DOA estimation based on compressed sensing with gain/phase uncertainties

A new direction‐of‐arrival (DOA) estimation method for the sparse receiving array with gain/phase uncertainties is proposed. Because of the sparsity of the received signals, compressed sensing theory can be used to sample and recover receiving signals with less data. Owing to the existence of the gain/phase uncertainties, it would be difficult to estimate the DOA accurately when the sparse representation of the signals is not optimal. In order to reduce the influence of the gain/phase uncertainties on the sparse representation, the authors firstly transfer the array signal receiving model with the gain/phase uncertainties into an errors‐in‐variables (EIV) model, which treats the gain/phase uncertainties as an additive error matrix. Then a new DOA estimation method named simultaneous orthogonal matching pursuit‐total least squares algorithm based on the EIV model is proposed. The DOAs will be obtained by estimating the sparse coefficients through iterations with the proposed method. Simulation results show that the sparse regularised total least squares algorithm is able to provide a more accurate DOA estimation with the gain/phase uncertainties than the existing calibration algorithms even with the sparse array.