Widely Linear MVDR Beamformers for Noncircular Signals Based on Time-Averaged Second-Order Noncircularity Coefficient Estimation

The optimal widely linear (WL) minimum variance distortionless response (MVDR) beamformer, which has a powerful performance for the reception of a noncircular signal, was proposed by Chevalier in 2009. Nevertheless, in spectrum monitoring or passive listening, the optimal WL MVDR beamformer is hard to implement due to an unknown second-order (SO) noncircularity coefficient. This paper aims at estimating the time-averaged SO noncircularity coefficient of a desired noncircular signal, whose waveform is unknown but whose steering vector is known, in the context of the optimal WL MVDR beamformer. The proposed noncircularity coefficient estimator can process 2N - 1 rectilinear signals at most using an array of N sensors. Moreover, a frequency-shift WL MVDR beamforming algorithm is proposed for a noncircular signal having a nonnull frequency offset or carrier residue, jointly with the estimation of the frequency offset of the rectilinear signal. Due to the inevitable estimation error of the time-averaged SO noncircularity coefficient, a diagonal loading technique is used to enhance the robustness of the optimal WL beamformers. Simulations are shown to verify the effectiveness of the proposed algorithms.