Non-circular signals for nested array: sum-difference co-array and direction of arrival estimation algorithm

Nested array has aroused remarkable attention due to the capability to obtain both enhanced degrees of freedom (DOFs) and enlarged array aperture, whereas only difference co-array is employed. Here, the authors construct the sum co-array of nested array by utilising the non-circular (NC) characteristic and, subsequently, the sum-difference (SD) co-array is obtained by careful crafting of the sum co-array and the typical difference co-array, which doubles the resulting co-array aperture and, simultaneously, further increases the achievable DOF compared with the difference co-array of nested array. Moreover, to circumvent the time-consuming two-dimensional spectral search, the authors proposed the reduced-dimension multiple signals classification (MUSIC) algorithm with the SD (SD-RD-MUSIC) co-array of the nested array by discarding the NC phase. Resultantly, the proposed SD-RD-MUSIC co-array algorithm can resolve more signals and obtain more accurate direction of arrival estimates. In addition, the effectiveness and superiority of the proposed method are validated by numerical simulations.