Petre Stoica

MUSIC, maximum likelihood, and Cramer-Rao bound

The performance of the MUSIC and ML methods is studied, and their statistical efficiency is analyzed. The Cramer-Rao bound (CRB) for the estimation problems is derived, and some useful properties of the CRB covariance matrix are established. The relationship between the MUSIC and ML estimators is investigated as well. A numerical study is reported of the statistical efficiency of the MUSIC estimator for the problem of finding the directions of two plane waves using a uniform linear array. An exact description of the results is included.<<ETX>>

MIMO Radar with Colocated Antennas

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.

On robust Capon beamforming and diagonal loading

The Capon (1969) beamformer has better resolution and much better interference rejection capability than the standard (data-independent) beamformer, provided that the array steering vector corresponding to the signal of interest (SOI) is accurately known. However, whenever the knowledge of the SOI steering vector is imprecise (as is often the case in practice), the performance of the Capon beamformer may become worse than that of the standard beamformer. Diagonal loading (including its extended versions) has been a popular approach to improve the robustness of the Capon beamformer. We show that a natural extension of the Capon beamformer to the case of uncertain steering vectors also belongs to the class of diagonal loading approaches, but the amount of diagonal loading can be precisely calculated based on the uncertainty set of the steering vector. The proposed robust Capon beamformer can be efficiently computed at a comparable cost with that of the standard Capon beamformer. Its excellent performance for SOI power estimation is demonstrated via a number of numerical examples.

Generalized linear precoder and decoder design for MIMO channels using the weighted MMSE criterion

We address the problem of designing jointly optimum linear precoder and decoder for a MIMO channel possibly with delay-spread, using a weighted minimum mean-squared error (MMSE) criterion subject to a transmit power constraint. We show that the optimum linear precoder and decoder diagonalize the MIMO channel into eigen subchannels, for any set of error weights. Furthermore, we derive the optimum linear precoder and decoder as functions of the error weights and consider specialized designs based on specific choices of error weights. We show how to obtain: (1) the maximum information rate design; (2) QoS-based design (we show how to achieve any set of relative SNRs across the subchannels); and (3) the (unweighted) MMSE and equal-error design for fixed rate systems.

Optimal designs for space-time linear precoders and decoders

We introduce a new paradigm for the design of transmitter space-time coding that we refer to as linear precoding. It leads to simple closed-form solutions for transmission over frequency-selective multiple-input multiple-output (MIMO) channels, which are scalable with respect to the number of antennas, size of the coding block, and transmit average/peak power. The scheme operates as a block transmission system in which vectors of symbols are encoded and modulated through a linear mapping operating jointly in the space and time dimension. The specific designs target minimization of the symbol mean square error and the approximate maximization of the minimum distance between symbol hypotheses, under average and peak power constraints. The solutions are shown to convert the MIMO channel with memory into a set of parallel flat fading subchannels, regardless of the design criterion, while appropriate power/bits loading on the subchannels is the specific signature of the different designs. The proposed designs are compared in terms of various performance measures such as information rate, BER, and symbol mean square error.

Performance study of conditional and unconditional direction-of-arrival estimation

A numerical and analytical study of conditional and unconditional direction-of-arrival (DOA) estimation is presented. Explicit expressions for the unconditional Cramer-Rao bounds on the DOA estimation accuracy and the covariance matrix of the conditional maximum likelihood method are given. It is shown that many DOA estimation methods have the same asymptotic statistical properties under conditional and unconditional models. The situation of two narrowband plane signals impinging on a uniformly spaced linear array is discussed. >

Maximum likelihood methods for direction-of-arrival estimation

Five methods of direction-of-arrival (DOA) estimation which can be derived from the maximum-likelihood (ML) principle are considered. The ML method (MLM) results from the application of the ML principle to the statistics of the observed raw data. The standard multiple signal classification (MUSIC) procedure, called MUSIC-1, is obtained as a brute-force approximation of the MLM. An improved MUSIC procedure, named MUSIC-2, is obtained by applying the ML principle to the statistics of certain linear combinations of the sample noise space eigenvectors. A procedure which compromises between the good performance of the MLM and the computational simplicity of MUSIC is a method of direction estimation (MODE-1) which is derived as a large sample realization of the MLM. A fifth method, called MODE-2, is obtained by using the ML principle on the statistics of certain linear combinations of the sample eigenvectors. MODE-2 is computationally less demanding than the MLM (it is of the same complexity as MODE-1) and statistically more efficient. A numerical comparison of these five DOA estimation methods is presented. It confirms the analytic results on their theoretical performance levels. >

MIMO Radar Signal Processing

PREFACE. CONTRIBUTORS. 1 MIMO Radar - Diversity Means Superiority (Jian Li and Petre Stoica). 1.1 Introduction. 1.2 Problem Formulation. 1.3 Parameter Identifiability. 1.4 Nonparametric Adaptive Techniques for Parameter Estimation. 1.5 Parametric Techniques for Parameter Estimation. 1.6 Transmit Beampattern Designs. 1.7 Conclusions. Appendix IA Generalized Likelihood Ratio Test. Appendix 1B Lemma and Proof. Acknowledgments. References. 2 MIMO Radar: Concepts, Performance Enhancements, and Applications (Keith W. Forsythe and Daniel W. Bliss). 2.1 Introduction. 2.2 Notation. 2.3 MIMO Radar Virtual Aperture. 2.4 MIMO Radar in Clutter-Free Environments. 2.5 Optimality of MIMO Radar for Detection. 2.6 MIMO Radar with Moving Targets in Clutter: GMTI Radars. 2.7 Summary. Appendix 2A A Localization Principle. Appendix 2B Bounds on R(N). Appendix 2C An Operator Norm Inequality. Appendix 2D Negligible Terms. Appendix 2E Bound on Eigenvalues. Appendix 2F Some Inner Products. Appendix 2G An Invariant Inner Product. Appendix 2H Kronecker and Tensor Products. Acknowledgments. References. 3 Generalized MIMO Radar Ambiguity Functions (Geoffrey San Antonio, Daniel R. Fuhrmann, and Frank C. Robey). 3.1 Introduction. 3.2 Background. 3.3 MIMO Signal Model. 3.4 MIMO Parametric Channel Model. 3.5 MIMO Ambiguity Function. 3.6 Results and Examples. 3.7 Conclusion. References. 4 Performance Bounds and Techniques for Target Localization Using MIMO Radars (Joseph Tabrikian). 4.1 Introduction. 4.2 Problem Formulation. 4.3 Properties. 4.4 Target Localization. 4.5 Performance Lower Bound for Target Localization. 4.6 Simulation Results. 4.7 Discussion and Conclusions. Appendix 4A Log-Likelihood Derivation. Appendix 4B Transmit-Receive Pattern Derivation. Appendix 4C Fisher Information Matrix Derivation. References. 5 Adaptive Signal Design For MIMO Radars (Benjamin Friedlander). 5.1 Introduction. 5.2 Problem Formulation. 5.3 Estimation. 5.4 Detection. 5.5 MIMO Radar and Phased Arrays. Appendix 5A Theoretical SINR Calculation. References. 6 MIMO Radar Spacetime Adaptive Processing and Signal Design (Chun-Yang Chen and P. P. Vaidyanathan). 6.1 Introduction. 6.2 The Virtual Array Concept. 6.3 Spacetime Adaptive Processing in MIMO Radar. 6.4 Clutter Subspace in MIMO Radar. 6.5 New STAP Method for MIMO Radar. 6.6 Numerical Examples. 6.7 Signal Design of the STAP Radar System. 6.8 Conclusions. Acknowledgments. References. 7 Slow-Time MIMO SpaceTime Adaptive Processing (Vito F. Mecca, Dinesh Ramakrishnan, Frank C. Robey, and Jeffrey L. Krolik). 7.1 Introduction. 7.2 SIMO Radar Modeling and Processing. 7.3 Slow-Time MIMO Radar Modeling. 7.4 Slow-Time MIMO Radar Processing. 7.5 OTHr Propagation and Clutter Model. 7.6 Simulations Examples. 7.7 Conclusion. Acknowledgment. References. 8 MIMO as a Distributed Radar System (H. D. Griffiths, C. J. Baker, P. F. Sammartino, and M. Rangaswamy). 8.1 Introduction. 8.2 Systems. 8.3 Performance. 8.4 Conclusions. Acknowledgment. References. 9 Concepts and Applications of A MIMO Radar System with Widely Separated Antennas (Hana Godrich, Alexander M. Haimovich, and Rick S. Blum). 9.1 Background. 9.2 MIMO Radar Concept. 9.3 NonCoherent MIMO Radar Applications. 9.4 Coherent MIMO Radar Applications. 9.5 Chapter Summary. Appendix 9A Deriving the FIM. Appendix 9B Deriving the CRLB on the Location Estimate Error. Appendix 9C MLE of Time Delays - Error Statistics. Appendix 9D Deriving the Lowest GDOP for Special Cases. Acknowledgments. References. 10 SpaceTime Coding for MIMO Radar (Antonio De Maio and Marco Lops). 10.1 Introduction. 10.2 System Model. 10.3 Detection In MIMO Radars. 10.4 Spacetime Code Design. 10.5 The Interplay Between STC and Detection Performance. 10.6 Numerical Results. 10.7 Adaptive Implementation. 10.8 Conclusions. Acknowledgment. References. INDEX.

Space-time block codes: a maximum SNR approach

In Tarokh et al. (1999) space-time block codes were introduced to obtain coded diversity for a multiple-antenna communication system, in this work, we cast space-time codes in an optimal signal-to-noise ratio (SNR) framework and show that they achieve the maximum SNR and, in fact, they correspond to a generalized maximal ratio combiner. The maximum SNR framework also helps in calculating the distribution of the SNR and in deriving explicit expressions for bit error rates. We bring out the connection between the theory of amicable orthogonal designs and space-time codes. Based on this, we give a much simpler proof to one of the main theorems on space-time codes for complex symbols. We present a rate 1/2 code for complex symbols which has a smaller delay than the code already known. We also present another rate 3/4 code which is simpler than the one already known, in the sense it does not involve additions or multiplications. We also point out the connection between generalized real designs and generalized orthogonal designs.

On Probing Signal Design for MIMO Radar

A multiple-input multiple-output (MIMO) radar system, unlike a standard phased-array radar, can choose freely the probing signals transmitted via its antennas to maximize the power around the locations of the targets of interest, or more generally to approximate a given transmit beampattern, and also to minimize the cross-correlation of the signals reflected back to the radar by the targets of interest. In this paper, we show how the above desirable features can be achieved by designing the covariance matrix of the probing signal vector transmitted by the radar. Moreover, in a numerical study, we show that the proper choice of the probing signals can significantly improve the performance of adaptive MIMO radar techniques. Additionally, we demonstrate the advantages of several MIMO transmit beampattern designs, including a beampattern matching design and a minimum sidelobe beampattern design, over their phased-array counterparts.