Wireless Communications

The use of space-division multiple access (SDMA) in the downlink of a multiuser multiple-input, multiple-output (MIMO) wireless communications network can provide a substantial gain in system throughput. The challenge in such multiuser systems is designing transmit vectors while considering the co-channel interference of other users. Typical optimization problems of interest include the capacity problem - maximizing the sum information rate subject to a power constraint-or the power control problem-minimizing transmitted power such that a certain quality-of-service metric for each user is met. Neither of these problems possess closed-form solutions for the general multiuser MIMO channel, but the imposition of certain constraints can lead to closed-form solutions. This paper presents two such constrained solutions. The first, referred to as "block-diagonalization," is a generalization of channel inversion when there are multiple antennas at each receiver. It is easily adapted to optimize for either maximum transmission rate or minimum power and approaches the optimal solution at high SNR. The second, known as "successive optimization," is an alternative method for solving the power minimization problem one user at a time, and it yields superior results in some (e.g., low SNR) situations. Both of these algorithms are limited to cases where the transmitter has more antennas than all receive antennas combined. In order to accommodate more general scenarios, we also propose a framework for coordinated transmitter-receiver processing that generalizes the two algorithms to cases involving more receive than transmit antennas. While the proposed algorithms are suboptimal, they lead to simpler transmitter and receiver structures and allow for a reasonable tradeoff between performance and complexity.

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Zero-forcing methods for downlink spatial multiplexing in multiuser MIMO channels

We provide an overview of the extensive 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 on the available channel information at either the receiver or transmitter, the channel signal-to-noise ratio, and the correlation between the channel gains on each antenna element. We then focus attention on the capacity region of the multiple-access channels (MACs) and the largest known achievable rate region for the broadcast channel. In contrast to single-user MIMO channels, capacity results for these multiuser MIMO channels are quite difficult to obtain, even for constant channels. We summarize results for the MIMO broadcast and MAC for channels that are either constant or fading with perfect instantaneous knowledge of the antenna gains at both transmitter(s) and receiver(s). We show that the capacity region of the MIMO multiple access and the largest known achievable rate region (called the dirty-paper region) for the MIMO broadcast channel are intimately related via a duality transformation. This transformation facilitates finding the transmission strategies that achieve a point on the boundary of the MIMO MAC capacity region in terms of the transmission strategies of the MIMO broadcast dirty-paper region and vice-versa. Finally, we discuss capacity results for multicell MIMO channels with base station cooperation. The base stations then act as a spatially diverse antenna array and transmission strategies that exploit this structure exhibit significant capacity gains. This section also provides a brief discussion of system level issues associated with MIMO cellular. Open problems in this field abound and are discussed throughout the paper.

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Capacity limits of MIMO channels

Random matrix theory has found many applications in physics, statistics and engineering since its inception. Although early developments were motivated by practical experimental problems, random matrices are now used in fields as diverse as Riemann hypothesis, stochastic differential equations, condensed matter physics, statistical physics, chaotic systems, numerical linear algebra, neural networks, multivariate statistics, information theory, signal processing and small-world networks. This article provides a tutorial on random matrices which provides an overview of the theory and brings together in one source the most significant results recently obtained. Furthermore, the application of random matrix theory to the fundamental limits of wireless communication channels is described in depth.

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Random Matrix Theory and Wireless Communications

Space-time codes (STC) are a class of signaling techniques, offering coding and diversity gains along with improved spectral efficiency. These codes exploit both the spatial and the temporal diversity of the wireless link by combining the design of the error correction code, modulation scheme and array processing. STC are well suited for improving the downlink performance, which is the bottleneck in asymmetric applications such as downstream Internet. Three original contributions to the area of STC are presented in this dissertation. First, the development of analytic tools that determine the fundamental limits on the performance of STC in a variety of channel conditions. For trellis-type STC, transfer function based techniques are applied to derive performance bounds over Rayleigh, Rician and correlated fading environments. For block-type STC, an analytic framework that supports various complex orthogonal designs with arbitrary signal cardinalities and array configurations is developed. In the second part of the dissertation, the Virginia Tech Space-Time Advanced Radio (VT-STAR) is designed, introducing a multi-antenna hardware laboratory test bed, which facilitates characterization of the multiple-input multiple-output (MIMO) channel and validation of various space-time approaches. In the third part of the dissertation, two novel space-time architectures paired with iterative processing principles are proposed. The first scheme extends the suitability of STC to outdoor wireless communications by employing iterative equalization/decoding for time dispersive channels and the second scheme employs iterative interference cancellation/decoding to solve the error propagation problem of Bell-Labs Layered Space-Time Architecture (BLAST). Results show that remarkable energy and spectral efficiencies are achievable by combining concepts drawn from space-time coding, multiuser detection, array processing and iterative decoding.

Space-Time Codes for High Data Rate Wireless Communications

Information theory research has shown that the rich-scattering wireless channel is capable of enormous theoretical capacities if the multipath is properly exploited In this paper, we describe a wireless communication architecture known as vertical BLAST (Bell Laboratories Layered Space-Time) or V-BLAST, which has been implemented in real-time in the laboratory Using our laboratory prototype, we have demonstrated spectral efficiencies of 20-40 bps/Hz in an indoor propagation environment at realistic SNRs and error rates To the best of our knowledge, wireless spectral efficiencies of this magnitude are unprecedented and are furthermore unattainable using traditional techniques

V-BLAST: an architecture for realizing very high data rates over the rich-scattering wireless channel

Narrowband multiple-input-multiple-output (MIMO) measurements using 16 transmitters and 16 receivers at 2.11 GHz were carried out in Manhattan. High capacities were found for full, as well as smaller array configurations, all within 80% of the fully scattering channel capacity. Correlation model parameters are derived from data. Spatial MIMO channel capacity statistics are found to be well represented by the separate transmitter and receiver correlation matrices, with a median relative error in capacity of 3%, in contrast with the 18% median relative error observed by assuming the antennas to be uncorrelated. A reduced parameter model, consisting of 4 parameters, has been developed to statistically represent the channel correlation matrices. These correlation matrices are, in turn, used to generate H matrices with capacities that are consistent within a few percent of those measured in New York. The spatial channel model reported allows simulations of H matrices for arbitrary antenna configurations. These channel matrices may be used to test receiver algorithms in system performance studies. These results may also be used for antenna array design, as the decay of mobile antenna correlation with antenna separation has been reported here. An important finding for the base transmitter array was that the antennas were largely uncorrelated even at antenna separations as small as two wavelengths.

Multiple-input-multiple-output measurements and modeling in Manhattan

This paper presents analysis for spatial and temporal variations of multiple-input-multiple-output (MIMO) channels at the mobile. The channel study is based on the narrowband measurements at 2.11 GHz in Manhattan, New York with 16 transmitting antennas and 16 receiving antennas. Doppler spread and angle of arrival (AOA) are derived from the temporal correlation of field components. The results show that the AOA at the mobile is not uniformly distributed. The restricted AOA distribution results in approximately twice the correlation distance and correlation time than the predicted values from the Jakes (1974) model. The measured median coherence time is at least a few seconds for stationary channels, and 90 ms at a mobile pedestrian speed of 3 km/hr. These observations hold for both vertically and horizontally polarized antennas. The measured median RMS angular spread at the mobile is 22.5/spl deg/ for horizontally polarized antennas and 25.5/spl deg/ for vertically polarized antennas.

Spatial and temporal variations of MIMO channels and impacts on capacity

The capacity advantage of multiple input-multiple output (MIMO) channels lays in the decomposition of the channel into several spatial sub-channels. Knowledge of the channel at the transmitter can further increase the system capacity. This effect has been theoretically demonstrated. Here we illustrate the potential of channel state information (CSI) at the transmitter using actual channel measurements of a system with 4 transmitters and 4 receivers in an indoor environment, under line-of-sight and non line-of-sight conditions, considering both infinite and finite allowable modulation sizes. We show that CSI at the transmitter is more beneficial in the case of low signal to noise ratio and in cases where the channel richness is limited. In terms of achievable spectral efficiency, 60% of the theoretical capacity can be obtained without advanced coding techniques, as long as eigen mode transmission is used, and the performance is similar for all power and rate allocation schemes that we investigate

P.W. Wolniansky

Papers

V-BLAST: an architecture for realizing very high data rates over the rich-scattering wireless channel

Multiple-input-multiple-output measurements and modeling in Manhattan

Spatial and temporal variations of MIMO channels and impacts on capacity

Capacity and Rate Performance of MIMO Systems with Channel State Information at the Transmitter