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 have provided a review of some recent results on the emerging technology of MIMO radar with colocated antennas. We have shown that the waveform diversity offered by such a MIMO radar system enables significant superiority over its phased-array counterpart, including much improved parameter identifiability, direct applicability of adaptive techniques for parameter estimation, as well as superior flexibility of transmit beampattern designs. We hope that this overview of our recent results on the MIMO radar, along with the related results obtained by our colleagues, will stimulate the interest deserved by this topic in both academia and government agencies as well as industry.

MIMO Radar with Colocated Antennas

MIMO (multiple-input multiple-output) radar refers to an architecture that employs multiple, spatially distributed transmitters and receivers. While, in a general sense, MIMO radar can be viewed as a type of multistatic radar, the separate nomenclature suggests unique features that set MIMO radar apart from the multistatic radar literature and that have a close relation to MIMO communications. This article reviews some recent work on MIMO radar with widely separated antennas. Widely separated transmit/receive antennas capture the spatial diversity of the target's radar cross section (RCS). Unique features of MIMO radar are explained and illustrated by examples. It is shown that with noncoherent processing, a target's RCS spatial variations can be exploited to obtain a diversity gain for target detection and for estimation of various parameters, such as angle of arrival and Doppler. For target location, it is shown that coherent processing can provide a resolution far exceeding that supported by the radar's waveform.

MIMO Radar with Widely Separated Antennas

http://www.eecs.northwestern.edu/~peters/references/LocalizationTechniquesMaoAustralia.pdf

Wireless sensor network localization techniques

A new array geometry, which is capable of significantly increasing the degrees of freedom of linear arrays, is proposed. This structure is obtained by systematically nesting two or more uniform linear arrays and can provide O(N2) degrees of freedom using only N physical sensors when the second-order statistics of the received data is used. The concept of nesting is shown to be easily extensible to multiple stages and the structure of the optimally nested array is found analytically. It is possible to provide closed form expressions for the sensor locations and the exact degrees of freedom obtainable from the proposed array as a function of the total number of sensors. This cannot be done for existing classes of arrays like minimum redundancy arrays which have been used earlier for detecting more sources than the number of physical sensors. In minimum-input-minimum-output (MIMO) radar, the degrees of freedom are increased by constructing a longer virtual array through active sensing. The method proposed here, however, does not require active sensing and is capable of providing increased degrees of freedom in a completely passive setting. To utilize the degrees of freedom of the nested co-array, a novel spatial smoothing based approach to DOA estimation is also proposed, which does not require the inherent assumptions of the traditional techniques based on fourth-order cumulants or quasi stationary signals. As another potential application of the nested array, a new approach to beamforming based on a nonlinear preprocessing is also introduced, which can effectively utilize the degrees of freedom offered by the nested arrays. The usefulness of all the proposed methods is verified through extensive computer simulations.

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Nested Arrays: A Novel Approach to Array Processing With Enhanced Degrees of Freedom

In this paper, radar is discussed in the context of a multiple-input multiple-output (MIMO) system model. A comparison is made between MIMO wireless communication and MIMO radar. Examples are given showing that many traditional radar approaches can be interpreted within a MIMO context. Furthermore, exploiting this MIMO perspective, useful extensions to traditional radar can be constructed. Performance advantages in terms of degrees of freedom and resolution are discussed. Finally, a MlMO extension to space-time adaptive processing (STAP) is introduced as applied to ground moving-target indication (GMTI).

Multiple-input multiple-output (MIMO) radar and imaging: degrees of freedom and resolution

A multi-input multi-output (MIMO) radar system, unlike standard phased-array radar, can transmit via its antennas multiple probing signals that may be correlated or uncorrelated with each other. This waveform diversity offered by MIMO radar enables superior capabilities compared with a standard phased-array radar. One of the common practices in radar has been range compression. We first address the question of ldquoto compress or not to compressrdquo by considering both the Cramer-Rao bound (CRB) and the sufficient statistic for parameter estimation. Next, we consider MIMO radar waveform optimization for parameter estimation for the general case of multiple targets in the presence of spatially colored interference and noise. We optimize the probing signal vector of a MIMO radar system by considering several design criteria, including minimizing the trace, determinant, and the largest eigenvalue of the CRB matrix. We also consider waveform optimization by minimizing the CRB of one of the target angles only or one of the target amplitudes only. Numerical examples are provided to demonstrate the effectiveness of the approaches we consider herein.

Range Compression and Waveform Optimization for MIMO Radar: A CramÉr–Rao Bound Based Study

The application of multiple-input multiple-output (MIMO) techniques to multistage radar offers a number of advantages, including improved resolution and sensitivity. Depending upon the radar's mode of operation, the array design and the environment, these advantages may or may not be significant. In this paper, a simple analytic model for ground moving target indicator (GMTI) radar detection is presented and its predictions are compared with simulation. Conventional single-input multiple output (SIMO) and MIMO GMTI radars are compared in terms of minimum detectable velocity, area-search rates and array sidelobes. Optimal waveform cross-correlation matrices are identified for MIMO radars, given different performance criteria. Finally, bounds are developed for MIMO arrays with uniformly sampled virtual apertures.

Multiple-input multiple-output (MIMO) radar: performance issues

In this paper, waveform optimization for multiple- input multiple-output (MIMO) radar systems is considered. Two types of waveform optimization are studied for static radar envi- ronments. Firstly, image-energy optimization using environmen- tally adaptive waveform design is considered. Secondly, waveform optimization for angle estimation in clutter-free environments is treated using Cramer-Rao bounds.

Waveform Correlation and Optimization Issues for MIMO Radar

Wireless communication using multiple-input multiple-output (MIMO) systems enables increased spectral efficiency for a given total transmit power. Increased capacity is achieved by introducing additional spatial channels that are exploited using space-time coding. In this paper, the environmental factors that affect MIMO capacity are surveyed. These factors include channel complexity, external interference, and channel estimation error. The maximum spectral efficiency of MIMO systems in which both transmitter and receiver know the channel (using channel estimate feedback) is compared with MIMO systems in which only the receiver knows the channel. Channel complexity is studied using both simple stochastic physical scattering and asymptotic large random matrix models. Both uncooperative (worst-case) and cooperative (amenable to multiuser detection) interference are considered. An analysis for capacity loss associated with channel estimation error at the transmitter is introduced.

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K.W. Forsythe

Papers

Multiple-input multiple-output (MIMO) radar and imaging: degrees of freedom and resolution

Range Compression and Waveform Optimization for MIMO Radar: A CramÉr–Rao Bound Based Study

Multiple-input multiple-output (MIMO) radar: performance issues

Waveform Correlation and Optimization Issues for MIMO Radar

Environmental issues for MIMO capacity