Multi-user MIMO downlink beamforming based on perturbation theory of generalized eigenvector

An efficient beam updating method for multi-user multiple-input multiple-output (MU-MIMO) downlink channels is considered in time-varying channels. Previously, the beam design method based on signal-to-leakage-plus-noise ratio (SLNR) was introduced with given channel matrices. The solution maximizing SLNR is obtained by a generalized eigen-decomposition with a pair of covariance matrices of desired signal and leakage plus noise. It is burdensome to calculate directly a generalized eigenvector at each time step in time-varying channels. To reduce the computational complexity in the beam design algorithm, the perturbation theory for a generalized eigenvector without any iteration is used for a simple update formula to obtain a new generalized eigenvector corresponding to the updated channel information. Through numerical simulations, the performance of the proposed beam design algorithm is verified.