A DOA Estimation Method in the presence of unknown mutual coupling based on Nested Arrays

A novel DOA method is proposed to deal with the DOA estimation in the presence of the unknown mutual coupling for nested arrays. By using a new expression of the steering matrix in the presence of mutual coupling, a novel expression of the receiving data vector in the virtual array field is available. Then, based on a modified direction matrix constructed with block matrix, which relates to space discretized sampling grid, the sparse Bayesian compressive sensing method applies to estimate a vector, which contains the signal powers information and the mutual coupling information. The problem of off-grid DOAs is also considered for sparse Bayesian compressive sensing. Based on the estimated vector, a peak searching is performed to estimate the initial DOA. Finally, the estimation of DOA is modified to initial estimate plus off-grid error value. The advantage of fully utilizing the degree of freedom of nested arrays is preserved in this proposed algorithm. Moreover, no complicated calculation is needed to obtain the mutual coupling coefficients or rearrange the position of array element. Theoretical analysis and simulation results show the effectiveness of the proposed algorithm.