Scalable Approach for Analytic Polynomial Subspace Projection Matrices for a Space-Time Covariance Matrix

In sensor array applications, it can be advantageous to project data onto a given signal subspace, for example, to improve the SNR or as part of direction finding algorithms. In the broadband case, a projection operator can be derived via polynomial matrices and, more specifically, from a space-time covariance matrix. Traditional methods perform a complete polynomial eigenvalue decomposition (PEVD) to achieve this, which can be computationally intensive. We propose a novel method to compute these subspace matrices directly, without the need for a full PEVD. Our approach is evaluated against existing methods using an ensemble of randomized para-Hermitian matrices, demonstrating significant improvements in both accuracy and computation time.