Statistics of adaptive nulling and use of the generalized eigenrelation (GER) for modeling inhomogeneities in adaptive processing

• Published in: IEEE transactions on signal processing Vol. 48; no. 5; pp. 1263 - 1273
• Main Author: Richmond, C.D.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.05.2000; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Adaptive filters; Applied sciences; Array signal processing; Context modeling; Convergence; Data analysis; Exact sciences and technology; Information, signal and communications theory; Interference constraints; Performance analysis; Signal and communications theory; Signal, noise; Statistical analysis; Statistics; Studies; Telecommunications and information theory; Testing; Waveform; Lateral lobe; Statistical analysis; Adaptive detection; Adaptive algorithm; System response; Adaptive processor; Adaptive estimation; Modeling; Adaptive method; Heterogeneity; Beamforming; Experimental result; Minimal variance; Covariance; Convergence rate; Signal processing; Numerical simulation; Performance analysis; Comparative study
• ISSN: 1053-587X; 1941-0476
• DOI: 10.1109/78.839974

This paper examines the integrity of the generalized eigenrelation (GER), which is an approach to assessing performance in an adaptive processing context involving covariance estimation when the adaptive processors are subject to undernulled interference. The GER is a mathematical relation, which if satisfied, often facilitates closed-form analysis of adaptive processors employing estimated covariances subject to inhomogeneities. The goal of this paper is to determine what impact this constraint has on the integrity of the adaptive nulling process. In order to examine the impact of the GER constraint on adaptive nulling, we establish fundamental statistical convergence properties of an adaptive null for the sample covariance-based (SCB) minimum variance distortionless response (MVDR) beamformer. Novel exact expressions relating the mean and variance of an adaptive null of a homogeneously trained beamformer to the mean and variance of a nonhomogeneous trained beamformer are derived. In addition, it is shown that the Reed et al. (1974) result for required sample support can be highly inaccurate under nonhomogeneous conditions. Indeed, the required sample support can at times depend directly on the power of the undernulled interference.