Optimized Design for Sparse Arrays in 3-D Imaging Sonar Systems Based on Perturbed Bayesian Compressive Sensing

Sparse planar array designs significantly reduce the hardware complexity and computational overhead in phased array 3-D imaging sonar systems. Recently, Bayesian compressive sensing (BCS) theory has been applied for synthesizing maximally sparse arrays, in which case, the problem is formulated as a pattern matching technique in a probabilistic fashion. Thus, in this study, a perturbed BCS-based method with a minimum inter-element spacing constraint is proposed. In particular, a modified BCS technique is first employed to synthesize the primary sparse array. Then, the position perturbations of the elements are determined via the first-order Taylor expansion to increase their degrees of freedom (DOFs). The position perturbations allow for continuous element arrangement, which compensates for the imperfection of discrete candidate sample locations. After that, an improved element merging technique combined with convex optimization was adopted to establish constraints on element spacing while mitigating beam pattern degradation. In practice, this is a feasible approach, which merges elements close to each other, leading to a sparser array with a minimum inter-element spacing. Our numerical results confirm the validity of the proposed method in matching accuracy, array sparsity, and constraining the minimum spacing between elements.