Bayesian Compressive Sensing as Applied to Directions-of-Arrival Estimation in Planar Arrays

The Bayesian compressive sensing (BCS) is applied to estimate the directions of arrival (DoAs) of narrow-band electromagnetic signals impinging on planar antenna arrangements. Starting from the measurement of the voltages induced at the output of the array elements, the performance of the BCS-based approach is evaluated when data are acquired at a single time instant and at consecutive time instants, respectively. Different signal configurations, planar array geometries, and noise conditions are taken into account, as well. 1. Introduction In the last few years, we assisted to an extraordinary and still growing development and use of compressive sensing (CS)-based methods [1] in a wide number of applicative contexts such as communications [2], biomedicine [3], radar [4], and microwave imaging [5, 6]. CS has proven to be a very effective resolution tool when the relationship between the problem data and the unknowns is linear, and these latter are sparse (or they can be sparsified) with respect to some representation bases. In this paper, a probabilistic version of the CS, namely, the Bayesian compressive sensing (BCS) [7], is used for estimating the directions of arrival (DoAs) of electromagnetic signals impinging on an array of sensors in a planar arrangement. Since the DoAs of the incoming signals are few with respect to the whole set of angular directions, they can be modeled as a sparse vector. Accordingly, the estimation problem at hand can be reformulated as the retrieval of such a sparse signal vector whose nonnull entries are related to the unknown angular directions of the signals. Compared to the state-of-the-art estimation methods (e.g., the multiple signal classification (MUSIC) [8], the signal parameters via rotational invariance technique (ESPRIT) [9], the maximum likelihood (ML) DoAs estimators [10], and the class of techniques based on learning-by-examples (LBE) strategies [11–13]), CS-based approaches have shown several interesting advantages. Likewise LBE-based methods, the computationally expensive calculation of the covariance matrix is not necessary since the voltages measured at the output of the array elements can be directly processed. CS-based methods turn out to be fast and also work with single time-instant (snapshot) data acquisitions. Moreover, unlike MUSIC and ESPRIT that require the incoherence of the impinging signals and a set of measurements larger than the number of signals, careful DoA estimates can be yielded also when the number of arriving signals is greater than the array sensors as well as in the presence of