Improved Element-Based Lattice Reduction Algorithms for Wireless Communications

Lattice-reduction (LR)-aided linear detectors (LDs) have shown great potentials for wireless communications due to their low complexity and high performance. However, most of the existing LR algorithms do not directly aim at minimizing the asymptotic error performance of LDs, which is dominated by the shortest longest vector (SLV) in the dual space. To find sub-optimal solutions to the SLV reduction, element-based lattice reduction (ELR) algorithms were recently proposed by performing column-addition operations. In this paper, we propose improved ELR algorithms (called ELR⁺) by performing generalized column-addition operations. We find that the problem that minimizes a basis vector by a generalized column-addition operation can be formulated as a closest vector problem (CVP). By solving the CVP that minimizes the longest basis vector for each basis update, the proposed ELR⁺ algorithms find sub-optimal solutions to the SLV reduction problem with high performance. Simulations illustrate that the proposed ELR⁺ algorithms show superior performance relative to the state-of-the-art LRs for linear detection, including Korkin-Zolotarev reductions.