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This paper investigates the effect of low-resolution analog-to-digitalconverters (ADCs) on device activity detection in massive machine-typecommunications (mMTC). The low-resolution ADCs induce two challenges on thedevice activity detection compared with the traditional setup with theassumption of infinite ADC resolution. First, the codebook design for signalquantization by the low-resolution ADC is particularly important since a gooddesign of the codebook can lead to small quantization error on the receivedsignal, which in turn has significant influence on the activity detectorperformance. To this end, prior information about the received signal power isneeded, which depends on the number of active devices $K$. This is sharplydifferent from the activity detection problem in traditional setups, in whichthe knowledge of $K$ is not required by the BS as a prerequisite. Second, thecovariance-based approach achieves good activity detection performance intraditional setups while it is not clear if it can still achieve goodperformance in this paper. To solve the above challenges, we propose acommunication protocol that consists of an estimator for $K$ and a detector foractive device identities: 1) For the estimator, the technical difficulty isthat the design of the ADC quantizer and the estimation of $K$ are closelyintertwined and doing one needs the information/execution from the other. Wepropose a progressive estimator which iteratively performs the estimation of$K$ and the design of the ADC quantizer; 2) For the activity detector, wepropose a custom-designed stochastic gradient descent algorithm to estimate theactive device identities. Numerical results demonstrate the effectiveness ofthe communication protocol.

Device Activity Detection in mMTC with Low-Resolution ADC: A New Protocol