Sparse Array Synthesis with Two-Stage Progressive BCS and Undirected Graph-Based Spacing Constraint

Sparse arrays are widely used to achieve full array performance with fewer elements to reduce the cost of array and beamforming computation. Sparse array synthesis methods such as Bayesian compressed sensing (BCS) yield small element numbers; however, they are limited by the tradeoff between complexity and accuracy. Herein, a novel sparse array synthesis method with two-stage progressive BCS and an undirected graph-based element spacing constraint is proposed. The two-stage progressive BCS includes fast on-grid sparsification and accurate off-grid global re-estimation. First, the multitask BCS is solved using a relevance vector machine to efficiently select elements from candidate positions. Subsequently, a convex surrogate cost function is applied to the global re-estimation of the element weights to increase the beam pattern matching accuracy of the sparse array. Global optimization can improve the array performance. In addition, to satisfy the spacing constraint, a weighted merging method based on an undirected graph is proposed and inserted between the two stages to merge elements that are too close, which ensures the processability of the array. Simulations and experiments involving a variety of arrays were conducted to confirm the advantages of the method with regard to array sparsity, sidelobe suppression, beam pattern matching accuracy, and array processability. The proposed method achieved accurate and effective sparse array synthesis and outperformed existing methods.