireless fading channels. The proposed model is more general and realistic than the usual i.i.d. model and allows 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 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 reveals the existence of "pin-hole" channels which exhibit low spatial fading correlation at both ends of the link but still have poor rank properties and hence low ergodic capacity. 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.

Multielement system capacities are usually thought of as limited only by correlations between elements. It is shown here that degenerate channel phenomena called "keyholes" may arise under realistic assumptions which have zero correlation between the entries of the channel matrix H and yet only a single degree of freedom. Canonical physical examples of keyholes are presented. For outdoor environments, it is shown that roof edge diffraction is perceived as a "keyhole" by a vertical base array that may be avoided by employing instead a horizontal base array.

We present a new model for multipleinput multiple-output (MIMO) outdoor wireless fading channels which is more general and realistic than the usual i.i.d. model. We investigate the channel capacity as a function of parameters such as the local scattering radius at the transmitter and the receiver, the distance between the transmit (TX) and receive (RX) arrays, and the antenna beamwidths and spacing. We point out the existence of "pinhole " channels which exhibit low fading correlation between antennas but still have poor rank properties and hence low capacity. Finally we show that even at long ranges high channel rank can easily be obtained under mild scattering conditions.

Abstract—This paper treats multiple-input multiple-output (MIMO) antenna subset selection employing space-time coding. We consider two cases differentiated based on the type of channel knowledge used in the selection process. We address both the selection algorithms and the performance analysis. We first consider the case when the antenna subsets are selected based on exact channel knowledge (ECK). Our results assume the transmission of orthogonal space-time block codes (with emphasis on the Alamouti code). Next, we treat the case of antenna subset selection when statistical channel knowledge (SCK) is employed by the selection algorithm. This analysis is applicable to general space-time coding schemes. When ECK is available, we show that the selection algorithm chooses the antenna set that maximizes the channel Frobenius norm leading to both coding and diversity gain. When SCK is available, the selection algorithm chooses the antenna set that maximizes the determinant of the covariance of the vectorized channel leading mostly to a coding gain. In case of ECK-based selection, we provide analytical expressions for average SNR and outage probability improvement. For the case when SCK-based selection is used, we derive expressions for coding gain. We also present extensive simulation studies, validating our results. Index Terms—Antenna subset selection, MIMO, space-time coding.

Abstract—We consider the capacity of a narrowband point to point communication system employing multiple-element antenna arrays at both the transmitter and the receiver with covariance feedback. Under covariance feedback the receiver is assumed to have perfect Channel State Information (CSI) while at the transmitter the channel matrix is modeled as consisting of zero mean complex jointly Gaussian random variables with known covariances. Specifically we assume a channel matrix with i.i.d. rows and correlated columns, a common model for downlink transmission. We determine the optimal transmit precoding strategy to maximize the Shannon capacity of such a system. We also derive closed form necessary and sufficient conditions on the spatial covariance for when the maximum capacity is achieved by beamforming. The conditions for optimality of beamforming agree with the notion of waterfilling over multiple degrees of freedom. I.

A random matrix model is introduced that probabilistically describes the spatial and temporal multi--path propagation between a transmitting and receiving antenna array with a limited number of scatterers for mobile radio and indoor environments. The model characterizes the channel by its richness delay profile which gives the number of scattering objects as a function of the path delay. Each delay is assigned the eigenvalue distribution of a random matrix that depends on the number of scatterers, receive antennas, and transmit antennas. The model allows to calculate signal--to--interference--and--noise ratios and channel capacities for large antenna arrays analytically and quantifies up to what extent rich scattering improves performance.