Rick S. Blum, Lehigh University, USA, Alexander M. Haimoivch, New Jersey Institute of Technology, USA and Jian Li, University of Florida, USA
MIMO (multiple-input multiple-output) radar refers to an emerging sensing technology that employs multiple transmitters and receivers. It seeks to exploit the ability to probe a target with multiple waveforms and to jointly process the echoes observed at multiple sensors. MIMO radar utilizes multiple antennas that transmit correlated or uncorrelated waveforms, the nomenclature suggesting unique features that set MIMO radar apart from the existing literature on radar and that have a relation to MIMO communications. Driven by new possibilities that open up with this approach to radar, and by the potential to cross-fertilize with the immensly succesful MIMO communications, there has been a growing interest in MIMO radar as reflected by an increasing body of publications and presentations. This tutorial seeks to introduce participants to the main concepts, potential applications, and challenges of MIMO radar. The tutorial focuses on two MIMO radar architectures: collocated antennas and distributed antennas.
In this part, we focus on the merits of the waveform diversity allowed by transmit and receive antenna arrays containing elements that are colocated. For the latter type of MIMO radar systems, we provide here an overview of recent results showing that the said waveform diversity enables the MIMO radar superiority in several fundamental aspects, including: 1) significantly improved parameter identifiability, 2) direct applicability of adaptive arrays for target detection and parameter estimation, 3) much enhanced flexibility for transmit beampattern design, and 4) waveform optimality for more accurate target parameter estimation and imaging. Specifically, we show that 1) the maximum number of targets that can be uniquely identified by the MIMO radar is up to Mt times that of its phased-array counterpart, where Mt is the number of transmit antennas, 2) the echoes due to targets at different locations can be linearly independent of each other, which allows the direct application of many adaptive techniques to achieve high resolution and excellent interference rejection capability, 3) the probing signals transmitted via its antennas can be optimized to obtain several transmit beampattern designs with superior performance, and 4) the probing signals can also be optimized by considering several design criteria, including minimizing the trace, determinant, and the largest eigenvalue of the Cramer-Rao bound (CRB) matrix, to improve the radar parameter estimation and imaging performance. The waveform optimization is performed with respect to covariance matrix R of the waveforms, because optimizing directly with respect to the signal waveform matrix X is a more complicated problem due to X having more unknowns than R and the dependence of various performance measures on X is more intricate than the dependence on R (as R is a quadratic function of X. Hence with R obtained in a previous (optimization) stage, our problem is to determine a signal waveform matrix X whose covariance matrix is equal or close to R, and which also satisfies some practically motivated constraints (such as constant-modulus or low peak-to-average-power ratio (PAR) constraints). We will explain how a cyclic optimization algorithm can be used for the synthesis of such an X with good auto- and cross-correlation properties. Finally, we discuss the use of an instrumental variables approach to design receive filters that can be used to minimize the impact of scatterers in nearby range bins on the received signals from the range bin of interest (the so-called range compression problem). Many numerical examples will be provided to demonstrate the effectiveness of the proposed methodologies.
MIMO systems have had great impact on wireless communications. The signal model for MIMO radar with distributed antennas bears similarities to the communications signal model, suggesting the possibility of interesting cross-fertilization of ideas between MIMO communications and MIMO radar. We will start this Part II of the tutorial by demonstrating that complex targets contain a large number of scatterers that result in diverse RCS patterns as a function of aspect angle. We will specify the conditions for decorrelation of the elements of the channel matrix in terms of separation between antennas, target size, target range, and carrier wavelength. We will discuss parallels to MIMO communication, in particular the similar roles that the transmission medium (channel) and target play in respectively, communication and radar. We will show that combining target returns resulting from independent illuminations yields a diversity gain akin to the diversity gain obtained in the communication problem over fading channels when the data is transmitted through independent channels. We will develop the optimal detectors for MIMO radar, and for comparison, for other radar architectures. Optimal processing combines sensor outputs non-coherently. Signal to noise ratio conditions will be pointed out for which the MIMO radar architecture is best suited. We will also discuss constant false alarm detectors and their properties. From the non-coherent combination of sensor outputs, we will switch to MIMO radar with coherent processing of sensor outputs. We will show that MIMO radar can locate targets with high resolution and can resolve between closely spaced targets. The localization resolution is of the scale of the carrier wavelength. The Cramer-Rao lower bound on the achievable accuracy will be discussed, and it will be shown to depend on both the carrier frequency and the sensors’ locations. The geometric dilution of precision (GDOP) contours will be employed to map the relative performance accuracy for a given layout of sensors. We will point out that high resolution target localization is challenged by ambiguity sidelobes. Ways to control the ambiguity sidelobes will be discussed. Examples will be provided throughout the presentation including of other MIMO radar applications, for example, in moving target detection. Finally, we will discuss the design of waveforms for MIMO radar with distributed antennas. Particular emphasis will be given to waveforms that maintain orthogonality over a range of time delays.
The presenters are coauthors of book chapters in MIMO Radar Signal Processing to be published by John Wiley in 2008.
Part I
Part II
Jian Li received the M.Sc. and Ph.D. degrees in electrical engineering from The Ohio State University, Columbus, in 1987 and 1991, respectively.
From April 1991 to June 1991, she was an Adjunct Assistant Professor with the Department of Electrical Engineering, The Ohio State University, Columbus. From July 1991 to June 1993, she was an Assistant Professor with the Department of Electrical Engineering, University of Kentucky, Lexington. Since August 1993, she has been with the Department of Electrical and Computer Engineering, University of Florida, Gainesville, where she is currently a Professor. Her current research interests include spectral estimation, statistical and array signal processing, and their applications.
Dr. Li is a Fellow of IEEE and a Fellow of IET. She is a member of Sigma Xi and Phi Kappa Phi. She received the 1994 National Science Foundation Young Investigator Award and the 1996 Office of Naval Research Young Investigator Award. She was an Executive Committee Member of the 2002 International Conference on Acoustics, Speech, and Signal Processing, Orlando, Florida, May 2002. She was an Associate Editor of the IEEE Transactions on Signal Processing from 1999 to 2005, an Associate Editor of the IEEE Signal Processing Magazine from 2003 to 2005, and a member of the Editorial Board of Signal Processing, a publication of the European Association for Signal Processing (EURASIP), from 2005 to 2007. She has been a member of the Editorial Board of Digital Signal Processing -- A Review Journal, a publication of Elsevier, since 2006. She is presently a member of two of the IEEE Signal Processing Society technical committees: the Signal Processing Theory and Methods (SPTM) Technical Committee and the Sensor Array and Multichannel (SAM) Technical Committee. She is a co-author of a paper that has received the Best Student Paper Award at the 2005 Annual Asilomar Conference on Signals, Systems, and Computers in Pacific Grove, California.
Alexander M. Haimovich received the B.Sc. degree in electrical engineering from the Technion, Israel, in 1977, the M.Sc. degree in electrical engineering from Drexel University, in 1983, and the Ph.D. degree in systems from the University of Pennsylvania, in 1989. From 1983 to 1992, he worked in the industry in a variety of capacities on defense-related systems. Since 1992, he has been with the New Jersey Institute of Technology (NJIT), Newark, where he is currently a Professor of Electrical and Computer Engineering. From 2003-2005, he served as the Director of the New Jersey Center for Wireless Telecommunications, a state-funded consortium consisting of NJIT, Princeton University, Rutgers University, and the Stevens Institute of Technology. His research interests include multiple-input multiple-output (MIMO) systems for radar and communications, wireless networks, and geolocation problems. He served as Chair of the Communication Theory Symposium at Globecom 2003, and is currently an Associate Editor for IEEE Communication Letters. He was a Guest Editor for the European Journal of Applied Signal Processing: Special Issue on Turbo Coding.
Rick S. Blum received a B.S. in Electrical Engineering from the Pennsylvania State University in 1984 and his M.S. and Ph.D in Electrical Engineering from the University of Pennsylvania in 1987 and 1991. From 1984 to 1991 he was a member of technical staff at General Electric Aerospace in Valley Forge, Pennsylvania and he graduated from GE`s Advanced Course in Engineering. Since 1991, he has been with the Electrical and Computer Engineering Department at Lehigh University in Bethlehem, Pennsylvania where he is currently a Professor and holds the Robert W. Wieseman Chaired Research Professorship in Electrical Engineering. His research interests include communications, sensor networking, sensor processing and related topics in the areas of signal processing and communications. He is currently an associate editor for the IEEE Communications Letters and he is on editorial board for the Journal of Advances in Information Fusion of the International Society of Information Fusion. He was an associate editor for IEEE Transactions on Signal Processing and edited special issues for this journal and for JSAC. He was a member of the Signal Processing for Communications Technical Committee of the IEEE Signal Processing Society and is a member of the Communications Theory Technical Committee of the IEEE Communication Society. He is also on the awards Committee of the IEEE Communication Society. Dr. Blum is a Fellow of the IEEE, an IEEE Third Millennium Medal winner, a member of Eta Kappa Nu and Sigma Xi, and holds several patents. He was awarded an ONR Young Investigator Award in 1997 and an NSF Research Initiation Award in 1992. His IEEE Fellow Citation ``for scientific contributions to detection, data fusion and signal processing with multiple sensors'' acknowledges some early contributions to the field of sensor networking.