Synthesis of planar sparse arrays by perturbed compressive sampling framework

Abstract

Recently, compressive sensing (CS) theory has been applied for synthesising maximally sparse arrays, in which the best subset of sampling element locations is chosen to compose a sparse array for matching a desired radiation pattern. However, their performances are strongly depended on the proper setting of the initial sampling locations, which are typically obtained by gridding the continuous array aperture. Such a setting is usually hard to handle for large planar array synthesis. To address this problem, a precision and effective method based on the perturbed compressive sampling (PCS) is proposed. Position perturbation variables are augmented to the traditional CS-based model, which allow continuous element placement. Then, a joint sparse recovery approach is used to optimise the excitations and position perturbations of the elements simultaneously. Moreover, the authors implement an extended PCS model with a secondary grid strategy to reduce the modelling error and the computational cost. The proposed design problem is solved with a general sparse recovery solver, named FOCal under-determined system solver. Numerical results show that the method yields a higher array sparsity, a faster computational speed and a better pattern matching accuracy than the existing CS-based methods.