Structured Covariance Estimation From Spatial Spectra For Adaptive Beamforming

Abstract

The covariance matrix for a sensor array observing a stationary space-time process is determined by the individual sensor element locations, the directional response and noise of those elements, and the spatial spectrum of the process. Under this model the covariance matrix has a particular structure that can be exploited, improving adaptive beamformer performance both in terms of the number of snapshots required for good performance and robustness against correlated signal and interference environments. These performance improvements are particularly bene¯cial for large aperture arrays with large numbers of sensor elements that are operating in non-stationary and multi-path environments. No closed form solution exists for estimating structured covariance for the general problem of an unknown number of signals in non-white noise. We look to exploit the naturally intuitive interpretation of the process in the azimuth-elevation or frequency-wavenumber domains to address the problem. This dissertation develops a covariance from spatial spectrum (CSS) method by ¯rst estimating the spectrum of the process, and then applying standard spectral to covariance transforms. The initial characterization in the transform domain, either direction of arrival or wavenumber, provides a natural reinforcement of the underlying space-time process model. Additionally, spectral estimation techniques take advantage of the number of spatial samples, in particular for arrays with many elements, in a manner simple snapshot averaging cannot. While ad-hoc, such a structured covariance technique can provide near optimal performance for passive signal detection or recovery with very few snapshots. The ¯rst objective of this work is to understand the performance of minimum vari- ance distortionless response adaptive beamforming when covariance is estimated from the spatial spectrum. Positive de¯niteness of the covariance matrix and estimation bias are investigated. Performance predictions are developed for the case of a uniform line array and classical power spectral estimation techniques. This analysis highlights the need to explicitly deal with mixed spectra that arise in environments containing both point source and spatially-spread signals. Thomson's multi-taper spectral estimation neatly combines both the convenience of the non-parametric spectral estimation algorithms and the required harmonic analysis to handle such mixed spectra. Adaptive beamformer performance is as- sessed for various interference and noise environments against existing snapshot de¯cient algorithms. Extensions to support arbitrary array geometry are considered. A correlated signal and interference environment cannot be modeled as a stationary space-time process. A second objective of this work is to investigate how constraining the covariance to a stationary space-time process model mitigates signal cancellation due to correlation between the signal and interference. Reduction in correlation, and the resultant covariance bias are investigated. Adaptive beamformer performance in the presence of correlated signal and interference is assessed. Structured covariance methods may su®er performance losses when real world conditions violate model assumptions. The ¯nal objective of this work is to understand the impacts of non-ideal array manifold response. The CSS techniques developed in the dissertation are extended to account for such non-ideal response. Adaptive beamformer performance is assessed for various interference and noise environments in the presence of random and deterministic array manifold response errors. Bene¯ts to spectral estimation when using the non-ideal response processing are also seen.