James Ward

Cramer-Rao bounds for target angle and Doppler estimation with space-time adaptive processing radar

Space-time adaptive processing (STAP) can substantially improve airborne radar performance in environments with interference (clutter and/or jamming). This paper considers target parameter estimation with the STAP radar. The maximum-likelihood estimator for target angle and Doppler is reviewed. Cramer-Rao bounds for target angle and Doppler estimation accuracy are derived for an arbitrary interference scenario. These bounds show that in clutter, angle accuracy depends on the target Doppler and vice-versa. They are useful for quantifying the best-case degradation in estimator accuracy due to interference, and for determining the fractions of the Doppler space and coverage sector over which a specified level of accuracy can be achieved.

Beampattern Synthesis via a Matrix Approach for Signal Power Estimation

We present new beampattern synthesis approaches based on semidefinite relaxation (SDR) for signal power estimation. The conventional approaches use weight vectors at the array output for beampattern synthesis, which we refer to as the vector approaches (VA). Instead of this, we use weight matrices at the array output, which leads to matrix approaches (MA). We consider several versions of MA, including a (data) adaptive MA (AMA), as well as several data-independent MA designs. For all of these MA designs, globally optimal solutions can be determined efficiently due to the convex optimization formulations obtained by SDR. Numerical examples as well as theoretical evidence are presented to show that the optimal weight matrix obtained via SDR has few dominant eigenvalues, and often only one. When the number of dominant eigenvalues of the optimal weight matrix is equal to one, MA reduces to VA, and the main advantage offered by SDR in this case is to determine the globally optimal solution efficiently. Moreover, we show that the AMA allows for strict control of main-beam shape and peak sidelobe level while retaining the capability of adaptively nulling strong interferences and jammers. Numerical examples are also used to demonstrate that better beampattern designs can be achieved via the data-independent MA than via its VA counterpart.

Maximum likelihood angle and velocity estimation with space-time adaptive processing radar

Airborne surveillance radar performance can be improved with space-time adaptive processing (STAP) to cancel ground clutter and interference. This paper considers maximum likelihood (ML) angle and velocity estimation for airborne radar employing STAP. The ML estimator requires a two-dimensional optimization. A computationally efficient quasi-Newton approach is proposed, whereby a positive definite approximate Hessian is formed using only the secondary data processed by three adaptive space-time filters. The algorithm is naturally initialized by the target detection location within a coarsely spaced angle-Doppler filter bank. Monte-Carlo simulations show that the new algorithm nearly achieves the Cramer-Rao bound and outperforms conventional one-dimensional estimators, which suffer from location-dependent biases when employed in STAP scenarios.

Source motion mitigation for adaptive matched field processing

Application of adaptive matched field processing to the problem of detecting quiet targets in shallow water is complicated by source motion, both the motion of the target and the motion of discrete interferers. Target motion causes spreading of the target peak, thereby reducing output signal power. Interferer motion increases the dimensionality of the interference subspace, reducing adaptive interference suppression. This paper presents three techniques that mitigate source motion problems in adaptive matched field processing. The first involves rank reduction, which enables adaptive weight computation over short observation intervals where motion effects are less pronounced. The other two techniques specifically compensate for source motion. Explicit target motion compensation reduces target motion mismatch by focusing snapshots according to a target velocity hypothesis. And time-varying interference filtering places time-varying nulls on moving interferers not otherwise suppressed by adaptive weights. The three techniques are applied to volumetric array data from the Santa Barbara Channel Experiment and are shown to improve output signal-to-background-plus-noise ratio by more than 3 dB over the standard minimum-variance, distortionless response adaptive beam-former. Application of the techniques in some cases proves to be the difference between detecting and not detecting the target.

A comparison of robust adaptive beamforming algorithms

An important problem in adaptive beamforming algorithm design is robustness to steering vector uncertainty. A white-noise gain constraint (WNGC) has historically been an effective approach. Recently, the robust Capon beamforming class of algorithms has been developed to provide robustness through the use of a steering vector uncertainty region and an implicit steering vector estimation step as part of the beamformer. Like WNGC, the RCB algorithm can be shown to produce weight vectors based upon a diagonal loading of the covariance matrix. This paper provides some direct comparison of WNGC and RCB approaches for scenarios of interest. Geometrical interpretations of RCB algorithms provide insights to their optimality. Both approaches have a parameter than can be used to tune the performance from aggressive to conservative. Major observed differences are that RCB provides more accurate power estimates, focuses its high loading more locally, but exhibits higher white noise gain near sources.

Space-time adaptive processing with sparse antenna arrays

Sparse, or thinned arrays can provide the resolution and accuracy of a large aperture without the hardware expense of a fully populated array. This paper examines application of thinned arrays to an airborne radar that employs space-time adaptive processing (STAP) to reject ground clutter. It is shown that the rank of the clutter covariance matrix depends on the precise thinned configuration. Upper and lower bounds for the clutter covariance matrix are provided. An irregularly spaced thinned array can have the same rank as a filled array if all potential synthetic aperture positions get sampled at least once during the coherent processing interval. Beamspace STAP approaches with irregularly spaced arrays generally require more degrees of freedom (DOF) than that of a filled array because a thinned array beamspace transform cannot generally effect shifted subaperture beams. With additional DOF (and still much less than fully adaptive) a randomly spaced thinned array beamspace approach call still provide relatively low loss and avoid the additional angle-Doppler blind zones that result from regularly spaced thinned arrays.

Evaluation of reduced-rank, adaptive matched field processing algorithms for passive sonar detection in a shallow-water environment

This paper evaluates the performance of several reduced-rank, adaptive matched field processing (AMFP) algorithms for passive sonar detection in a shallow-water environment. Effective rank reduction improves the stability of adaptive beamformer weight calculation when the number of available snapshots is limited. Here, rank-reduction techniques with various criteria for subspace selection are evaluated within a common framework and compared to the full-rank conventional and minimum-variance (MVDR) beamformers. Results from real data demonstrate that rank reduction, properly applied can improve AMFP detection performance in practical system implementations.

Source localization using adaptive subspace beamformer outputs

Maximum likelihood (ML) parameter estimation for multi-dimensional adaptive problems is addressed. Multiple adaptive outputs are ordinarily combined by utilizing the full dimension data. However, many adaptive problems utilize subspace processing for each adaptive beam which can increase the difficulty of many super-resolution techniques. This paper shows that the steering vector structure can be utilized to allow ML techniques for a fixed grid of hypothesis vectors to be computationally feasible for many scenarios.

Adaptive processing for airborne surveillance radar

Future airborne surveillance radars will be required to detect and locate targets in the presence of intense ground clutter and interference. This paper presents an overview of the radar problem and the classes of adaptive algorithm architectures that may be employed. We describe the characteristics of the target and interference signals in the spatial and temporal dimensions observed by a pulse-Doppler radar. A combination of spatial and space-time adaptive processing (STAP) techniques are required to mitigate the variety of interference sources to be expected. Computational complexity and estimation of the interference force consideration of partially adaptive, or reduced-dimension adaptive architectures. A combination of fixed preprocessor filtering and judicious choice of training strategies, can result in substantial dimensionality reduction while maintaining near-optimum performance.

Optimal Array Pattern Synthesis via Matrix Weighting

We present new array beampattern synthesis approaches via semidefinite relaxation (SDR) for arbitrary array. Compared to the conventional approaches of using weight vectors at the array output for array pattern synthesis, which we refer to as the vector weighting approaches (VWA), weight matrices are used at the array output by MWA for much improved flexibility for optimal array pattern synthesis, and globally optimal solutions can be determined efficiently due to convex optimization formulations. Numerical examples are presented to show the excellent performance of MWA.