An AMP-Based Asymptotic Analysis For Nonlinear One-Bit Precoding

TL;DR

This paper introduces an AMP-based analytical framework to study the asymptotic behavior of nonlinear one-bit precoding schemes, providing explicit SEP expressions and demonstrating potential performance improvements over existing methods.

Contribution

It develops a novel AMP-based analysis for nonlinear one-bit precoding, deriving closed-form SEP expressions and showing performance gains over SQUID.

Findings

Asymptotic characterization of the precoding scheme using AMP.

Closed-form expression for symbol error probability (SEP).

Performance gains over SQUID with proper parameter tuning.

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.