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.

翻译：本文针对瑞利衰落信道下一类非线性一位预编码方案进行渐近分析。所研究的方案对经典的最小均方误差（MMSE）模型采用“凸松弛后量化”（CRQ）的处理方法，该框架将经典的一位预编码器SQUID作为特例包含在内。为分析其渐近特性，我们基于近似消息传递（AMP）构建了一个新颖的理论分析框架。我们证明，所研究方案的统计特性可通过一个标量化的“信号加高斯噪声”模型进行渐近表征。基于此，我们进一步推导出大系统极限下符号错误概率（SEP）的闭式表达式，该表达式定量刻画了系统参数与模型参数对SEP性能的共同影响。仿真结果验证了理论分析的正确性，同时表明通过合理调节模型参数，所提方案可获得优于SQUID的性能增益。