Direction of Arrival Estimation Using Sparse Nested Arrays With Coprime Displacement

Direction of arrival (DOA) estimation using new proposed array geometries named sparse nested arrays with coprime displacement (SNACD) is discussed in this paper. The SNACD has sparse subarrays with nested relationship, and the displacement between the subarrays is coprime to the inter-element spacing of the smaller subarray. This geometry can combine the properties of nested array and coprime array, which can simultaneously achieve virtual uniform array with large aperture in co-array domain and reduce the mutual coupling influence in physical-array domain. In the co-array domain, the coprime parameter estimations are separated into the virtual direction matrix and source vector, respectively. Based on this data model, several DOA estimation methods can be applied, like the spatial smooth multiple signal classification (SS-MUSIC) and atomic norm minimization based grid-less (ANM-GL) method, which both are robust to the grid mismatch problem. To further reduce the complexity, we proceed to propose a Discrete Fourier transform with offset compensation (DFT-OC) method, which requires neither eigenvalue decomposition nor sparse recovery. The final unique DOA estimation is achieved from the intersection of the coprime estimations, which are achieved with automatically pairing. Compared to coprime array and nested array based methods, the proposed scheme obtains better DOA estimation accuracy and higher angular resolution with mutual coupling influence. Multiple simulations are presented to verify the effectiveness of our approach.