This paper investigates the effect of low-resolution analog-to-digital converters (ADCs) on device activity detection in massive machine-type communications (mMTC). The low-resolution ADCs induce two challenges on the device activity detection compared with the traditional setup with the assumption of infinite ADC resolution. First, the codebook design for signal quantization by the low-resolution ADC is particularly important since a good design of the codebook can lead to small quantization error on the received signal, which in turn has significant influence on the activity detector performance. To this end, prior information about the received signal power is needed, which depends on the number of active devices $K$. This is sharply different from the activity detection problem in traditional setups, in which the knowledge of $K$ is not required by the BS as a prerequisite. Second, the covariance-based approach achieves good activity detection performance in traditional setups while it is not clear if it can still achieve good performance in this paper. To solve the above challenges, we propose a communication protocol that consists of an estimator for $K$ and a detector for active device identities: 1) For the estimator, the technical difficulty is that the design of the ADC quantizer and the estimation of $K$ are closely intertwined and doing one needs the information/execution from the other. We propose a progressive estimator which iteratively performs the estimation of $K$ and the design of the ADC quantizer; 2) For the activity detector, we propose a custom-designed stochastic gradient descent algorithm to estimate the active device identities. Numerical results demonstrate the effectiveness of the communication protocol.

翻译：本文研究了低分辨率模数转换器（ADC）对大规模机器类型通信（mMTC）中设备活跃性检测的影响。与假设无限ADC分辨率的传统设置相比，低分辨率ADC给设备活跃性检测带来了两个挑战。第一，低分辨率ADC用于信号量化的码本设计尤为重要，因为良好的码本设计可以减小接收信号的量化误差，进而对活跃性检测器的性能产生显著影响。为此，需要关于接收信号功率的先验信息，而该信息取决于活跃设备数量$K$。这与传统设置中的活跃性检测问题截然不同，因为在传统设置中，基站（BS）无需以先验知识的形式知道$K$的值。第二，基于协方差的方法在传统设置中能够实现良好的活跃性检测性能，但尚不清楚该方法在本文场景中是否仍能保持优异表现。针对上述挑战，我们提出了一种通信协议，包含$K$的估计器和活跃设备身份的检测器：1）对于估计器，技术难点在于ADC量化器的设计与$K$的估计紧密交织，执行一项任务需要另一项任务的信息或执行结果。我们提出了一种渐进式估计器，通过迭代方式交替进行$K$的估计和ADC量化器的设计；2）对于活跃性检测器，我们提出了一种定制的随机梯度下降算法来估计活跃设备身份。数值结果验证了该通信协议的有效性。