Hybrid Vector Perturbation Precoding: The Blessing of Approximate Message Passing

Vector perturbation (VP) precoding is a promising technique for multiuser communication systems operating in the downlink. In this work, we introduce a hybrid framework to improve the performance of lattice reduction (LR) aided (LRA) VP. Firstly, we perform a simple precoding using zero forcing (ZF) or successive interference cancellation (SIC) based on a reduced lattice basis. Since the signal space after LR-ZF or LRSIC precoding can be shown to be bounded to a small range, then along with sufficient orthogonality of the lattice basis guaranteed by LR, they collectively pave the way for the subsequent application of an approximate message passing (AMP) algorithm, which further boosts the performance of any suboptimal precoder. Our work shows that the AMP algorithm in compressed sensing can be beneficial for a lattice decoding problem whose signal constraint lies in Z and entries of the input lattice basis not necessarily being i.i.d. Gaussian. Numerical results show that the developed hybrid scheme can provide performance enhancement with negligible increase in the complexity.