A Unified and Flexible Eigen-Solver for Rank-Deficient Matrix in MIMO Precoding/Beamforming Applications

Eigenvalue decomposition (EVD) is a widely adopted technique to separate signal, interference, and noise subspaces. The paper presents a unified eigen-solver based on QR decomposition (QRD) to generate eigenpairs associated with the largest eigenvalues or zero eigenvalues, which are required in the MIMO hybrid beamforming systems that need interference suppression. A non-uniformly constrained deflation is proposed, which forces the matrix to deflate in the beginning and efficiently allocates the computation power to the eigenpairs related with the largest eigenvalues. The computation complexity of generating interested eigenpairs is also evaluated for various matrix dimensions. The results demonstrate that the non-uniformly constrained deflation is effective and more computations can be saved if the desired number of eigenpairs is smaller than the rank of the matrix.