Practical HKZ and Minkowski Lattice Reduction Algorithms

Recently, lattice reduction has been widely used for signal detection in multiinput multioutput (MIMO) communications. In this paper, we present three novel lattice reduction algorithms. First, using a unimodular transformation, a significant improvement on an existing Hermite-Korkine-Zolotareff-reduction algorithm is proposed. Then, we present two practical algorithms for constructing Minkowski-reduced (M-reduced) bases. To assess the output quality, we compare the orthogonality defect of the reduced bases produced by LLL algorithm and our new algorithms, and find that in practice M-reduced basis vectors are the closest to being orthogonal. An error-rate analysis of suboptimal decoding algorithms aided by different reduction notions is also presented. To this aim, the proximity factor is employed as a measurement. We improve some existing results and derive upper bounds for the proximity factors of Minkowski-reduction-aided decoding (MRAD) to show that MRAD can achieve the same diversity order with infinite lattice decoding (ILD).