Unit Circle Roots Property for Sensor Array Signal Processing

This paper presents a new general proof that the roots of the polynomial corresponding to the minimum variance filter computed using the true Toeplitz covariance matrix must fall on the unit circle (UC). Unlike a previous proof applicable to the Minimum Variance Distortionless Response (MVDR) case only, the new proof does not rely on Wiener-Khinchin theorem to map the problem into frequency domain. Furthermore, the proof is applicable to a general class of sensor array signal processing problems beyond MVDR. Next, new closed-form solutions of UC roots constrained (UCRC) MVDR beamformer and Adaptive Matched Filter (AMF) will demonstrate significant performance improvement than the conventional, non-UC counterparts. The proposed approach will also be shown to achieve superior performance improvement at smaller aperture sizes than the conventional approaches, justifying its suitability for applications with reduced SWAP requirements.