A Low Complexity Diversity Achieving Decoder Based on a Two-Stage Lattice Reduction in Frequency-Selective MIMO Channels

Based on the V-BLAST zero-padded block transmission scheme in the frequency-selective multiple-input multiple-output channels, we propose a two-stage lattice-reduction (LR)-aided decoder and prove analytically that it can achieve the maximum diversity gain, which is equal to the product of the number of receive-antennas and the number of multipath channel taps. In the proposed decoding method, at first, we decouple the detection problem into several reduced-size detection problems and perform the lattice reduction algorithm for the decoupled blocks. Then, by choosing a proper threshold, a clustering algorithm divides the blocks into the maximum two clusters. We prove that the corresponding blocks of the first cluster achieve the full diversity through their linear equalization. For the remainder of the blocks, based on the entire observations of the second cluster, we propose an LR-aided detection method, which decodes the information symbols in this cluster with full diversity. Our proposed two-stage LR-aided algorithm performs better than the conventional LR-aided detection in terms of both the decoding computational complexity and the error probability. Additionally, we prove analytically that at high signal-to-noise ratio, the decoding complexity of the proposed decoder is equal to that of decoding the first cluster.