Unfolded Coprime Linear Array with Three Subarrays for Non-Gaussian Signals: Configuration Design and DOA Estimation

Abstract

In this paper, we investigate the problem of sparse array design for the direction of the arrival (DOA) of non-Gaussian signals and exploit the unfolded coprime linear array with three subarrays (UCLATS) to obtain physical sensors location. With the motivation from the large consecutive degree of freedom (DOF), we optimize the process of obtaining physical sensors location from two steps. Specifically, the first is to model the process of obtaining the longest consecutive virtual sum co-array from a given number of physical array elements into a global postage-stamp problem (GPSP), whose solution can be employed to determine the locations of the longest possible consecutive sum co-array (2-SC) and initial physical array. The second step is to multiply the location of the virtual sum co-array by appropriate coprime coefficients to generate UCLATS and then multiply the initial physical array position by the same corresponding coefficients to obtain physical sensors location. Besides, an algorithm is proposed to obtain DOA estimates, which employs the discrete Fourier transform (DFT) method and partial spectrum searching multiple signal classification (PSS-MUSIC) algorithm to obtain initial estimates and fine estimates, respectively, termed as the DFT-MUSIC method. Compared with the traditional total spectrum searching MUSIC (TSS-MUSIC) algorithm, the DFT-MUSIC method performs the same asymptotical performance of DOA estimation with less than 10% complex multiplication times, which can be verified by numerical simulations under the same condition.