A Novel Fix-Effective-LLL Algorithm Using Fast-Givens Rotations for MIMO System

摘要

Effective Lenstra-Lenstra-Lovasz (E-LLL) is an effective lattice reduction algorithm in Multi-Input-Multi-Output (MIMO) system. Size reduction and columns swaps are performed for pairs of consecutive basis vectors in E-LLL algorithm. Also comparing to LLL algorithm, the concern of numerical stability of E-LLL is raised. However, the complexity of E-LLL algorithm is still very high. In this paper, we try to introduce some methods to reduce the complexity of E-LLL algorithm. Firstly, a novel Fix-Effective Lenstra-Lenstra-Lovasz (F-E-LLL) algorithm is proposed. By revising the iteration criterion, F-E-LLL algorithm has more chance to skip the size reduction and basis vector swapping procedure. Meanwhile, fast-Givens rotations are applied to E-LLL algorithm for improving the computation efficiency. The reduction of complexity is achieved by substantially reducing the number of multiplication operations. Simulation results show that using fast-Givens rotations can significantly reduce the times of floatingpoint operations (flops) and the whole algorithm complexity is also cut down.