James H. Michels

Parametric adaptive matched filter for airborne radar applications

The parametric adaptive matched filter (PAMF) for space-time adaptive processing (STAP) is introduced via the matched filter (MF), multichannel linear prediction, and the multichannel LDU decomposition. Two alternative algorithmic implementations of the PAMF are discussed. Issues considered include sample training data size and constant false alarm rate (CFAR). Detection test statistics are estimated for airborne phased array radar measurements, and probability of detection is estimated using simulated phased array radar data for airborne surveillance radar scenarios. For large sample sizes, the PAMF performs close to the MF; performance degrades slightly for small sample sizes. In both sample size ranges, the PAMF is tolerant to targets present in the training set.

Theory of the Stochastic Resonance Effect in Signal Detection—Part II: Variable Detectors

In Part I of this paper [ldquoTheory of the Stochastic Resonance Effect in Signal Detection: Part I-Fixed Detectors,rdquo IEEE Transactions on Signal Processing, vol. 55, no. 7, pt. 1, pp. 3172-3184], the mechanism of the stochastic resonance (SR) effect for a fixed detector has been examined. This paper analyzes the stochastic resonance (SR) effect under the condition that the detector structure or its parameters can also be changed. The detector optimization problem with SR noise under both Neyman-Pearson and Bayesian criteria is examined. In the Bayesian approach when the prior probabilities are unknown, the minimax approach is adopted. The form of the optimal noise pdf along with the corresponding detector as well as the maximum achievable performance are determined. The developed theory is then applied to a general class of weak signal detection problems. Under the assumptions that the sample size N is large enough and the test statistics satisfies the conditions of central limit theorem, the optimal SR noise is shown to be a constant vector and independent of the signal strength for both Neyman-Pearson and Bayesian criteria. Illustrative examples are presented where performance comparisons are made between the original detector and the optimal SR noise modified detector for different types of SR noise.

A parametric multichannel detection algorithm for correlated non-Gaussian random processes

This paper addresses the problem of adaptive multichannel signal detection in additive correlated non-Gaussian noise using a parametric model-based approach. The adaptive signal detection problem has been addressed extensively for the case of additive Gaussian noise. However, the corresponding problem for the non-Gaussian case has received limited attention. The additive non-Gaussian noise is assumed to be modeled by a spherically invariant random process (SIRP). The innovations based detection algorithm for the case of constant signal with unknown complex amplitude is derived. The resulting receiver structure is shown to be equivalent to an adaptive matched filter compared to a data dependent threshold. Performance analysis of the derived receiver for the case of a K-distributed SIRV is presented.

Reducing Probability of Decision Error Using Stochastic Resonance

The problem of reducing the probability of decision error of an existing binary receiver that is suboptimal using the ideas of stochastic resonance is solved. The optimal probability density function of the random variable that should be added to the input is found to be a Dirac delta function, and hence, the optimal random variable is a constant. The constant to be added depends upon the decision regions and the probability density functions under the two hypotheses and is illustrated with an example. Also, an approximate procedure for the constant determination is derived for the mean-shifted binary hypothesis testing problem

Statistical analysis of the non-homogeneity detector for STAP applications

Abstract : We present a statistical analysis of the recently proposed non-homogeneity detector (NHD) for Gaussian interference statistics. We show that a formal goodness-of-fitness test can be constructed by accounting for the statistics of the generalized inner product (GIP) used as the NHD test statistic. Specifically, the Normalized-GIP is shown to follow a central-F distribution and admits a canonical representation in terms of two statistically independent Chi-squared distributed random variables. Moments of the GIP can be readily calculated as a result. These facts are used to derive the goodness-of-fit tests, which facilitate intelligent training data selection. Additionally, we address the issue of space-time adaptive processing (STAP) algorithm performance using the NHD as a pre-processing step for training data selection. Performance results for the adaptive matched filter (AMF) method are reported using simulated as well as measured data.

Performance of STAP Tests in Gaussian and Compound-Gaussian Clutter

Abstract Michels, James H., Himed, Braham, and Rangaswamy, Muralidhar, Performance of STAP Tests in Gaussian and Compound-Gaussian Clutter, Digital Signal Processing , 10 (2000), 309–324. The performance of a recently proposed model-based space–time adaptive processing detection method is considered here and compared with several candidate algorithms. Specifically, we consider signal detection in additive disturbance consisting of compound-Gaussian clutter plus Gaussian thermal white noise. Consideration is given to both detection and constant false alarm rate robustness with respect to clutter texture power variations. Finally, the performance of the new test is assessed using small training data support size.

Performance of Parametric and Covariance Based STAP Tests in Compound-Gaussian Clutter

Abstract Michels, J. H., Rangaswamy, M., and Himed, B., Performance of Parametric and Covariance Based STAP Tests in Compound-Gaussian Clutter, Digital Signal Processing12 (2002) 307–328 The performance of a parametric space–time adaptive processing method is presented here. Specifically, we consider signal detection in additive disturbance containing compound-Gaussian clutter plus additive Gaussian thermal white noise. Performance is compared to the normalized adaptive matched filter and the Kelly GLRT receiver using simulated and measured data. We focus on the issues of detection and false alarm probabilities, constant false alarm rate, robustness with respect to clutter texture power variations, and reduced training data support.

Noise Enhanced Parameter Estimation

This paper investigates the phenomenon of noise enhanced systems for a general parameter estimation problem. When the estimator is fixed and known, the estimation performance before and after the addition of noise are evaluated. Performance comparisons are made between the original estimators and noise enhanced estimators based on different criteria. The form of the optimal noise probability density function (pdf) is determined. The results are further extended to the general case where the noise is introduced to the system via a transformation. For the case where the estimator is fixed and unknown, approaches are also proposed to find the optimum noise. Finally, two illustrative examples are presented where the performance comparison is made between the optimal noise modified estimator and Gaussian noise modified estimator.

Noise Enhanced Nonparametric Detection

This paper investigates potential improvement of nonparametric detection performance via addition of noise and evaluates the performance of noise modified nonparametric detectors. Detection performance comparisons are made between the original detectors and noise modified detectors. Conditions for improvability as well as the optimum additive noise distributions of the widely used sign detector, the Wilcoxon detector, and the dead-zone limiter detector are derived. Finally, a simple and fast learning algorithm to find the optimal noise distribution solely based on received data is presented. A near-optimal solution can be found quickly based on a relatively small dataset.

Stochastic resonance: An approach for enhanced medical image processing

This paper presents a novel application of the stochastic resonance effect in medical image processing. Aiming to improve system performance, two noise modified image processing schemes are proposed. Performances of several medical image processing systems are shown to improve when suitable stochastic resonance noise is added.