We consider angular-domain channel estimation in massive MIMO systems using one-bit analog-to-digital converters (ADCs) with various thresholding schemes at the receivers. We first derive the performance bounds for estimating angular-domain channel parameters, including the angles-of-arrival (AoA), angles-of-departure (AoD) and the associated path gains. Specifically, we derive 1) the deterministic Cramér-Rao bound (CRB) when all of the angular-domain channel parameters are treated as deterministic unknowns; 2) the hybrid CRB when some parameters have known prior probability density functions (pdfs) while the rest are assumed to be deterministic unknowns; 3) the Bayesian CRB when all of them have known prior pdfs. We also consider using the maximum likelihood (ML) method for channel estimation and a computationally efficient relaxation based cyclic algorithm (referred to as 1bRELAX) to obtain the ML estimates. When the prior information is available, the maximum a posteriori (MAP) and joint ML-MAP (JML-MAP) estimators are derived. We also use the one-bit Bayesian information criterion (1bBIC) to determine the number of scattering paths. Numerical examples are provided to verify the derived performance bounds with different thresholding schemes and demonstrate the performance of the proposed channel estimation algorithms.

中文翻译：

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一位大规模 MIMO 系统的角域信道估计：性能界限和算法


我们考虑使用一位模数转换器 (ADC) 以及接收器处的各种阈值方案来进行大规模 MIMO 系统中的角域信道估计。我们首先推导估计角域信道参数的性能界限，包括到达角（AoA）、出发角（AoD）和相关的路径增益。具体来说，我们推导 1) 当所有角域信道参数被视为确定性未知数时，确定性 Cramér-Rao 界（CRB）； 2）当某些参数具有已知的先验概率密度函数（pdf）而其余参数被假设为确定性未知时，混合CRB； 3) 当所有人都知道先验概率密度函数时的贝叶斯 CRB。我们还考虑使用最大似然（ML）方法进行信道估计和计算高效的基于松弛的循环算法（称为1bRELAX）来获得ML估计。当先验信息可用时，将导出最大后验 (MAP) 和联合 ML-MAP (JML-MAP) 估计量。我们还使用一位贝叶斯信息准则（1bBIC）来确定散射路径的数量。提供了数值示例来验证使用不同阈值方案得出的性能界限，并演示了所提出的信道估计算法的性能。