We consider channel estimation for an uplink massive multiple-input multiple-output (MIMO) system where the base station (BS) uses an array with low-resolution (1-2 bit) analog-to-digital converters and a spatial Sigma-Delta ($\Sigma\Delta$) architecture to shape the quantization noise away from users in some angular sector. We develop a linear minimum mean squared error (LMMSE) channel estimator based on the Bussgang decomposition that reformulates the nonlinear quantizer model using an equivalent linear model plus quantization noise. We also analyze the uplink achievable rate with maximal ratio combining (MRC), zero-forcing (ZF), and LMMSE receivers and provide a lower bound for the achievable rate with the MRC receiver. Numerical results show superior channel estimation and sum spectral efficiency performance using the $\Sigma\Delta$ architecture compared to conventional 1- or 2-bit quantized massive MIMO systems.

翻译：我们考虑对一个大型多投入多输出(MIIMO)上链路系统进行频道估计,基础站使用低分辨率(1-2位)模拟数字转换器和空间Sigma-Delta(Sigma\Delta$)结构阵列,以便从某些角段用户那里形成四分制噪音。我们根据Bussgang分解法开发了一条线性最低平均正方差(LMMSE)频道估计仪,该模型使用等量线性线性模型加上定量噪声来重新配置非线性量化模型。我们还分析了与最大比率相结合(MRC)、零叉化(ZF)和LMMSE接收器的可实现率,并为与MRC接收器的可实现率提供了较低的约束。与常规的1或2位四分解大型IMO系统相比,数字结果显示频道估计和光谱效率表现优于$(Sigma\Delta$)结构。