Method for DOA Estimation of Coprime Arrays Through Joint Auxiliary Arrays with Atomic Norm Minimization in the Presence of Gain-Phase Errors

Coprime arrays (CPA) are extensively applied to estimate the direction of arrival (DOA). Yet, the effectiveness of existing DOA estimation algorithms for coprime arrays is predicated on the precise calibration of the array. Gain-phase errors in the sensors, when present, are magnified by the co-array, greatly impacting the performance of DOA estimation algorithms. To address the issue, this paper proposes a joint DOA estimation algorithm combining auxiliary arrays with atomic norm minimization. Exploiting the sub-array decomposition feature of coprime array, gain-phase error estimation is accomplished with the addition of precisely calibrated auxiliary arrays. Besides, the estimated gain-phase errors are used to correct the covariance of the signals received by the array. By combining array interpolation, all virtual sensors are fully utilized, and the interpolated virtual received signals are reconstructed into a Toeplitz matrix. The covariance matrix of these signals is then refined using atomic norm minimization, preparing the data for the final DOA estimation performed by subspace algorithms. In addition, for comparative analysis, the Cramér–Rao bound has also been derived under the condition of gain-phase errors, providing a benchmark for the performance of the proposed algorithm.