A gridless method for direction finding with sparse arrays in nonuniform noise

The performance of direction finding methods would deteriorate due to unknown nonuniform noise. To cope with this problem, we propose a novel gridless direction finding method based on atomic norm minimization exploiting sparse linear array in nonuniform noise. Specifically, after eliminating the concentrated nonuniform noise related term in coarray signal, the concept of array interpolation is used to recover both the noiseless counterpart of the removed term as well as the holes in coarray. Thus, the effect of nonuniform noise is removed. Besides, we impose a new constraint based on the estimation error distribution of the noise independent terms in the coarray signal. The regularization parameter can thus be selected directly from the Chi-square distribution probability table. In the proposed method, the tedious selection of regularization parameter and the effect of grid mismatch are avoided. Moreover, we derive the corresponding semidefinite programming (SDP) form. With its optimal solution, eigen-decomposition with high complexity is avoided for subsequent DOA estimation. Different from the traditional SDP form, it has an additional transformation matrix composed of the estimation error. Simulations show that the proposed method owns the highest estimation accuracy than previous algorithms in the nonuniform noise.