**ASAP 2003**

**Space-Time
Adaptive Processing Using Sparse Arrays **

Michael
Zatman

MIT
Lincoln Laboratory

244
Wood Street

Lexington,
MA 02420

Phone:
(781) 981-2543

Email: zatman@ll.mit.edu

**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

Email: jsb@isl-inc.com

Joseph
Guerci

DARPA-SPO

3701 N. Fairfax Drive

Arlington, VA 22203

Phone: (703) 248-1548

Email:
jguerci@darpa.mil

**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 **

Fabian Lapierre and Jacques Verly

University of LiÃ¨ge, Belgium

Department of Electrical Engineering
and Computer Science

Sart-Timan, Building B28

B-4000 LiÃ¨ge

Belgium

Phone: +32 4 366 37 41

Email: f.Lapierre@ulg.ac.be

**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**

Norman Owsley and John Tague

Office of Naval Research

Code 321US

4001 N. 9^{th} Street

Arlington, VA 22203

Phone: (703) 243-1160, ext. 233

Email: owsleyn@onr.navy.mil

**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.
**w**_{a} 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 **w**_{a} 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

** _{ } **
(A2)

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**

Jian Wang and R. Lynn Kirlin

University of Victoria

Department of Electrical Engineering

Victoria, B.C.

Canada

Phone: (250) 472-4255

Email: jwang@ece.uvic.ca

**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 **

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 **

Andrew Fletcher and Frank C. Robey

MIT Lincoln Laboratory

244 Wood Street

Lexington, MA 02420

Phone: (781) 981-2732

Email: fletcher@ll.mit.edu

**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 **

Adam Bojanczyk

Cornell University

School of Electrical and Computer
Engineering

335 Rhodes Hall

Ithaca, NY 14850

Phone: (607) 255-4296

Email: adamb@ece.cornell.edu

**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

SAIC

23 Clara Drive, Suite 206

Mystic, CT 06355

Phone: (860) 572-2384

Email: john.p.ianniello@saic.com

**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 **

Yi Jiang, Zhisong Wang, and Jian Li

University of Florida

ECE Department

P.O. Box 116130

Gainesville, FL 32611

Phone: (352) 392-5241

Email: yjiang@dsp.ufl.edu

Petre
Stoica

Uppsala University

Department of Systems and Control

P.O. Box 27

SE-751 05 Uppsala

Sweden

Email: ps@syscon.uu.se

**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 R^{2}CB.

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

Louis
Scharf and Edwin Chong

Colorado State University

Electrical and Computer Engineering

Fort Collins, CO 80521

Phone: (970) 484-2537

Email: scharf@engr.colostate.edu

L.
Todd McWhorter

Mission
Research Corporation

3665
JFK Parkway

Building
1, Suite 206

Fort
Collins, CO 80525

Phone:
(970) 282-4400, ext. 25

Email:
*mcwhorter@aster.com*

Michael
Zoltowski

Purdue University

School of Electrical Engineering

1285 Electrical Engineering Bldg.

West Lafayette, IN 47907-1285

Phone: (317) 494-3512

Email: mikedz@ecn.purdue.edu

J.
Scott Goldsteini

SAIC International

4001 Fairfax Drive, Suite 675

Arlington, VA 22203

Phone: (703) 741-7826

Email: jay.s.goldstein@saic.com

**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.

Vahid
Tarokh

Division of Engineering and Applied
Sciences

Harvard University

33 Oxford Street Room MD 347

Cambridge, MA 02138, USA

Phone: (617) 384-5026

Email: vahid@deas.harvard.edu

**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**

Danial
Bliss and Amanda Chan

MIT Lincoln Laboratory

244 Wood Street

Lexington, MA 02420

Phone: (781) 981-3300

Email: bliss@ll.mit.edu

**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 **

Patrick Bidigare

Veridian Ann Arbor R&D Center

3300 Plymouth Road

Ann Arbor, MI 48130

Phone: (734) 994-1200, ext. 2792

Email: Patrick.Bidigare@veridian.com

**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

Email: forsythe@ll.mit.edu

**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

Email: Christ@ll.mit.edu

**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

DARPA/ATO

3701 N. Fairfax Drive

Arlington, VA 22203-1714

Phone: (703) 696-2333

Email: tkooij@darpa.mil

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

Email: rsharma@ll.mit.edu

**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 **

Anthony Devaney

Northeastern University

Department of Electrical and Computer
Engineering

Dana Building

Boston, MA 02115

Phone: (617) 373-5284

Email: devaney@ece.neu.edu

**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 **

Tariq Bakir and Russell Mersereau

Georgia Institute of Technology

563 Lovejoy Street, NW

Atlanta, GA 30313

Phone: (404) 872-0810

Email: bakirts@ece.gatech.edu

**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 **

Yingbo Hua, Senjian An, and Yong Xiang

University of California, Riverside

Department of Electrical Enigineering

Riverside, CA 92521

Phone: (909) 787-2853

Email: yhua@ee.ucr.edu

**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 **

Vijay Varadarajan and Jeffrey Krolik

Duke University

Department of Electrical and Computer
Engineering

Box 90291

Durham, NC 27708

Phone: (919) 660-5274

Email: vv@ee.duke.edu

**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 **

Todd McWhorter

Mission
Research Corporation

3665
JFK Parkway

Building
1, Suite 206

Fort
Collins, CO 80525

Phone:
(970) 282-4400, ext. 25

Email:
*mcwhorter@aster.com*

Louis Scharf

Department
of Electrical and Computer Engineering

Colorado
State University

Fort
Collins, CO 80523

Phone:
(970) 491-2979

Email:
*scharf@engr.colostate.edu*

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.

References

[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.

1994.

[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 **

Daniel R. Fuhrmann

Washington University

Department of Electrical Engineering

Campus Box 1127

St. Louis, MO 63130

Phone: (314) 935-6163

Email: danf@ee.wustl.edu

**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.

DARPA/IXO

3701 N. Fairfax Drive

Arlington, VA 22203

Phone: (703) 696-2331

Email: asteinhardt@darpa.mil

**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.