High power consumption and hardware cost have motivated using low-resolution analog-to-digital converters (ADCs) for practical massive multiple-input multiple-output (mMIMO) systems. In this paper, we consider a general mMIMO multi-way relaying system with a multi-level mixed-ADC architecture in which each antenna is connected to an ADC pair with an arbitrary resolution. By leveraging on Bussgang’s decomposition theorem and Lloyd-Max algorithm for quantization, tight closed-form approximations are derived for the average achievable rates of zero-forcing (ZF) relaying considering both perfect and imperfect channel state information (CSI). To handle such a challenging setup, we develop a novel method for the achievable rate analysis using distributions of the singular values of Gaussian matrices and properties of Haar matrices. We demonstrate that the average achievable rate has an almost linear relation with the square of the average of quantization coefficients pertaining to the ADC resolution profile. In addition, in the medium to high SNR region, the ADC resolutions have a more significant effect on the rate compared to the number of antennas. Our work also reveals that the performance gap between the perfect and imperfect CSI cases is smaller for lower ADC resolutions, hence imperfect CSI is better tolerated at lower resolutions.

中文翻译：

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具有低分辨率 ADC 的大规模 MIMO 多路中继网络的性能分析

高功耗和硬件成本促使将低分辨率模数转换器 (ADC) 用于实际的大规模多输入多输出 (mMIMO) 系统。在本文中，我们考虑具有多级混合 ADC 架构的通用 mMIMO 多路中继系统，其中每个天线都连接到具有任意分辨率的 ADC 对。通过利用 Bussgang 的分解定理和用于量化的 Lloyd-Max 算法，考虑到完美和不完美的信道状态信息 (CSI)，推导出了迫零 (ZF) 中继的平均可实现速率的严格封闭形式近似值。为了处理这种具有挑战性的设置，我们开发了一种使用高斯矩阵奇异值分布和 Haar 矩阵属性进行可实现速率分析的新方法。我们证明了平均可实现速率与与 ADC 分辨率分布相关的量化系数平均值的平方几乎呈线性关系。此外，在中高 SNR 区域，与天线数量相比，ADC 分辨率对速率的影响更为显着。我们的工作还表明，对于较低的 ADC 分辨率，完美和不完美 CSI 案例之间的性能差距较小，因此在较低分辨率下可以更好地容忍不完美 CSI。