Extensions of Co-Prime Array for Improved DOA Estimation With Hole Filling Strategy

Although co-prime array is more attractive than nested array in reducing mutual coupling benefiting from a sparser structure, it generates a difference co-array with multiple holes that can considerably decrease the number of uniform degrees of freedom (uDOFs) when spatial smoothing methods are employed. In this paper, we present a hole filling strategy for co-prime array to improve its difference co-array. Specifically, we propose a novel co-prime array with a filled difference co-array (CAFDC) by introducing two extra subarrays, which can significantly increase the number of achievable uDOFs. However, CAFDC is sensitive to mutual coupling because a densely assembled subarray is involved. To tackle this problem, we first derive the location expressions of the sensors in CAFDC for the largest difference co-array with a fixed number of sensors and then enlarge the inter-element spacing of its dense subarray. The resulting co-prime array can effectively mitigate mutual coupling effect by restricting the number of sensor pairs with small separations and produce a two-hole difference co-array with no loss of uDOFs, termed as co-prime array with a two-hole difference co-array (CATHDC). In addition, simulation results are provided to demonstrate the superiority of the newly proposed co-prime arrays over existing sparse arrays in DOF, mutual coupling and direction-of-arrival (DOA) accuracy.