An Efficient Greedy LLL Algorithm for MIMO Detection

Lenstra-Lenstra-Lovász (LLL) algorithm has been adopted as a lattice reduction (LR) technique for multiple-input multiple-output (MIMO) detection to improve error performance without exponential complexity. However, implementing the LLL algorithm is still challenging. During the execution of each LLL iteration, the column swap operations may not happen in some cases, which is not efficient in terms of convergence speed. To address this issue, some greedy LLL variants have recently been proposed, which only select the iterations with column swap each time so that the number of LLL iterations can be reduced compared to the original LLL algorithm. In this paper, we propose an efficient greedy LLL algorithm, based on the relaxed Lovász condition to search the candidate set of LLL iterations and the relaxed decrease of LLL potential to select an LLL iteration each time. Besides, we also present an efficient implementation of the proposed algorithm. Compared to the existing greedy LLL algorithms, simulations show that the proposed greedy LLL not only converges faster but also exhibits much lower complexity (save over 55% and 62% complexity in average for 4 × 4 and 8 × 8 MIMO systems) while maintaining similar error performance in LR-aided MIMO detectors.