A fast complex lattice reduction algorithm for SIC-based MIMO detection

Recently, lattice-reduction-aided detection in multiple-input multiple-output (MIMO) systems has attracted significant research efforts for its capability of achieving full diversity performance with low complexity. However, most lattice reduction algorithms are not designed directly to enhance the bit error ratio (BER) performance. In this paper, a fast lattice reduction (FLR) algorithm for complex-valued matrices, which aims at maximizing the minimal signal to noise ratios (SNR) of all layers, is proposed for V-BLAST (Vertical Bell Laboratories Layered Space-Time) systems, employing presorting technique and complex Givens rotation to reduce its computational complexity. The SNRs of all layers are related to the diagonal elements of the triangular matrix via QR decomposition of the channel matrix, and can be optimized by a series of iterations which can be efficiently implemented by exploiting the complex Givens rotation, while the average number of iterations is significantly diminished by utilizing the low complexity pre-sorting technique. Our analysis reveals that the proposed SIC-FLR decoder can significantly reduce the computational complexity without sacrificing any performance. Simulation results show that the proposed algorithm achieves the same performance as the state-of-art complex LLL (Lenstra-Lenstra-Lovász) algorithm only with a fraction of complexity.