I. Introduction
The use of persymmetry is common in many signal processing contexts; just to give some examples, for communication problems it was exploited in [1], for radar applications in [2] and [3], for direction of arrival estimation in [4], for matched-filter-bank spectral estimators in [5], and for the development of forward-backward averaging linear prediction techniques in [6]. It induces a special structure to the steering vector and the interference covariance matrix whose suitable exploitation can lead to interesting processing gains [7]. More precisely, a sensing system equipped with a symmetrically spaced linear array or using symmetrically spaced pulse trains could collect data statistically symmetric in forward and reverse directions. This results into an interference covariance matrix which shares a so-called “doubly” symmetric form, i.e., Hermitian about its principal diagonal and persymmetric about its cross diagonal
Note that the Toeplitz covariance matrix given by a uniformly spaced pulse train (or array) is a special case of the persymmetry.
[2], [8]. The mentioned structure represents a design constraint which forces dependences among the unknowns and reduces the number of parameters to be estimated. Before proceeding, it is worth pointing out that the persymmetric property is not limited to linear arrays but it arises in a large class of geometries such as standard rectangular arrays, uniform cylindrical arrays (with an even number of elements), and some standard exagonal arrays [7].