MMSE Beamforming with Cyclical Sub-Vector Optimization

A cyclic sub-vector optimisation (CSVO) beamforming approach is investigated. With the proposed algorithm, an array beamforming vector is partitioned into a number of sub-vectors of small sizes, allowing reduced-dimension processing. Then multiple optimisation cycles are carried out by the block coordinate descent method, which leads to an optimal beamforming vector. The proposed scheme still needs to compute the matrix inversion, but the size of the matrix can be flexibly chosen and the computational complexity is manageable. The proof of the convergence and complexity analysis is given. The simulation results demonstrate the effectiveness and fine features of the proposed algorithm. Although the convergence rate of the CSVO is slightly slower, the CSVO has lower computational complexity than that of the diagonal loading conjugate gradient applied to normal equations algorithm. In comparison with other sub-vector approaches, the proposed algorithm gains a faster convergence rate and improved stability.