WLB-DSCA method for strictly non-circular signals in coprime array

Widely linear beamforming (WLB) performs better than conventional adaptive beamforming, however its performance is restricted by array geometry. Coprime array can improve the beamforming performance compared with uniform linear array given the number of sensors. In this paper, a WLB with difference-sum co-array (WLB-DSCA) is devised for strictly non-circular (SNC) signals in coprime array. We vectorize the augmented covariance matrix of coprime array to produce a DSCA. To efficiently exploit all information of continuous and discontinuous virtual sensors in DSCA, we introduce the sparse representation of DSCA. A norm minimization optimization problem is formulated and then solved to localize the SNC signals in DSCA. We formulate a joint covariance and pseudo covariance matrices optimization problem to determine the powers of SNC signals. The augmented interference-plus-noise covariance matrix (AINCM) is reconstructed. Lastly, the augmented weight vector of the proposed WLB-DSCA is computed. Numerical results validate that the proposed WLB-DSCA is capable of handling SNC signals in coprime array.