An AMP-Based Asymptotic Analysis For Nonlinear One-Bit Precoding
Zheyu Wu, Junjie Ma, Ya-Feng Liu, Bruno Clerckx
TL;DR
This work analyzes nonlinear one-bit precoding under Rayleigh-like conditions via a convex-relaxation-then-quantization framework (CRQ) and an approximate message passing (AMP) based approach. It derives a scalar signal-plus-Gaussian-noise model that asymptotically characterizes the transmit design and uses it to obtain a closed-form SEP in the large-system limit. The results reveal how system and model parameters shape SEP and show potential gains over the SQUID precoder by tuning the CRQ regularization parameters, supported by simulations. The approach offers a versatile AMP-based toolkit for analyzing broad nonlinear one-bit precoding schemes in massive MIMO, with implications for practical design and performance guarantees.
Abstract
This paper focuses on the asymptotic analysis of a class of nonlinear one-bit precoding schemes under Rayleigh fading channels. The considered scheme employs a convex-relaxation-then-quantization (CRQ) approach to the well-known minimum mean square error (MMSE) model, which includes the classical one-bit precoder SQUID as a special case. To analyze its asymptotic behavior, we develop a novel analytical framework based on approximate message passing (AMP). We show that, the statistical properties of the considered scheme can be asymptotically characterized by a scalar ``signal plus Gaussian noise'' model. Based on this, we further derive a closed-form expression for the symbol error probability (SEP) in the large-system limit, which quantitatively characterizes the impact of both system and model parameters on SEP performance. Simulation results validate our analysis and also demonstrate that performance gains over SQUID can be achieved by appropriately tuning the parameters involved in the considered model.