Mirrored coprime array design using sum‐difference coarray optimisation

Abstract

The sum-difference coarray (SDCA) is the union of the sum coarray (SCA) and difference coarray (DCA), which has higher degrees-of-freedom (DOF) than that of the DCA, resulting in a better direction-of-arrival (DOA) estimation performance. However, existing passive sparse arrays require spatial and temporal information to construct SDCA. In this study, a mirrored coprime array (MCA) is designed to implement SDCA using only spatial information. First, the SCA and DCA are recovered from the vectorised covariance matrix via the transform matrix. A Tikhonov regularisation method is proposed to reduce the rank-deficiency effect of the transform matrix. The SCA has the potential to fill the holes in the DCA by adjusting the mirror position since the mirror determines the virtual sensor locations of the SCA. Then, the closed-form expressions of the mirror position and virtual array aperture are derived for the hole-free SDCA. The consecutive lags of the optimised SDCA are much larger than those of the DCA, significantly increasing the DOF. Numerical simulations verify that the MCA outperforms the non-mirrored one with respect to the DOA estimation accuracy and resolution.