Robust Frequency Invariant Beamforming based on Convex Optimization

In real applications, the performance of the adaptive beamformers degrades severely due to model mismatch. Normally the robust wideband beamformer was realized by simply applying the narrowband robust beamforming method to each frequency band. Since the beam responses vary with frequencies, the resultant beamforming output would have spectral distortion for the desired signal. In this paper, the problem of the robustness of the wideband beamformer which is frequency invariant is addressed. The frequency invariant characteristic was realized by minimizing mainlobe spatial response variance. Then, the interferenceplus-noise covariance was reconstructed through integrating the Capon spectrum over a region separated from the direction of the desired signal. Moreover, the mismatch between the presumed steering vector and the actual steering vector was estimated. The overall optimization problem is convex and could be implemented with the second order cone programming. The performance of the proposed method was validated by simulation experiments. Simulation results demonstrate that the proposed algorithm provides strong robustness against array mismatch. The improvement of the output signal to interference plus noise ratio (SINR) is significant compared to other methods across a wide range of input signal to noise ratio (SNR).