Underdetermined Direction-of-Arrival Estimation Using Difference Coarray in the Presence of Unknown Nonuniform Noise

The coarray techniques, e.g., nested and coprime arrays, can significantly improve degrees of freedom (DOFs) via constructing a so-called difference coarray, which enables underdetermined direction-of-arrival (DOA) estimation within reach in the presence of unknown nonuniform noise. There are repeated lags in the difference coarray, which also contain useful statistical information. In this paper, the repeated lags are properly used for DOA estimation algorithm design in unknown nonuniform noise environments. Specifically, the number of repeated lags in the difference coarray is rigorously given. Then these repeated lags and unique lags are judiciously rearranged to form a pseudo data set, which is composed of linearly independent vectors. Based on the pseudo data set, we propose two algorithms for DOA estimation in the presence of unknown nonuniform noise. One is a searching algorithm without source number knowledge (SASNK), and the other is a multi-snapshot compressive sensing method (MSCS) with better DOA estimation performance. The MSCS also does not require source number information. Numerical results are included to showcase the effectiveness of the proposed algorithms.