Improving the Robustness of the Dominant Mode Rejection Beamformer With Median Filtering

Abstract

Abraham’s and Owsley’s dominant mode rejection (DMR) beamformer modifies Capon’s minimum variance distortionless response beamformer to force suitable constraints in the covariance matrix estimation process to reduce degrees of freedom. DMR estimates the ensemble covariance matrix (ECM) from a low-rank sample covariance matrix (SCM) by replacing the eigenvalues of the noise subspace with the sample mean of those same eigenvalues. This estimated noise power is negatively biased when the dominant subspace dimension is overestimated, which is common in practical implementations of the DMR. The proposed median DMR exploits the Marchenko-Pastur distribution to estimate the noise power from the median of the SCM eigenvalues. Simulations found that the median estimator was more robust to overestimating the dominant subspace dimension, exhibiting a lower mean squared error than the mean estimator. Simulations also found that the median DMR improves the white noise gain (WNG) when compared to the standard DMR in snapshot deficient scenarios with overestimated interferer subspace dimension. Higher WNG implies increased robustness to array perturbations. This work compares the median DMR to standard DMR in simulations with perturbed array element phase responses in a scenario with two interferers and background white noise. The median DMR preserved deeper notches than standard DMR in this scenario, increasing the output signal-to-noise ratio by roughly 1 dB.

Keywords

• Adaptive beamformer (ABF)
• dominant mode rejection (DMR)
• median filtering random matrix theory (RMT)
• sample covariance matrix (SCM)