Optimal Hole-Filling Strategies for Arbitrary Sparse Sensor Arrays

In a sparse array, the holes in the corresponding difference co-array limit the length of the consecutive subarray, which in turn reduces the number of achievable uniform degrees of freedom. In recent years, methods have been proposed to fill the holes in the difference co-array for several types of sparse arrays. These methods address the hole-filling task by adding sensors in appropriate places of the sparse array or by rearranging the existing sensors. The existing hole-filling methods are not necessarily optimal, and each one can only be applied to a specific type of sparse arrays. In this paper, we propose general hole-filling methods applicable to any type of sparse arrays. These methods utilize the minimum number of added sensors necessary to fill the holes in the difference co-array associated with the sparse array, making them optimal. The proposed hole-filling strategies achieve this by solving an optimization problem while also maintaining the ability to keep mutual coupling effect among the sensors of the final array at a desired low level. Several examples are provided where the performance of the proposed methods is compared with existing hole-filling methods. The results of these comparisons demonstrate the superior performance of the proposed methods in terms of achievable uniform degrees of freedom, mutual coupling effect, and direction-of arrival estimation accuracy.