Robust Differential Beamforming with Rectangular Arrays

In this paper, we introduce a robust approach for rectangular differential beamforming. We present a 2-D multistage spatial mean operator which operates independently on the columns and rows of the observation signals of a uniform rectangular array (URA). The multistage approach enables high flexibility: two design parameters, Q_c and Q_r, set the number of mean stages in the array columns and rows, respectively. Then, we design a rectangular differential beamformer and apply it to the output of the spatial operator. We demonstrate that the first mean operation improves the white noise robustness of the resulting beamformer. We focus on the maximum directivity factor (MDF) and null-constrained maximum directivity factor (NCMDF) differential beamformers and analyze their performances in terms of both the white noise gain (WNG) and directivity factor (DF) measures. We show that the configuration (Q_c, Q_r) constitutes a useful mean to mitigate the white noise amplification of differential beamformers in low frequencies.