Direction-of-arrival estimation via coarray with model errors

Direction-of-Arrival (DoA) estimation with Coarray can resolve O(N²) sources via only O(N) physical sensor elements. When it comes to model errors, i.e., manual coupling, gain and/or phase errors, and sensor location errors, whether Coarray is still effective for degree-of-freedom (DoF) enhancement has not been proved yet. In addition, calibration of the Coarray is also an open problem, which deserves more attentions. This paper formulates the error models of Coarray at first and then proves that the problem of Coarray calibration can be reformulated into an equivalent one of imperfect uniform linear array correction; meanwhile, DoF enhancement is promised. Based on these models, the problem of Coarray calibration, more specifically, joint DoA and error coefficients estimation, can be solved via the existing state-of-the-art array calibration schemes. An excellent scheme named sparse Bayesian array calibration is adopted as an example to estimate DoA and error coefficients jointly in this paper. Simulation results illustrate that for DoA estimation with imperfect Coarray, the calibrated estimator is effective for DoF enhancement and more robust than uncalibrated subspace method.