Sparse DOA Estimation Algorithm Based on Fourth-Order Cumulants Vector Exploiting Restricted Non-Uniform Linear Array

Non-uniform linear array (NLA) has been widely used in the direction-of-arrival (DOA) estimation owing to its significant advantage of effectively expanding array aperture. In recent years, its related researches have been advanced due to the introduction of nested arrays and co-prime arrays. However, these NLAs require one or even many adjacent antennas whose spacing is the half wavelength of the incident source. In the practical application of the DOA estimation, if the frequency of the incident source is very high, the distances between adjacent antennas cannot reach half wavelength because of the existence of the actual antenna diameter. In this paper, a design method of the restricted NLA is proposed to solve this problem. First, a new NLA is designed by restricting the minimum spacing of adjacent elements, the set of fourth-order antenna spacing differences, and the maximum aperture of the array. Then, in order to solve the ambiguity problem in the DOA estimation caused by the spacing of adjacent antennas larger than half wavelength, we construct a single snapshot measurement sparse signal model by utilizing the fourth-order cumulants vector of the received signal after dimension reduction and by obtaining the estimation of DOA via a sparse reconstruction algorithm. Finally, compared with the minimum redundancy arrays, nested arrays, and co-prime arrays, the simulation experiments show that the proposed restricted NLAs have better performances of the DOA estimation.