Widely linear minimum dispersion beamforming for sub-Gaussian noncircular signals

•We propose two WL-MD based beamforming for sub-Gaussian noncircular signals.•The proposed beamformers have good performance even in high SNR and are able to process more signals than sensors.•The SOCP formulations are given to solve the proposed beamformers.

We propose two widely linear minimum dispersion based beamforming for sub-Gaussian noncircular signals: widely linear minimum dispersion distortionless response (WL-MDDR) and widely linear quadratically constrained minimum dispersion (WL-QCMD). In the nonideal conditions, taking full advantages of noncircularity and sub-Gaussian properties of signals, the proposed algorithms are shown to achieve good performance even in high signal-to-noise ratio and process more signals than the number of sensors. The WL-MDDR beamformer is designed when the information about the steering vector and noncircularity coefficient of the desired signal is precise, while the WL-QCMD beamformer is robust against arbitrary errors in the steering vector and noncircularity coefficient. Numerical simulations verify the effectiveness of the proposed algorithms.