Robust wideband adaptive beamforming based on covariance matrix reconstruction in the spatial-frequency domain

Without the response variation constraint, the main-lobe responses of wideband beamforming usually vary with the frequencies of interest, and the beam pointing may deviate from the incident angle of the desired signal. If the interference-plus-noise covariance matrix (INCM) is directly replaced by the sample covariance matrix, the desired signal in the sample data may result in self-null problem, which can lead to the degradation of the performance of wideband beamformers. Through frequency division, a novel wideband adaptive beamforming is proposed by reconstructing the INCM and solving the convex optimisation problem. Using fast Fourier transform (FFT), the time-domain samples are transformed into the frequency field, and the covariance matrix of each subband can be obtained from the frequency-domain data. In the spatial-frequency domain, the INCM and signal-plus-noise covariance matrix can be respectively reconstructed by integrating the stacked steering vector and the Capon spatial spectrum over the corresponding angular region. Then, we establish the optimisation criteria, that is, minimising the output interference-plus-noise power, minimising the main-lobe spatial response variation, and constraining the response deviation of the desired signal. A novel convex optimisation model can be established, and then the weight coefficients for time-domain wideband beamforming can be obtained by solving the optimisation problem. The simulation and experimental results demonstrate that the proposed beamformer can provide better performance compared with other tested beamformers and maintain good robustness in various applications.