Efficient Greedy LLL Algorithms for Lattice Decoding

The Lenstra-Lenstra-Lovasz (LLL) algorithm has been adopted as a lattice reduction (LR) technique for multiple-input multiple-output (MIMO) communications to improve performance with low complexity. However, implementing the LLL algorithm is still challenging due to slow convergence especially for large channel matrices. One of the main reasons is that the column swap may not happen in some LLL iterations, which leads to more iterations. To address it, some greedy LLL algorithms have recently been proposed, which only perform the iterations with column swaps. In this paper, we propose two efficient greedy LLL algorithms for various LR-aided MIMO detectors. First, both algorithms use a relaxed Lovasz condition to search the candidate set of LLL iterations. Then, to select an LLL iteration in the candidate set each time, one is based on a relaxed decrescence of LLL potential, and the other takes the error performance of the LR-aided MIMO detectors into consideration. The proposed two algorithms are proved to collect full receive diversity in both LR-aided linear and successive-interference-cancellation detectors. Furthermore, compared to existing greedy LLL algorithms, simulations show that the proposed two algorithms not only converge faster but also exhibit much lower complexity while maintaining comparable error performance in LR-aided MIMO detectors.