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 assumption of infinite ADC resolution. First, the codebook design for signal quantization by the low-resolution ADCs is particularly important since a good codebook design 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）中设备活动检测的影响。与传统假设无限ADC分辨率的设置相比，低分辨率ADC给设备活动检测带来了两个挑战。首先，低分辨率ADC对信号进行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，进而对活动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，而这取决于活动设备数量$K$。这与传统设置中的活动检测问题截然不同，在传统设置中，基站无需预先知道$K$值。其次，基于协方差的方法在传统设置中能实现良好的活动检测性能，但尚不清楚该方法在本文中是否仍能保持良好的性能。为解决上述挑战，我们提出一种包含$K$值估计器和活动设备身份检测器的通信协议：1）对于估计器而言，技术难点在于ADC量化器的设计与$K$值的估计紧密交织，进行其中一项工作需要另一项的信息或执行结果。我们提出了一种渐进式估计器，通过迭代方式交替完成$K$值的估计和ADC量化器的设计；2）对于活动检测器，我们提出了一种定制化的随机梯度下降算法来估计活动设备身份。数值结果验证了该通信协议的有效性。