Unified coprime array with multi-period subarrays for direction-of-arrival estimation

The original coprime array is a sparse geometry with a pair of one-period subarrays, where the interelement spacing and number of sensors are coprime so that no elements overlap except at the zeroth position. In this paper, we unify the coprime array by extending two subarrays from one period to multiple periods. Each subarray can have an arbitrary number of periods and therefore more than one element of the unified structure coincide. The resulting configuration treats the nested array as well as the existing coprime structures, such as the original coprime array, the extended one and the coprime array with compressed inter-element spacing (CACIS) as its special cases. The new coprime array has a lower peak side-lobe level than the nested array and the CACIS. An improved structure based on the multi-period coprime array is further proposed to improve the degrees-of-freedom (DOF) of the unified geometry with one of the subarrays displaced by a certain number of spacings. Although the improved configuration does not reach the same DOF as the CACIS and the coprime array with displaced subarrays (CADiS), it can acquire a low peak side-lobe level with the DOF not being decreased too much. Different from CADiS, we focus on the analysis and proper choice of the displacement to acquire more consecutive lags. The properties of coarray of the proposed array design strategy are provided as well. Finally, the direction-of-arrival estimation, physical aperture and peak side-lobe level performance of the unified structures are examined through numerical simulations.