Positive-definite Toeplitz completion in DOA estimation for nonuniform linear antenna arrays. II. Partially augmentable arrays

Abstract

For pt. I see ibid., vol.46, p.2458-71 (1998). This paper considers the problem of direction-of-arrival (DOA) estimation for multiple uncorrelated plane waves incident on "partially augmentable" antenna arrays, whose difference set of interelement spacings is not complete. The DOA estimation problem for the case when the number of sources exceeds the number of contiguous covariance lags gives rise to the covariance matrix completion problem. Maximum-entropy (ME) positive-definite (p.d.) completion for partially specified Toeplitz covariance matrices is developed using convex programming techniques. By this approach, the classical Burg (1975) ME extension problem for the given set of covariance lags is generalized for the situation when some lags are missing. For DOA estimation purposes, we find the p.d. Toeplitz matrix with fixed eigensubspace dimension that is the closest approximation of the ME-completed matrix. Computer simulation results are presented to demonstrate the high DOA estimation accuracy of the proposed technique compared with the corresponding Cramer-Rao bound.