  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.
