A novel hybrid fix‐LLL lattice reduction algorithm for MIMO detection system

Abstract

Lenstra–Lenstra–Lovász (LLL) is an effective lattice reduction algorithm for multiple‐input multiple‐output (MIMO) systems, which was considered to achieve full diversity in the MIMO fading channel. In the LLL algorithm, size reduction is performed for pairs of consecutive basis vectors, and the concern of numerical stability is raised. However, the whole complexity of the LLL algorithm is of polynomial order, and its characteristics of the convergence perform poor in MIMO system. In this paper, a variant version, named the novel hybrid algorithm, which combines both fix measurement and round measurement, is proposed. By modifying the iteration criterion and choosing proper values of the parameters, the algorithm has a large probability to skip the size reduction and cause a faster convergence, It means in one algorithm iteration the LLL potential can be reduced as much as possible. Also, the performance bound derived by the proximity factor shows that the hybrid LLL has a minor performance loss compared to the LLL algorithm. As a direct consequence, in simulation results, the hybrid LLL algorithm can make a better compromise between the rate of convergence, complexity of the algorithm, and algorithmic performance. © 2016 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.