Spectral estimation for sensor arrays

TLDR: In this paper, a mathematical framework is developed in which to analyze and design spectral estimation algorithms for correlation-matching spectral estimates, which leads to the extendibility question: does there exist any positive spectrum on the spectral support that exactly matches a given set of correlation samples?

Abstract: The array processing problem is briefly discussed and an abstract spectral estimation problem is formulated. This problem involves the estimation of a multidimensional frequency-wave vector power spectrum from measurements of the correlation function and knowledge of the spectral support. The investigation of correlation-matching spectral estimates leads to the extendibility question: does there exist any positive spectrum on the spectral support that exactly matches a given set of correlation samples? In answering this question, a mathematical framework is developed in which to analyze and design spectral estimation algorithms. Pisarenko's method of spectral estimation, which models the spectrum as a sum of impulses plus a noise component, is extended from the time series case to the more general array processing case. Pisarenko's estimate is obtained as the solution of a linear optimization problem, which can be solved using a linear programming algorithm such as the simplex method.