Efficient synthesis of sparse arrays as the solution of an inversion problem within the bayesian compressive sensing framework

Abstract

Designing sparse arrays requires the solution of a nonlinear inversion problem because of the dependence of the radiation pattern on the locations and the weights of the array elements. Unfortunately, the design of sparse layouts is usually a very challenging problem with respect to the synthesis of their filled counterparts since, although convenient from several viewpoints, they usually present a reduced control of the arising beam shape, the peak sidelobe level (PSL) as well as the mainbeam width [1]–[17]. Accordingly, several design techniques have been proposed to suitably address these issues. The sparse array design techniques have been usually conceived either as the solution of a “thinning” problem where the functional depends on the array PSL [4]–[15], or as the selection of the element positions an weights which exhibit a target pattern [16]–[17]. While a large set of approaches have been introduced for thinning both linear and planar arrangements (e.g., random architectures [2], stochastic optimizers [4]–[11] and analytical methods [12]–[15]), few methodologies have been developed for the solution of the latter synthesis problem [14]–[16] although recently an innovative approach based on the formulation of the sparse array synthesis problem as a “Compressive Sensing (CS) retrieval” one has been presented [18]–[19]. Such a method formulates the synthesis inversion problem at hand by imposing suitable sparseness constraints as regularization terms, then re-casting it in a probabilistic framework exploiting the so-called Bayesian Compressive Sensing formulation [20]. Successively, the an efficient Relevance Vector Machine (RVM) is applied to determine the array synthesis unknowns [21].