A Robust Fast Dominant Mode Rejection Algorithm

The Dominant Mode Rejection (DMR) algorithm is a variant of the classical Minimum Variance Distortionless Response (MVDR) algorithm. In DMR, the algorithm estimates the ensemble covariance matrix (ECM) by averaging the noise subspace eigenvalues from the sample covariance matrix (SCM), which is a low-rank approximation of the true covariance matrix. Compared to MVDR, DMR performs better in suppressing strong interference sources and small snapshot processing. However, DMR faces challenges. Accurate estimation of the dimension of the dominant mode subspace is crucial for its performance. Both overestimation and underestimation of this subspace dimension can impact the algorithm's effectiveness. Additionally, the computational complexity of DMR primarily lies in the eigenvalue decomposition of the data covariance matrix. As the number of array elements increases, the computational burden grows significantly. To address these issues, this study employs Lanczos-type iteration and random approximation to achieve rapid decomposition of the dominant mode subspace. During the Lanczos recursion, the algorithm assesses and estimates the dimension of the dominant mode space. Furthermore, to mitigate the impact of subspace dimension estimation, the Marchenko-Pastur distribution is used to estimate the median of the SCM eigenvalues, replacing the mean value. These techniques not only reduce computational overhead but also enhance white noise gain, resulting in a more robust algorithm against array perturbations.