Robust Adaptive Beamforming: A Coherence Constrained Approach Inspired by Random Matrix Theory
Abstract
Research Problem and Objectives:Conventional beamforming (CBF) and adaptive beamforming (ABF) play major roles in many military, civilian, and industrial systems as effective means of spatial discrimination in the presence of competing interfering signals. ABF solutions optimized for maximum signal-to-interference-plusnoise ratio (SINR) result in beamforming filter weights that depend on the data covariance and the signal array response vector. The effectiveness of practical application of such solutions, however,is limited by (i) data stationarity (needed for data covariance estimation), and (ii) knowledge of the true signal array response vector. Robust ABF methods attempt to address these two critical issues via a slight reformulation of the ABF problem statement, and many solutions result in some form of diagonal loading of the data covariance. Such robust ABF solutions are justifiably interpreted as hybrid beamformers that engage the tradespace between conventional beamforming, i.e. CBF,and data adaptive beamforming, i.e. ABF. The objective of the current proposed research effort is to (i) leverage random matrix theory to gain insights into robust adaptive beamforming, (ii) use these insights to develop new alternative robust ABF approaches congruent with findings, and (iii) assess the performance and competitiveness of these new alternative robust ABF approaches.Technical Approach:A recent random matrix theory based analysis has established the joint probability distribution for two power spectral estimates, where one is CBF-based and the other is ABF-based, revealing that their statistical coupling is governed by the geometric cosine (or coherence) between their filter weights asweighted by the true data covariance. The current proposed research effort will build on this reveal by formulating an alternative robust ABF criterion that constrains filter weight coherence with the maximum output SINR filter, while minimizing the filter response to array errors. Optimizing this criterion over the filter weights results in a new robust ABF algorithm. The performance and competitiveness of this alternative coherence constrained robust ABF algorithm will be assessed via a clairvoyant (data covariance assumed known) output SINR analysis, and a finite sample (data covariance assumed unknown) analysis. The clairvoyant analysis will likewise assess the signal-to-array errors ratio that is expected to compete with attempts to maximize filter output SINR. Random matrix theory will be used to facilitate the finite sample analysis of the coherence constrained robust ABF approach.Anticipated Outcome ofResearch:This proposed research effort is expected to provide new insights into robust ABF in general, and ultimately the development of a viable, effective, and practical alternative robust ABF approach for passive sonar of value to the United States Navy. The proposed alternative problem formulation has a practically advantageous interpretation (namely, the coherence metric is the same as SINR loss), and the robust ABF solutions will possess inherently superior robustness to increasing interference due to the coherence constraint.*Approved for Public Release
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Mar 24, 2023
- Source ID
- N000142312107
Entities
People
- Christ D. Richmond
Organizations
- Duke University
- Office of Naval Research
- United States Navy