Robust Adaptive Beamforming Based on Covariance Matrix Reconstruction with Gaussian Random Dimensionality Reduction

The performance of adaptive beamforming will deteriorate severely under small sample support, especially when the number of snapshots is smaller than the number of sensors. In this paper, we propose an effective algorithm for robust adaptive beamforming under small sample. Firstly, we utilize standard Guassian random matrices to construct projection matrices for dimension reduction of sample covariance matrix (SCM) and steering vector (SV). Subsequently, the dimensionality-reduced SCM and SV are used to obtain more accurate Capon power spectrum in the case of small sample. By integrating the corresponding Capon power spectrum over the angular sector without desired signal, the interference-plus-noise covariance matrix (INCM) is then reconstructed. Moreover, the SV of desired signal is estimated by solving a quadratic programming problem. Finally, the weight vector of the beamformer is calculated based on the reconstructed INCM and the estimated SV. Simulation results demonstrate the effectiveness and robustness of the proposed algorithm.