Three-level Nested Array: Optimization for Degree of Freedom and Mutual Coupling

Aiming at the problems of low degree of freedom and high mutual coupling of current nested arrays, this paper adopts uniform linear array (ULA) to cascade, and proposes a three-level nested array with high degree of freedom and low mutual coupling. This structure not only retains the original advantages of nested array and has closed-form expression of physical array positions and degree of freedom, but also vastly reduces the mutual coupling. Firstly, the mutual coupling matrix is introduced to the traditional echo signal model, and the echo signal model under the mutual coupling condition is established. Secondly, the layout of the three-level nested array is given, and the optimal configuration and the closed-form expression of the degree of freedom of the physical array elements under the structure of "difference co-array" are derived. Finally, compressed sensing (CS) technology is used for direction of arrival（DOA）estimation. Simulation results show that compared with the existing nested arrays, the proposed three-level nested array can effectively improve the degree of freedom and reduce the mutual coupling without increasing the number of physical sensors, thus improving the performance of DOA estimation.