A promising approach to deal with the high hardware cost and energy consumption of massive MIMO transmitters is to use low-resolution digital-to-analog converters (DACs) at each antenna element. This leads to a transmission scheme where the transmitted signals are restricted to a finite set of voltage levels. This paper is concerned with the analysis and optimization of a low-cost quantized precoding strategy, referred to as linear-quantized precoding, for a downlink massive MIMO system under Rayleigh fading. In linear-quantized precoding, the signals are first processed by a linear precoding matrix and subsequently quantized component-wise by the DAC. In this paper, we analyze both the signal-to-interference-plus-noise ratio (SINR) and the symbol error probability (SEP) performances of such linear-quantized precoding schemes in an asymptotic framework where the number of transmit antennas and the number of users grow large with a fixed ratio. Our results provide a rigorous justification for the heuristic arguments based on the Bussgang decomposition that are commonly used in prior works. Based on the asymptotic analysis, we further derive the optimal precoder within a class of linear-quantized precoders that includes several popular precoders as special cases. Our numerical results demonstrate the excellent accuracy of the asymptotic analysis for finite systems and the optimality of the derived precoder.

翻译：降低大规模MIMO发射机高硬件成本与能耗的一个有前景方案是在每个天线单元采用低分辨率数模转换器（DAC）。这导致传输信号被限制在有限电压电平集合的传输方案。本文针对瑞利衰落下的下行大规模MIMO系统，研究一种称为线性量化预编码的低成本量化预编码策略的分析与优化。在线性量化预编码中，信号首先经线性预编码矩阵处理，随后由DAC逐分量量化。本文在发射天线数与用户数以固定比值趋于无穷大的渐近框架下，分析此类线性量化预编码方案的信号与干扰加噪声比（SINR）及符号错误概率（SEP）性能。我们的结果为以往研究中基于Bussgang分解的启发式论证提供了严格的理论依据。基于渐近分析，我们进一步推导出一类包含多种常见预编码器作为特例的线性量化预编码器的最优预编码器。数值结果验证了渐近分析对有限系统的极佳精度以及所推导预编码器的最优性。