We present an analytical framework for the channel estimation and the data decoding in massive multiple-input multiple-output uplink systems with 1-bit analog-to-digital converters (ADCs). First, we provide a closed-form expression of the mean squared error of the channel estimation for a general class of linear estimators. In addition, we propose a novel linear estimator with significantly enhanced performance compared with existing estimators with the same structure. For the data decoding, we provide closed-form expressions of the expected value and the variance of the estimated symbols when maximum ratio combining is adopted, which can be exploited to efficiently implement maximum likelihood decoding and, potentially, to design the set of transmit symbols. Comprehensive numerical results are presented to study the performance of the channel estimation and the data decoding with 1-bit ADCs with respect to the signal-to-noise ratio (SNR), the number of user equipments, and the pilot length. The proposed analysis highlights a fundamental SNR trade-off, according to which operating at the right noise level significantly enhances the system performance.

翻译：我们提出了一个频道估算和数据解码分析框架,用于使用1位模拟数字转换器(ADCs)的大型多输出多输出连接系统进行频道估算和数据解码。首先,我们用一个封闭式的形式表示一般类线性估测器的频道估算平均平方误差;此外,我们提出一个新的线性估测器,其性能与结构相同的现有估测器相比显著提高;关于数据解码,我们提供了在采用最大混合率时预期值和估计符号差异的封闭式表达,可以利用这一表达法有效地实现最大可能性解码,并有可能设计一套传输符号。我们提出了全面的数字结果,以研究频道估算的性能和与1位ADC数据解码的性能,即信号对音比、用户设备的数量和试验长度。拟议的分析突出了SNR交易的基本条件,根据这一条件,在正确的噪音水平上运行将大大增强系统的性能。