Synthesis of Sparse Linear Arrays via Low-Rank Hankel Matrix Completion

In this paper, we propose a method to synthesize sparse linear arrays using low-rank Hankle matrix completion. With the given metrics (e.g., peak sidelobe level, mainlobe width) of the desired beampattern, we synthesize a sparse linear array directly by designing a low-rank Hankel matrix under appropriate constraints. A low-rank matrix completion problem is formulated with Hankle structure constraint, and an effective solver is presented using log-det heuristic. Different from existing work that requires reference array and reference beampattern, our method synthesizes sparse linear arrays directly according to the desired beampattern metrics. In this way, our method is more flexible and avoids the selection of reference array/beampattern. Moreover, due to maintaining the Hankel structure, the proposed method can achieve more accurate estimation on element positions. Additionally, the proposed method can be easily extended and applied to various sparse array synthesis scenarios. Representative simulations are conducted to validate the effectiveness and superiority of the proposed method. It is shown that the proposed method synthesizes desired beampatterns with fewer antenna elements, comparing to existing work.