A Fast Gridless Sparse Method for Robust DOA Estimation in the Presence of Gain-phase Errors

A new gridless sparse method (GLSM) is proposed to estimate the direction of arrival (DOA) and gain-phase errors simultaneously for a uniform linear array (ULA). We convert angular space to frequency space and establish a data model in the frequency domain. First, the cost function based on the covariance fitting criterion is transformed into a semidefinite programming (SDP) problem to estimate DOA and noise variance without previous calibration information. Second, gain errors are calculated by the estimated noise variance and the covariance matrix. Third, phase errors are obtained by decomposition of the covariance matrix, which has been pre-processed by a space smoothing technique. Finally, DOA estimation is improved further after the array errors are fully calibrated. Compared with traditional methods, the proposed method is robust to correlations of signal sources, and parameters are estimated without joint iteration. Moreover, there is no need for discrete grid points in the angular space, which results in grid mismatches and computation loads, so the proposed method is more accurate and faster. Simulation results verify the effectiveness of the proposed method.