Elements Failure Robust Compensation in 2D Phased Arrays for DOA Estimation With M-ary PSK Signals

Constant modulus algorithm (CMA) has been widely used in direction of arrival (DOA) estimation for constant modulus signals. However, CMA fails completely when dealing with array elements failure. In this paper we devise an algorithm to solve CMA fault-tolerance deficiency. The compensation of failed elements in 2D arrays is achieved by a Replace, Replicate, Reconstruct and Remove (4R) algorithm. The 4R-2D-CMA starts by replacing a failed-element signal by the nearest operating array element signal, then, after computing the covariance matrix, the corrupted rows and columns corresponding to failed elements in both elevation and azimuth are replicated from their Centro-symmetric counterparts to correct the covariance distortion. Replication step takes advantage of a special structure of two perpendicular Centro-symmetric arrays producing a Centro-Hermitian matrix. Afterwards, a 2D-CMA algorithm is used for decomposition to produce azimuth and elevation directions matrices. After decomposition, a linear phase correction is used before the covariance matrix is reconstructed. Finally, a second decomposition is used to obtain final DOAs. The number of constant modulus (CM) sources is estimated from a robust spectrogram analysis. Results for an SNR of -3 dB with 11% of elements failure show almost full recovery and hence prove the effectiveness of the novel approach.