This paper describes the first application of the fully adaptive radar (FAR) framework for cognition to the process of radar imaging. A cognitive radar adapts to its surroundings based on its perceptions of the environment, offering improved performance for a multitude of radar applications. We implemented an autoregressive backprojection (ARBP) imaging technique for the circular synthetic aperture radar (SAR) video within the structure of the FAR framework, allowing the system to adapt its down-range and cross-range resolutions to keep the detected targets visually distinct. This simple demonstration paves the way for more advanced adaptive imaging scenarios in the future. Application of the technique to the GOTCHA volumetric SAR data set demonstrated its capability in a realistic scenario in the presence of clutter and limited target persistence. When applied to the GOTCHA data set, the adaptive imaging system's cumulative executive optimization cost (CEOC), which is used to quantify the overall performance, was 41.3% smaller than the constant, fine resolution case. This significant improvement in CEOC comes at the expense of occasionally failing to meet imaging performance goals as the system adjusts to changes in the environment.

The maximum a posteriori penalty function (MAP-PF) approach is applied to tracking the bearing and bearing rate of multiple wideband sources in unknown colored noise. The track estimation problem is formulated directly from the array data using the maximum a posteriori (MAP) estimation criterion. The penalty function (PF) method of nonlinear programming is used to obtain a tractable solution. A sequential update procedure is developed in which penalized maximum likelihood estimates of target bearings, spectra, and noise parameters are computed and then used as synthetic measurements in a set of Kalman filter trackers. The two steps are coupled via the penalty function. During parameter estimation, the penalty function prevents erroneous outlier estimates which can cause the tracker to lose track. During the tracking step, it determines the influence of the parameter estimates on the final track estimates by adaptively adjusting the measurement error variance. Performance is demonstrated on a typical sonar scenario.

The maximum a posteriori penalty function (MAP-PF) approach is applied to target position tracking with a network of sensor arrays. The track estimation problem is formulated directly from the array data using the MAP estimation criterion. The penalty function method of nonlinear programming is used to obtain a tractable solution. A sequential update procedure is developed in which penalized maximum likelihood estimates of target bearing and power are computed for each array, and then used as synthetic measurements in an extended Kalman filter. The two steps are coupled via the penalty function. The current target state is used to guide the bearing estimation, and estimated signal powers control the influence of the bearing estimates from each array on the final track estimate. The algorithm can be implemented in a decentralized manner where bearing estimation is performed at the arrays, and track estimation is performed at a central processing site.

In typical parameter estimation problems, the signal observation is a function of the parameter set to be estimated as well as some background (environmental/system) parameters assumed known. The assumed background could differ from the true one, leading to biased estimates even at high signal-to-noise ratio (SNR). To analyze this background mismatch problem, a Ziv-Zakai-type lower bound on the mean-square error (MSE) is developed based on the mismatched likelihood ratio test (MLRT). At high SNR, the bound incorporates the increase in MSE due to estimation bias; at low SNR, it includes the threshold effect due to estimation ambiguity. The kernel of the bound's evaluation is the error probability associated with the MLRT. A closed-form expression for this error probability is derived under a random signal model typical of the bearing estimation/passive source localization problem. The mismatch is then analyzed in terms of the related ambiguity functions. Examples of bearing estimation with system (array shape) mismatch demonstrate that the developed bound describes the simulations of the maximum-likelihood estimate well, including the sidelobe-introduced threshold behavior and the bias at high SNR.

The problem of broadband range and bearing estimation is considered. It is demonstrated that the MUSIC technique can be implemented with an efficient search procedure, alternating maximization, for estimating range and bearing. Range-bearing estimation performance is compared via simulation to MVDR and to the Cramer-Rao lower bound. Experimental range estimation results with sea test data are also provided for a closing object emitting broadband and narrowband acoustic energy.

Decision feedback equalization (DFE) is a very effective receiver component that cancels intersymbol interference without inducing noise amplification. However, it suffers from error propagation in the start-up phase and when the environment undergoes a sudden change. For DS-CDMA wireless systems, we develop robust measures to mitigate the catastrophic error propagation effect using appropriate constraints on the receiver weight vectors. These constraints are constructed from the spreading codes of the desired user to preserve its output energy. By doing so, a desirable level of signal output power is maintained to keep the error probability low, thus preventing decision errors from occurring or propagating. Moreover, the introduction of signal-preserving constraints offers capacity of multiple access interference suppression. Efficient adaptive implementations are developed, and simulations performed to verify the effectiveness of the proposed constrained DFE detectors. It is demonstrated that the constructed constraints can eliminate the training overhead, offering complete blind implementations for multiuser decision-directed DFE filters.

The problem of detecting the number of uncorrelated narrowband signals received by an array of sensors when the direction of arrival (DOA) and power level of each source is unknown is investigated. A multi-hypothesis generalized likelihood ratio test (GLRT) approach is used, resulting in a procedure which maximizes the likelihood function with respect to the number of signals and their DOAs and powers. A tuning mechanism for controlling the tradeoff between the probability of correct detection and the probability of false alarm is obtained by imposing a constraint on the minimum allowable value for the power level estimate. A sequential search over the number of sources is used for a computationally feasible solution. Performance comparisons are made to the minimum description length (MDL) and minimum variance distortionless response (MVDR) signal detection approaches.

In signal processing, there are problems where the processed signal output energy is maximized while the noise component is minimized. This gives rise to a max/min problem, which is equivalent to a generalized eigenvalue problem. Exemplary applications of the max/min formulation have been seen in Capon's blind beamforming method and the blind minimum output energy (MOE) detection in CDMA wireless communications. The solution to such a problem involves eigen-decomposition of a transformed data covariance matrix inverse, which is computationally expensive to implement. This paper offers an adaptive RLS solution to the optimal minimum power filtering problem without involving eigen-decompositions. It is based on a new recursive least square updating procedure that works for multiple linear constraints, and uses a one-dimensional subspace tracking method to update the filter weights. The performance is comparable with that of using the direct eigen-decomposition and matrix inversion.

An adaptive beamformer which is robust to uncertainty in source DOA is derived. The beamformer is a weighted sum of minimum variance distortionless response (MVDR) beamformers pointed at a set of candidate DOAs, where the relative contribution of each MVDR beamformer is determined from a combination of observed data and prior knowledge about the DOA. When SNR is high, the MVDR beamformer whose look direction is closest to the source dominates, and nearly optimal performance is obtained. When SNR is low, the weighted combination of beamformers has a wider main beam which is robust to DOA uncertainty.

The Bayesian Ziv-Zakai bound on the mean square error (MSE) in estimating a uniformly distributed continuous random variable is extended for arbitrarily distributed continuous random vectors and for distortion functions other than MSE. The extended bound is evaluated for some representative problems in time-delay and bearing estimation. The resulting bounds have simple closed-form expressions, and closely predict the simulated performance of the maximum-likelihood estimator in all regions of operation.

The extended Ziv-Zakai bound for vector parameters is used to develop a lower bound on the mean square error (MSE) in estimating the two-dimensional bearing of a narrowband planewave signal using planar arrays of arbitrary geometry. The bound has a simple closed form expression which is a function of the signal wavelength, the signal-to-noise ratio (SNR), the number of data snapshots, the number of sensors in the array, and the array configuration. Analysis of the bound suggests that there are several regions of operation, and expressions for the thresholds separating the regions are provided. In the asymptotic region where the number of snapshots and/or SNR are large, the bound approaches the inverse Fisher information. In the a priori performance region where the number of snapshots or SNR is small, the bound approaches the a priori covariance. In the transition region, the bound varies smoothly between the two extremes. Results from simulation of the maximum likelihood estimator (MLE) demonstrate that the bound closely predicts the performance of the MLE in all regions.

Bounds on the MSE in estimating the bearing of a planewave signal is of considerable interest in many fields. Of particular importance is the ability of a bound to closely characterize performance in the small error or asymptotic region, and the large error or ambiguity region, and to accurately predict the location of the threshold between the regions. The vector Ziv-Zakai bound is applied to the problem of estimating two-dimensional bearing with planar arrays of arbitrary geometry. The bound is calculated for square and circular arrays, and compared with the Weiss-Weinstein (1983, 1984) bound. The Ziv-Zakai bound is shown to be tighter than the Weiss-Weinstein bound in the threshold and asymptotic regions.