Lattice-reduction aided HNN for vector precoding

In this paper we propose a modification of the Hopfield neural networks for vector precoding, based on Lenstra, Lenstra, and Lovasz lattice basis reduction. This precoding algorithm controls the energy penalty for system loads α = K/N close to 1, with N and K denoting the number of transmit and receive antennas, respectively. Simulation results for the average transmit energy as a function of α show that our algorithm improves performance within the range 0.9 ≤ α ≤ 1, between 0.4 dB and 2.6 dB in comparison to standard HNN precoding. The proposed algorithm performs close to the sphere encoder (SE) while requiring much lower complexity, and thus, can be applied as an efficient suboptimal precoding method.