Sparse Linear Arrays for Direction-of-Arrival Estimation: A Tutorial Overview

Sparse linear arrays serve as the fundamental basis for sparse signal processing and have demonstrated remarkable direction-of-arrival (DOA) estimation performance. Due to the merit of resolving more signals with fewer sensors in severe mutual coupling environments, sparse arrays have garnered significant research interest in recent decades, prompting researchers to focus on various design criteria. This paper overviews recent advances dealing with sparse linear arrays designed for underdetermined DOA estimation. First, we briefly review the DOA estimation model and consolidate the performance metrics. Second, we review an extensive number of sparse linear array configurations and categorize existing works within a research-developed framework that encompasses three categories: (i) non-regular integer sparse arrays including minimum redundancy arrays and minimum holes arrays, (ii) regular integer sparse arrays including nested arrays and coprime arrays, and (iii) other sparse arrays including non-integer sparse arrays and composite Singer arrays. Further classifications are also provided based on different design methods. Moreover, we compare these configurations in terms of the number of sensors, degrees of freedom (DOFs), angular resolutions, leakage coefficient, and weight functions involved with mutual coupling. Lastly, we provide brief concluding remarks along with potential future research directions.