Off‐grid DOA estimation based on compressed sensing with gain/phase uncertainties

Abstract

A semi-definite programming-total least squares (SDP-TLS) method based on compressed sensing for the off-grid direction-of-arrival (DOA) estimation with gain/phase uncertainties is proposed. On a discrete grid, the accuracy of DOA estimation will degrade because of the basis mismatch when the true DOAs do not coincide with the angular grid that is divided. The accuracy of DOA estimation would be worse if the gain/phase uncertainties are present but overlooked. In order to eliminate the influence of the gain/phase uncertainties and solve the off-grid problem at the same time, a SDP-TLS method is proposed. First, the problem needed to be solved into a framework of total least-squares (TLS) is transformed. Then an alternating descent algorithm to solve this problem is developed. In the proposed algorithm, the off-grid DOA is estimated by semi-definite programming, using TLS approach to update gain/phase uncertainties through iterations. Simulation results show that the SDP-TLS method can help to improve the accuracy of off-grid DOA estimation with the gain/phase uncertainties than the existing algorithms.