ASAP 2003


Space-Time Adaptive Processing Using Sparse Arrays


Michael Zatman
MIT Lincoln Laboratory
244 Wood Street
Lexington, MA 02420
Phone:  (781) 981-2543

Abstract:  Sparse arrays exhibit narrower beamwidths and higher sidelobes than fully-filled arrays with the same number of elements. The minimum detectable velocity (MDV) performance of fast moving airborne or spaced based GMTI radars is typically aperture limited rather than Doppler resolution limited. In these cases the narrower beamwidth of a sparse array has the potential to improve the radar’s MDV performance, however, the higher sidelobes of sparse arrays may also degrade STAP performance. Two different theoretical perspectives – clutter rank and SINR loss - are used to determine how sparse is too sparse an array from the STAP viewpoint.

Of particular interest is how the combined ambiguities of the antenna beampattern and waveform influence STAP performance. The results show that up to a point, sparse arrays work well with unambiguous waveforms, filled arrays work well with ambiguous (e.g. Pulse-Doppler) waveforms, but the combination of sparse arrays and ambiguous waveforms leads to poor STAP performance. A novel STAP implementation for the processing of unambiguous waveforms such as single long phase encoded pulses is also described.

The results presented use the example a low-earth-orbit X-Band space-based radar, and investigate a number of different sparse array geometries.

Space-Time Beamforming with Knowledge-Aided Constraints


Jameson Bergin, Christopher M. Teixeira, and Paul Techeau
ISL, Inc.
8130 Boone Blvd.
Vienna, VA 22182

Joseph Guerci
3701 N. Fairfax Drive
Arlington, VA 22203
Phone:  (703) 248-1548

Abstract:  A major thrust of DARPA’s Knowledge-Aided Sensor Signal Processing and Expert Reasoning (KASSPER) Program is to develop radar signal processing algorithms that exploit the ever-expanding body of a priori knowledge about the sensor-operating environment.  Knowledge sources include digital terrain maps, land coverage data, and the locations of man-made features such as roads and buildings.  Since radar clutter is highly dependent on the various features represented by these knowledge sources (e.g., clutter power is a strong function of terrain height and slope), it is logical to believe that exploiting them will improve radar performance.

This paper presents a framework for incorporating knowledge sources directly in the space-time beamformer of airborne adaptive radars.  The algorithm derivation follows the usual linearly constrained minimum variance (LCMV) space-time beamformer with additional constraints based on a site-specific model of the clutter covariance matrix, which is computed using all available knowledge about the operating environment.  The quadratically constrained beamformer solution is shown to result in a beamformer for which the sample clutter covariance matrix is loaded with a scaled version of the modeled covariance matrix.  Therefore, this technique has been termed “colored loading” and results in a “blending” of the information contained in the observed radar data and the a priori knowledge sources.  It is also shown that the quadratically constrained beamformer can be implemented as a two-stage filter where the first stage deterministically filters the data to remove the clutter components represented by the a priori knowledge and the second stage adaptively cancels any residual clutter. 

The performance of the developed knowledge-aided beamforming techniques is demonstrated using both high-fidelity radar simulations as well as experimental data.  Finally, the sensitivity of knowledge-aided beamforming to errors in both the a priori knowledge sources and the radar sensor (e.g., antenna calibration errors) is addressed along with a preliminary investigation of computational complexity.

Registration-Based Solutions To The Range-Dependence Problem In Radar STAP

Presentation | Paper

Fabian Lapierre and Jacques Verly
University of Liège, Belgium
Department of Electrical Engineering and Computer Science
Sart-Timan, Building B28
B-4000 Liège
Phone:  +32 4 366 37 41

Abstract:  STAP data consist of "snapshots" collected at a series of successive ranges. Optimum STAP uses linear combinations of these samples. The calculation of the corresponding weights involves the estimation of the clutter covariance matrix.

In monostatic (MS) sidelooking configurations, an estimate at some range is obtained by averaging sample covariance matrices at neighboring ranges. This approach fails in all other MS and in all bistatic (BS) configurations, due to the deformation, with range, of the "clutter ridge" in the corresponding power spectral densities (PSD).

The new proposed range-dependence compensation methods are all based on a detailed understanding of the variation, with range, of the theoretical "direction-Doppler (DD) curve," which is the trace, in the 2D spectral domain, of all clutter samples at a constant range. There is a close correspondence between theoretical DD curves and practical clutter ridges of PSDs. Our new methods are based on the idea of registering the clutter ridges and of translating the desired registration back into the covariance-matrix domain. Even though we operate on experimental clutter ridges, our methods fully exploit a new comprehensive, mathematical theory of DD curves, which we have developed, but which is outside the scope of this paper.

We present three distinct methods that compensate for the range dependence in situations of increasing complexity. Each of these methods comes in two flavors: "open-loop," where the configuration parameters are known, and "data-adaptive," where they are unknown and autonomously estimates from the data. The most advanced method thus performs the range compensation for an arbitrary BS configuration with totally unknown parameters.

Simulations demonstrate the generality and robustness of the parameter-estimation algorithm. The performances of the new methods are quantified in terms of the SINR loss and compared to those of earlier methods such as Doppler Warping, High-Order Doppler Warping, and Derivative-Based Updating.

Robust ABF For Large Passive Sonar Arrays

Presentation | Paper

Norman Owsley and John Tague
Office of Naval Research
Code 321US
4001 N. 9th Street
Arlington, VA 22203
Phone:  (703) 243-1160, ext. 233

Abstract:  Adaptive beamforming for arrays having a large number of sensors in the presence of propagation model uncertainty requires both computational efficiency and model error robustness. Accordingly, a Generalized Sidelobe Cancellation (GSC) method [VT02] with a Dominant Mode Rejection (DMR) implementation that is steering direction invariant and robust to model error is presented. Steering direction invariant GSC (SDIGSC) is in contrast to the use of either the traditional signal blocking matrix output or beam-space adaptation that require the inversion of a different, albeit reduced-dimension auxiliary array data estimated covariance matrix for every beam steering direction. SDIGSC robustness is achieved through convex linear combination (blending) of the GSC filter weight vector with the inherently robust, non-adaptive conventional beamformer steering vector. The paper derives the SDIGSC and gives examples that illustrate SDIGSC performance relative to alternative element space robust DMR ABF algorithms.

Robust SDIGSC solves the minimum variance problem: minimize w.r.t. wa subject to the distortionless response (DR) constraint v = 1. The vector v is the N sensor array conventional beamformer (CBF) steering vector. The matrix A is an N-by-M auxiliary array selection matrix and wa is the M (< N) dimensional auxiliary array adaptive filter vector. This solution is

.                                                        (A1)

SDIGSC robustness to propagation model error is achieved with a blended CBF and GSC beamforming filter, w, with 0 < b < 1, formed according to


In (A2), b =  g / and g  is defined by the maximum allowable signal suppression due to signal model error [Ows02].

A Space-time Enhanced MUSIC Algorithm for HF Radar

Presentation | Paper

Jian Wang and R. Lynn Kirlin
University of Victoria
Department of Electrical Engineering
Victoria, B.C.
Phone:  (250) 472-4255

Abstract:  "In this paper we propose a new algorithm to estimate the direction of arrivals (DOAs) of superimposed cisoidal radar echoes from far-field targets. A potential practical application of this algorithm is high frequency ocean surveillance radar (HFOSR) detection of slow moving targets embedded in temporally correlated sea clutter that has a continuous spatial spectrum. The improvement provided by this algorithm is based on a model that more accurately represents the received high frequency (HF) Doppler radar array signal prior to spatial processing. A 2-D (spatial and temporal) pre-filtering matrix is structured and applied to the received array signal, which is finally combined with the high-resolution (MUSIC) method for DOA estimation. More specifically, we perform a linear transform (mapping) on a particular group of signals within a chosen space-frequency (sector-Doppler) area and thereafter eliminate or significantly attenuate other existing groups of signals from both spatial and temporal domains.

The main advantage of this algorithm is that it reduces the interference from groups of signals, noise and clutter having spatial or temporal spectra outside the space-frequency region of interest. Another advantage of the pre-filtering is that it pre-whitens the noise and clutter when their spectra are not spatially or temporally white.

Higher resolution, lower detection threshold, and lower estimation bias and variance are achieved by this algorithm compared to conventional beam-space MUSIC and sensor-space MUSIC. Both the theory and Monto Carlo simulations verify the effectiveness of our proposed algorithm."

Orthogonal Space-Time Coding for Self-Interference Suppression in Multi-Antenna Telemetry Transmission

Presentation | Paper

Michael A. Jensen, Ronald C. Crummett, and Adam L. Anderson
Department of Electrical and Computer Engineering
459 Clyde Building
Brigham Young University

Provo, UT  84602


Abstract:  The use of multiple antennas for air-to-ground telemetry transmission from air-vehicles and missiles is a common practice for overcoming signal obstruction created by vehicle maneuvering. Unfortunately, this practice also leads to self-interference nulls when the vehicle is oriented such that multiple antennas have a clear path to the ground station, resulting in dramatic degradation in the average signal integrity. While advanced beamforming can be used to overcome this problem, such an approach requires additional communication overhead and significant system complexity. Alternate approaches that maintain high signal integrity with low hardware complexity are highly desirable for operational telemetry systems.

This paper discusses application of orthogonal space-time codes, originally developed for communication in multipath channels, to overcome the self-interference effect observed in such systems. Specifically, Alamouti’s transmit diversity scheme and unitary differential space-time codes make excellent candidates as they are simple to implement and yet promise significant performance improvements. For example, detailed analysis of Alamouti’s scheme applied to dual-antenna systems shows that during even aggressive aircraft maneuvering, the transmission completely removes the self-interference effect provided that good channel estimates are available at the receiver. In cases where channel estimation is impractical, differential space-time coding can be used with little to no reduction in the actual communication throughput.

The paper and presentation will provide the mathematical foundations for application of orthogonal space-time coding to telemetry transmission and provide several computational examples of the performance gains associated with use of these techniques. A Maximum Likelihood procedure will also be assessed as a candidate channel estimation technique. The throughput performance of non-differential and differential schemes will be discussed for realistic air-vehicle motion.

Performance Bounds for Adaptive Coherence of Sparse Array Radar

Presentation | Paper

Andrew Fletcher and Frank C. Robey
MIT Lincoln Laboratory
244 Wood Street
Lexington, MA 02420
Phone:  (781) 981-2732

Abstract:  To achieve high signal-to-noise ratios (SNR) at long ranges with transportable moderately sized sensors, an architecture is proposed to combine several independent radar apertures into a coherently functioning unit.  The proposed system utilizes several distinct apertures that are to be adaptively cohered based on observed target returns.  Aside from independent aperture operation, two modes are presented.  In the first, coded waveforms from each of the apertures are used in a Multiple Input Multiple Output (MIMO) mode.  The independent, multi-static returns allow the estimation of several coherence parameters.  These estimates may then be used to produce a fully coherent transmit/receive mode, wherein all of the apertures cooperatively transmit a single waveform, which allows the system to perform as a fully coherent, sparse array.

The success of each of these modes, particularly the coherent transmit/receive mode, is dependant upon accurate estimates of the coherence parameters.  In particular, the one-way travel times between each aperture and the target and the local insertion phase of each aperture must be precisely estimated from observed returns.  This paper examines the estimation problem in the context of the Cramer-Rao lower bound.  Based upon this theoretical bound on the estimate accuracy, the desired performance gain lies within the theoretically achievable realm using the adaptive coherence process.

Numerical Sensitivity Of Weight Vector Computation Methods In Array Signal Processing

Presentation | Paper

Adam Bojanczyk
Cornell University
School of Electrical and Computer Engineering
335 Rhodes Hall
Ithaca, NY 14850
Phone:  (607) 255-4296

Abstract:  This paper is concerned with numerical accuracy of computing weight vectors in adaptive array systems by the Sample Matrix Inversion (SMI) technique. We consider three mathematical formulations of the SMI technique which form bases of commonly used algorithms for computing the weights.  These algorithms are derived from the normal equations, semi-normal equations, and least squares formulations. We develop perturbation theory and identify condition numbers for the three formulations. Although the formulations are mathematically equivalent, the corresponding algorithms may produce numerically different weight vectors. Our analysis shows that the algorithm based on the semi-normal equations formulation is as accurate as the algorithm based on the least squares formulation. As expected, the normal equations formulation leads to less accurate algorithms however it is the least expensive to implement. Computer simulations, which illustrate the results of our analysis, are included.


Model Based Array Element Localization for Single and Multiline Towed Arrays


John. P. Ianniello, Richard B. Evans, and Brian Sperry
23 Clara Drive, Suite 206
Mystic, CT 06355
Phone:  (860) 572-2384

Abstract:  Accurate array element localization (AEL) is the enabler for both conventional and adaptive beamforming, thus it is the key first step in any attempt to improve sonar system performance through the use of large towed arrays.  This paper will describe a model-based algorithm that has been applied to both single line and multiline arrays, and will demonstrate the accuracy of the AEL via beamforming of sea-test data.  

The core of our algorithm is a three-dimensional, dynamic cable model available in the literature.  This model is an implicit, second-order, finite difference approximation to the equations of motion, which does not appear to suffer from the instability problems often encountered in explicit models.  Our version of the model is coded in MATLAB, and modifies the original version to dynamically include ocean currents. The model, which is driven by tow ship speed, heading and ocean currents, includes all of the relevant physical parameters of the array.  A linearized Kalman filter incorporates compass and depth measurements to correct the model.  Acoustic element locations are determined at every time step via interpolation along the arc-length of the cable. The single line AEL algorithm is a straightforward application of this technique.  The multiline model is more complicated.  The multiline application we address is that of a tow-cable with a heavy depressor to which several arrays are attached at various points along the tow cable. We treat this as an uncoupled system in which the tow-cable motion is first determined and in turn drives the attached arrays.  In addition to compass and depth information inter-array pinger range data was available; we describe how all this information was used.  

Finally we present adaptive beamforming results for both the single and multiline arrays using sea test data.  For both data sets we show results with and without the AEL and illustrate the performance improvement realized.

Robust Capon Beamforming in the Presence of Coherent Interference

Presentation | Paper

Yi Jiang, Zhisong Wang, and Jian Li
University of Florida
ECE Department
P.O. Box 116130
Gainesville, FL 32611
Phone:  (352) 392-5241

Petre Stoica
Uppsala University
Department of Systems and Control
P.O. Box 27
SE-751 05 Uppsala

Abstract:  It is well known that the standard Capon beamformer (SCB) suffers from severe signal cancellation when the knowledge of the signal-of-interest (SOI) steering vector is imprecise, the number of snapshots is small (which can also be viewed as a steering vector error problem), or the interference is correlated with the SOI. Hence, the SCB performs poorly in some applications, such as in a global positioning system (GPS), where SOI steering vector errors and coherent multipath interferences exist.  In this paper, we propose a Capon beamformer that is robust against both SOI steering vector errors and coherent interferences provided that the directions of arrival (DOA) of the coherent multipaths are approximately known relative to the DOA of SOI. Numerical examples are presented to demonstrate the effectiveness of the proposed doubly robust Capon beamformer, which we will designate by the acronym R2CB.

Algebraic Equivalence of the Multistage Wiener Filter and the Conjugate Gradient Wiener Filter

Presentation | Paper

Louis Scharf and Edwin Chong
Colorado State University
Electrical and Computer Engineering
Fort Collins, CO 80521
Phone:  (970) 484-2537

L. Todd McWhorter
Mission Research Corporation
3665 JFK Parkway
Building 1, Suite 206
Fort Collins, CO 80525
Phone:  (970) 282-4400, ext. 25

Michael Zoltowski
Purdue University
School of Electrical Engineering
1285 Electrical Engineering Bldg.
West Lafayette, IN 47907-1285
Phone:  (317) 494-3512

J. Scott Goldsteini
SAIC International
4001 Fairfax Drive, Suite 675
Arlington, VA 22203
Phone:  (703) 741-7826

Abstract:  In this paper we show that there is no difference between quadratic minimization and stagewise filtering.  That is, for every iterative quadratic minimization problem there is a corresponding stagewise filtering problem, and vice-versa.  There is no difference between direction-vectors in iterative quadratic minimization and stagewise filters in the analysis stage of an iterative filter.  There is no difference between a line search for the optimum step size in an iterative optimization and the optimum weight computation in the synthesis stage of an iterative filter.  With these insights we establish the exact algebraic equivalence of the multistage Wiener filter and the conjugate gradient Wiener filter.  This is done from algebraic reasoning only, without the need to appeal to the line-by-line recursions of the two implementations.  There is, of course, a corresponding geometry that further illuminates the essence of stagewise filtering and iterative quadratic minimization.

Both the MSWF and the CGWF use a forward analysis stage, but the MSWF uses a backward synthesis and the CGWF uses a forward synthesis.  This difference results from the fact that the covariance structure of the data after it has been resolved onto the stagewise analysis filters is tridiagonal in the case of the MSWF and diagonal in the case of the CGWF.  These decompositions of the covariance structure at the output of the analysis filters suggest several ways to extend the theory of stagewise filtering.

Complementary Beamforming

Presentation | Paper

Vahid Tarokh
Division of Engineering and Applied Sciences
Harvard University
33 Oxford Street Room MD 347
Cambridge, MA 02138, USA
Phone:  (617) 384-5026

Abstract:  Smart Antenna improvements to CSMA based wireless systems suffer from the hidden beam problem. In this paper, we propose "Complementary Beamforming" which provides the first known solution.

Robust MIMO Wireless Communication in the Presence of Interference Using Ad Hoc Antenna Arrays

Presentation | Paper

Danial Bliss and Amanda Chan
MIT Lincoln Laboratory
244 Wood Street
Lexington, MA 02420
Phone:  (781) 981-3300

Abstract:  As the role of data communication increases in importance in the military, the development of robust, high data-rate wireless communication technology also increases in importance.  The future war-fighter will expect real-time situation awareness.  While much energy has been recently focused on high data-rate line-of-sight military communication, such as laser or satellite links, in active urban engagements, line-of-sight links are unlikely.  The communication links in these environments are characterized by complicated multipath, shadowing and jamming.

Wireless communication using multiple-input multiple-output (MIMO) systems enables increased data rates and link reliability for a given total transmit power.  Increased capacity is achieved by introducing additional spatial channels, which are exploited using space-time coding.  The spatial diversity improves the link reliability by reducing the adverse effects of link fading and shadowing.  Because antenna arrays are used at both the transmitter and receiver, interference can be mitigated naturally.

In this paper, MIMO communication is investigated using outdoor experimental data collected near the PCS frequency allocation (1790 MHz) in the presence of multiple jammers.  Coherence issues associated with implementing antenna arrays using ad hoc groups of users are addressed.  Channel complexity and channel stationarity are investigated.  Complexity is associated with channel matrix singular value distributions.  Stationarity is associated with the stability of channel singular value and singular vector structure over time.  An experimental example of demodulation of space-time turbo code using a multichannel multiuser detector (MCMUD) that compensates for delay and Doppler spread, as well as local oscillator mismatch, is presented.

MIMO Capacity of Radar as a Communication Channel

Presentation | Paper

Patrick Bidigare
Veridian Ann Arbor R&D Center
3300 Plymouth Road
Ann Arbor, MI 48130
Phone:  (734) 994-1200, ext. 2792

Abstract:  An RF tag is a wireless communication device that can embed information into a SAR or GMTI radar collection by receiving radar pulses, modifying these and transmitting them back to the radar.  This allows the radar system to be used as a communications channel.  This radar/tag channel may be viewed as a spatio-temporal MIMO channel, where the inputs are the pulses transponded by the tag and the outputs are all the pulses received by all of the radar receiver channels.  The interference in this channel is composed of thermal noise and clutter returns and has a rich covariance structure that has been studied extensively in the STAP community.

The radar/tag channel has an unusual MIMO structure.  In a MIMO channel with white interference, the capacity depends only on the singular values of the transfer matrix.  In our case, the singular values of the transfer matrix are independent of the number of spatial receive channels of the radar, yet adding more receivers can dramatically increase the capacity of the channel. 

This presentation explores the dependence of radar/tag channel capacity on the number of spatial receive channels available on the radar system.  We derive a formula for the capacity of a multichannel radar system and then calculate via simulation these capacities in the specific case of the Veridian DCS radar and the BAE SYSTEMS digital RF tag.  We assess the validity of our model by comparing our interference clutter covariance to that obtained from collected three channel radar data from the DCS.

Space-Time Codes for an Invariant Detector of Frequency-Hopped MIMO


Keith Forsythe
M.I.T. Lincoln Laboratory
244 Wood Street
Lexington, MA 02040
Phone:  (781) 281- 3243

Abstract:  Multiple-input, multiple-output (MIMO) communications has received considerable attention in recent years. The flat-fading channel, with identical, independently distributed gains between all transmitter and receiver pairs has been one of the MIMO channels studied extensively. Many studies have focused on channel capacity and coding in additive white Gaussian noise with a known channel transfer function.  By building invariances into the detector, a receiver can be made robust to unknown spatial covariances due to interference and unknown channel transfer functions.  This invariant receiver forms a metachannel whose capacity can be evaluated in the particular case of frequency-hopped waveforms with random fading hop to hop and white noise.  A family of space-time codes for the invariant detector is investigated and its performance compared with the derived capacity bounds. Theoretical predictions of performance in interference and in different fading conditions are presented and compared with simulation results for a concatenated coding architecture involving space-time inner codes and a low-density parity-check outer code.

Mean Squared Error Performance Prediction Of Maximum-Likelihood Signal Parameter Estimation


Christ D. Richmond
MIT Lincoln Laboratory
244 Wood Street
Lexington, MA 02420
Phone:  (781) 981-5954

Abstract:  Bounds on mean squared error (MSE) performance of parameter estimates play a vital role in the design of many systems.  In addition to indicating which factors limit system performance, bounds often offer a trade space for balancing system loss budgets (e.g. taper/mismatch losses, finite training losses, resolution, etc.). The Cramer-Rao bound (CRB) has been a popular choice in MSE performance prediction, primarily for it's simplicity of calculation and ease of interpretation.  It is well-known, however, that the CRB can be an inaccurate predictor of MSE in the absence of large signal-to-noise ratios (SNRs), the presence of non-linear operations on the data, and in situations where sample support is limited.  Several other bounds exists, however, that often do a better job predicting MSE performance of Maximum-Likelihood (ML) estimation in high, moderate, and low SNR regions, as well as predicting the well-known threshold SNR representing the boundary where CRB predictions breakdown.  These bounds are constructed within a Bayesian framework and include the Ziv-Zakai bound (ZZB) and Weiss-Weinstein bound (WWB).  Recent work extends ZZBs to vector parameter estimation and demonstrates good ML MSE prediction.

In this paper we explore a related approach to MSE performance prediction that relies upon a two-point probability calculation.  The first approach is based on an approximation made via the Union Bound for error analysis of Mary hypothesis testing problems.  By exploiting well-known techniques of multivariate statistical analysis often used in performance analysis of adaptive detection/estimation, these necessary probabilities are obtained for maximum-likelihood (ML) estimation and performance is compared with other bounds.

Beamforming and Directivity Index in the Nonlinear Acoustic Region


Theo Kooij
3701 N. Fairfax Drive
Arlington, VA 22203-1714
Phone:  (703) 696-2333

Yeshayahu (Shyke) Goldstein
Advanced Power Technologies, Inc.
1400-A Duke Street
Alexandria, VA 22314
Phone:  (703) 549-2412

Abstract:  Phased radar arrays were a technology breakthrough over the previously used dish antennas. The Aegis cruiser's phased array anti-missile radar is a well-known application. Similarly, traditional shaped underwater charges get directivity gain from reflecting energy back from unwanted directions into desired ones. They are the equivalent of parabolic radar antennas. As far as we have been able to ascertain, no one ever tried the equivalent of a directed explosion based on a phased array concept. This theoretical study looks at this problem, which is made more complex by the fact that the directivity occurs in a nonlinear pressure regime. The results shown have not been verified with real experiments, but they are an attempt to predict what we expect to happen. We'll use the standard non-directional similarity rules that are well accepted in predicting such pressures, time constants and nonlinear propagation relations of standard explosives such as TNT, pentolite, etc.

We will show how the non-linear rules affect the propagation and the Directivity Index (DI), and we'll consider the effects of focusing.

Blind Equalization algorithms for Multiple Channel Sampling Systems with Applications


Rajesh Sharma
MIT Lincoln Laboratory
244 Wood Street
Lexington, MA 02420
Phone:  (781) 981-3507

Abstract:  Blind equalization algorithms for communication channels, based on second order statistics, have received considerable attention in recent years.  Blind equalization of a single input single output LTI system is equivalent to blind equalization of a single input multiple output P-fold polyphase interpolation filter bank structure.  Motivated by multiple channel sampling systems, we develop blind equalization algorithms for the P-fold decimation portion of the polyphase filter bank structure.  These algorithms differ from those presented in the signal processing and communication literature.  Example applications discussed in the paper are one-dimensional sampling and multiple channel Synthetic Aperture Radar (SAR) imaging.

Imaging And Target Detection From Unstructured And Sparse Antenna Arrays

Presentation | Paper

Anthony Devaney
Northeastern University
Department of Electrical and Computer Engineering
Dana Building
Boston, MA 02115
Phone:  (617) 373-5284

Abstract:  The problem of detecting and locating one or more scatterers (targets) embedded in a known inhomogeneous background from data collected from an arbitrary distribution of transmitting and receiving antennas is of interest in a number of DOD applications that include the Air Force's Techsat 21 project as well as the Silent Sentry Project. In this talk a physics based approach to this class of problems is presented that uses the Distorted Wave Born Approximation (DWBA) to model the multistatic data matrix collected from such an unstructured, mixed antenna array. Based on this formulation two classes of problems are considered: (i) detecting and locating a finite set of point targets, (ii) imaging an arbitary distribution of point or extended targets. Problems of the first class are shown to admit solutions based on the Singular Value Decomposition (SVD) of the multistatic data matrix considered as a linear mapping from the finite vector space of transmitter inputs to the finite vector space of receiver outputs. In this case the SVD of the data matrix is shown to lead directly to generalized time-reversal algorithms that allow super-resolution location estimation so long as the number of targets is less than or equal to the smaller of the number of transmitter or receiver elements of the antenna array. Problems of the second class are also addressed using the SVD but this time it is based on the multistatic data matrix considered as a linear mapping from the Hilbert space of target distributions to the finite vector space of receiver outputs. In this case a generalized form of the filtered backpropagation algorithm is derived and shown to lead to a minimum norm image (pseudo-inverse) of the target distribution. The talk includes a discussion of the use of time-gating and Doppler filtering to reduce clutter and additive noise and the effects of errors in knowledge of the background Green function on algorithm performance. The general theory is applied in a computer simulation of TechSat 21 where the goal is to detect and locate a moving ground targets (MGT) from a sparse and unstructured antenna array orbiting above the ionosphere.

Blind Adaptive Dereverberation of Speech Signals Using Microphone Arrays

Presentation | Paper

Tariq Bakir and Russell Mersereau
Georgia Institute of Technology
563 Lovejoy Street, NW
Atlanta, GA 30313
Phone:  (404) 872-0810

Abstract:  This paper describes a blind adaptive method for the dereverberation of speech/audio signals in a closed room environment based on the use of multiple microphones (two or more) by utilizing the second-order statistics of the reverberated speech signals only. The spatial diversity provided by the microphone array creates the equivalent of multiple channels, where each channel is the impulse response of the source audio/speech signal to each microphone. Mathematically, this is equivalent to single-input multiple-output (SIMO) channel model.

The dereverberation is accomplished through an inversion procedure of the channels. The inverse filters, also called equalizers, are found by minimizing what we call a reduced Mutually Referenced Equalizers (MRE) error criterion. A reduced MRE criterion needs to be used because the reverberant channels are characterized by a very large order and finding the equalizers for every possible delay is impractical. Instead, our proposed method finds the equalizers at a much smaller subset of these delays making the method applicable to larger order channels. Another advantage of this approach is that the equalizers are found in a single stage process as opposed to other methods, which first have to estimate the channels through a blind channel estimation procedure and then find the inverses.

The error criterion is minimized through an iterative procedure that is implemented using linear adaptive filters which find a solution to a linear system of equations of the form Ax=b. The A matrix is a matrix of block correlation matrices at predetermined lags chosen to yield equalizers at predefined delays. The adaptive algorithm used can be one such as the LMS, RLS or any variant of them such as subband implementations.

The proposed method was tested on recorded reverberated speech signals with good dereverberation results.

Identification Of Unknown Uncorrelated Colored Signals Distorted By Unknown Convolutive Channels

Presentation | Paper

Yingbo Hua, Senjian An, and Yong Xiang
University of California, Riverside
Department of Electrical Enigineering
Riverside, CA 92521
Phone:  (909) 787-2853

Abstract:  A fundamental problem in adaptive sensor array processing is to identify unknown uncorrelated colored signals that are distorted by unknown convolutive channels. This problem is also known as blind identification of MIMO (multi-input-multi-output) systems. In this paper, we present a novel approach called BIDS (blind identification by decorrelating subchannels). The BIDS can identify an FIR (finite impulse response) MIMO system up to a scaling and permutation if the channel matrix (a polynomial matrix) of the system has a normal full rank and is column-wise coprime. This condition is weaker than that the channel matrix is irreducible and column-reduced. The latter condition is required by many other approaches such as the subspace approach by Loubaton et al. As a result, the BIDS has a much better performance against noise.

The BIDS first partitions the channel output signals into clusters of subgroups. For each group, the BIDS constructs a decorrelation filter that yields decorrelated signals. Under a (weak) condition, each of the decorrelated signals directly corresponds to one of the desired signals except for a convolutional distortion (without mixing). The output signals of the decorrelation filters can then be regrouped into a bank of SIMO (single-input-multiple-output) systems. The SIMO systems can be identified by an efficient maximum likelihood algorithm or other SIMO algorithms. Alternatively, the decorrelation filters can be directly exploited to yield the original MIMO channel matrix. This matrix can then be used in the recovery of the desired signals. The latter algorithm (named BIDS-2) is more robust than the former (named BIDS-1).

The BIDS algorithms are built upon a series of newly developed algebraic insights into the MIMO systems. These insights (associated with polynomial matrices) should be useful for further development of blind system identification.

Array Shape Tracking using Active Sonar Reverberation

Presentation | Paper

Vijay Varadarajan and Jeffrey Krolik
Duke University
Department of Electrical and Computer Engineering
Box 90291
Durham, NC 27708
Phone:  (919) 660-5274

Abstract:  This paper describes a method for array shape estimation from clutter (ASEC) for a towed active sonar array. In practice, towed arrays deviate from their nominal linear geometry due to own ship motion and ocean currents. Conventional beamforming of a distorted array under the linear array assumption can result in unacceptably high sidelobe levels.  High spatial sidelobes limit the minimum detectable velocity achieved using Doppler-sensitive active sonar waveforms due to leakage of reverberation, which is Doppler-spread by own ship motion. For adaptive beamformers, uncompensated array distortion can result in signal cancellation due to wavefront mismatch across the array.

Previous approaches to towed array shape estimation fall primarily into heading sensor based and data-driven approaches. In the former, Kalman filter based techniques have been implemented (Gray et al, 1993, and Newhall, 2002), using measurements from heading and depth sensors. 

The Kalman filter state equation can be derived from the Paidoussis equation (Paidoussis, 1966) (also known as the water-pulley model) for array dynamics. In some array designs, however, it may not be mechanically feasible to instrument the array with a sufficient number of heading sensors.  Among data driven approaches, strong far field sources of opportunity have been used to fit phase terms corresponding to the transverse displacements of the array using time delay estimation techniques (Owsley, 1981).  For active sonars in a strong reverberation, however, strong sources of opportunity may not always be available.  Among alternative data-driven approaches, radar clutter has been used to provide gain and phase calibration for a uniform linear array (ULA) (Robey et al, 1994). Calibration from clutter exploits the linear relationship between the clutter spatial and Doppler frequency for linear sidelooking arrays. This method was developed for gain-phase calibration rather than array shape estimation and requires relatively long coherent processing times not often available in sonar applications.

In this paper, we develop a method for array shape estimation and tracking of a towed array using spatially distributed Doppler-spread reverberation returns from a single sonar ping. The water-pulley model for array dynamics is combined with maximum likelihood (ML) estimation of array shape using clutter returns. More specifically, the array headings for an N element array are parameterized by L << N known basis functions. It has been shown previously (Varadarajan et al. 2002) that the deterministic relationship between the clutter spatial and Doppler frequencies for a distorted linear array causes it to be low-rank in the full dimension space-time vector space and in particular the rank is approximately twice the 1-D Brennan's rule for modest array shape distortions.

The low dimensionality of the clutter is exploited to facilitate ML estimation of the heading basis coefficients by fitting the reverberation snapshots to the modeled clutter subspace. An unconstrained non-linear ML cost function yields an ambiguous solution corresponding to an array shape flipped about its axis.  This ambiguity is resolved by using a constrained steepest descent algorithm, which incorporates observations from a single off-axis heading sensor. The ASEC algorithm consists of using these constrained ML estimates in a Kalman filter, which incorporates the water-pulley model for array dynamics. Simulation results using real heading sensor data from a TB-29 array in simulated multipath reverberation indicate that a five-fold reduction in sensor position RMSE can be achieved using ASEC versus dynamical model-only prediction of array shape.

Matched Subspace Detectors for Stochastic Signals

Presentation | Paper

Todd McWhorter
Mission Research Corporation
3665 JFK Parkway
Building 1, Suite 206
Fort Collins, CO 80525
Phone:  (970) 282-4400, ext. 25

Louis Scharf
Department of Electrical and Computer Engineering
Colorado State University
Fort Collins, CO 80523
Phone:  (970) 491-2979

Abstract:  Our aim in this paper is to extend the matched subspace detectors (MSDs) of [1-3] to the detection of stochastic signals.  In [1-3], the signal to be detected was assumed to be placed deterministically at an unknown location in a known signal subspace.  The basis for the subspace was irrelevant.  In this paper, the signal is assumed to be placed randomly at an unknown location in a known subspace.  If nothing is known apriori about the second-order moments of the placement, then the generalized likelihood ratio test (GLRT) for a stochastic signal turns out to be identical to the GLRT for a deterministic signal.  Consequently, the MSDs are more general than originally thought, applying to the detection of a signal whose mean value or covariance matrix is modulated by a subspace signal.  Moreover, the invariance sets for stochastic MSDs are identical to those of the corresponding deterministic MSD.  The results of this paper extend the theory of MSDs to radar and sonar problems where random target effects may be modeled, and to data communication problems where symbols are coded by subspaces, rather than coordinates of subspaces.


[1]  L.L. Scharf, Statistical Signal Processing. Addison-wesley, 1991.

[2]  L.L. Scharf and B. Friedlander, “Matched subspace detectors” IEEE Trans. SP, vol. 42, Aug.


[3]  S. Kraut, L.L. Scharf, and L.T. Whorter, “Matched and adaptive subspace detectors for

       radar, sonar, and data communication.” Submitted for review IEEE Trans. SP, June 1996.

       (Also available is a University of Colorado Technical Report).

Active-Testing Surveillance Systems, Or Playing Twenty Questions With A Radar

Presentation | Paper

Daniel R. Fuhrmann
Washington University
Department of Electrical Engineering
Campus Box 1127
St. Louis, MO 63130
Phone:  (314) 935-6163

Abstract:  A new paradigm for surveillance systems in which active testing, defined as online measurement choice using feedback from past observations, is proposed.  We model an active-testing surveillance system as a communication system in the usual information-theoretic or Bayesian sense, with the added feature that the channel can be manipulated by the observer.  Within this paradigm, the specific problem addressed is that of multiple target detection, when there is a constraint on the total energy available for illumination of target regions.  An iterative algorithm is developed in which the distribution of available energy is chosen to maximize the mutual information between the binary source vector (each bit representing target present/absent) and the observation.  A comparison can be drawn with the game "Twenty Questions" in which the observer asks the most informative question at each iteration in order to arrive at the correct answer as quickly as possible.

Although the problem formulation and algorithmic solution are idealized, we envision an application to GMTI radar with multiple datacubes and view angles, wherein the radar transmit parameters are under the control of an active testing algorithm.

Radar Signal Processing Considerations for Imaging in the Quantum Limit


Allan Steinhardt & Jack McCrae, Jr.
3701 N. Fairfax Drive
Arlington, VA 22203
Phone:  (703) 696-2331

Abstract:  Conventional wisdom suggests that the choice of a dish versus a phased array is based purely on the added ability of the phased array, traded against the extra cost. These abilities are "instantaneous" electronic scan, adaptive suppression of clutter and directional interference, and improved bearing estimation using monopulse. It can be argued that phased arrays are THE sensor venue on which all of ASAP is based. Hence it is interesting to see whether the conventional wisdom is correct. In this talk we prove it is wrong, in the quantum limit. We will present a radio astronomy case where the quantum limit arises, arguing that the results do in fact have practical significance.  Now, if everything else is equal and noise is absent, the broadside performance of dish and phased array systems of equal aperture is the same in the classical limit.  However, even in the absence of all other noise, photon statistics change this situation in the low signal (photon starved) limit.  The phased array must make multiple amplitude and phase measurements both of which are subject to noise, while the focal plane array is making a single intensity measurement only for a fixed solid angle.  Furthermore, as the photon number decreases, the uncertainty relation, Δn Δφ ≥ 1, drives the phase noise higher.  When trying to quantify this difference it quickly becomes apparent the real world situation is more complex than anticipated.  Simulations show that a phased array can outperform a dish against extended objects, even when the photon count gets small, whereas for point sources the situation is reversed.  These results suggest that the construction of phased arrays of larger numbers of increasingly smaller sub-elements will reach a point where performance suffers. We will quantify this crossover point for a specific case involving asteroid tracking.