Generalised singular value decompositionbased algorithm for multi-user multiple-input multiple-output linear precoding and antenna selection

Multi-user multiple-input multiple-output (MU-MIMO) linear precoding utilising generalised singular value decomposition (GSVD) is proposed. The authors precoding scheme maximises the signal-to-leakage and noise ratio (SLNR), so that it does not require any iteration to obtain precoding/decoding matrices, a feature that distinguishes it from previous signal to interference and noise ratio (SINR) maximising precoding schemes. The SLNR maximising precoding weight may be obtained by the generalised eigenvalue decomposition (GEVD). However, the covariance matrix whose GEVD is computed becomes near singular as the signal-to-noise ratio goes high. To overcome this numerical problem, the proposed precoding scheme avoids any matrix inversion and matrix `squaring` operations, removing redundant computational loads, and consequently saves computational resources and improves numerical accuracy. To further improve the system performance, an efficient antenna selection scheme using the GSVD is also proposed. The scheme does not require an exhaustive search to choose an active antenna set.