Sparse Array Beamforming Design for Coherently Distributed Sources

Recently, nonstructured sparse array designs have attracted wide interest due to their capability of providing optimum performance for environment-dependent adaptive beamforming. In this article, we develop a sparse array design approach for adaptive beamforming in the presence of spatially coherently distributed (CD) sources. The proposed approach formulates the design problem via maximizing the output signal-to-interference-plus-noise ratio (SINR), but it exploits the generalized array manifold of CD sources. Moreover, sequential convex programming is utilized to convert the nonconvex optimization problem into a series of convex subproblems. We also analyze the impact of source distributed shape on optimum array configuration and theoretically prove that when the CD sources are Gaussian-shaped, the uniform linear array (ULA) is exactly the optimum array configuration. The resulting optimum sparse arrays yield higher output SINR and better-shaped beampattern than the structured sparse arrays. Numerical results verify the superiority of the optimum sparse arrays obtained by the proposed approach over the structured sparse arrays.

I. Introduction

Adaptive arrays play an important role in many fields, such as radar, sonar, mobile communications, satellite navigation, and radio astronomy [1]. Resorting to beamforming, adaptive arrays can extract the signal-of-interest (SOI) from a particular direction while suppressing the interferers from other directions [2]–[4]. The beamforming performance is not only decided by the array weight but also by the array configuration [5], [6]. Compared with uniform linear arrays (ULAs), sparse array configurations offer enhanced array aperture and degrees of freedom while reducing the complexity of the system implementation [7]–[9]. In the past few decades, various sparse array configurations are developed to enhance the array aperture and degrees of freedom [10]–[15], and they include minimum redundancy arrays, nested arrays, coprime arrays, and others. However, these structured sparse arrays cannot achieve optimum performance for environment-dependent adaptive beamforming.