Computationally efficient fixed complexity LLL algorithm for lattice‐reduction‐aided multiple‐input–multiple‐output precoding

In multiple‐input–multiple‐output broadcast channels, lattice reduction (LR) preprocessing technique can significantly improve the precoding performance. Among the existing LR algorithms, the fixed complexity Lenstra–Lenstra–Lovasz (fcLLL) algorithm applying limited number of LLL loops is suitable for the real‐time communication system. However, fcLLL algorithm suffers from higher average complexity. Aiming at this problem, a computationally efficient fcLLL (CE‐fcLLL) algorithm for LR‐aided (LRA) precoding is developed in this study. First, the authors analyse the impact of fcLLL algorithm on the signal‐to‐noise ratio performance of LRA precoding by a power factor (PF) which is defined to measure the relation of reduced basis and transmit power of LRA precoding. Then, they propose a CE‐fcLLL algorithm by designing a new LLL loop and introducing new early termination conditions to reduce redundant and inefficient LR operation in fcLLL algorithm. Finally, they define a PF loss factor to optimise the PF threshold and the number of LLL loops, which can lead to a performance‐complexity tradeoff. Simulation results show that the proposed algorithm for LRA precoding can achieve better bit‐error‐rate performance than the fcLLL algorithm with remarkable complexity savings in the same upper complexity bound.