Device Activity Detection in mMTC With Low-Resolution ADCs: A New Protocol

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 <inline-formula> <tex-math notation="LaTeX">$K$ </tex-math></inline-formula>. This is sharply different from the activity detection problem in traditional setups, in which the knowledge of <inline-formula> <tex-math notation="LaTeX">$K$ </tex-math></inline-formula> 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 <inline-formula> <tex-math notation="LaTeX">$K$ </tex-math></inline-formula> 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 <inline-formula> <tex-math notation="LaTeX">$K$ </tex-math></inline-formula> are closely intertwined and doing one needs the information/execution from the other. We propose a progressive estimator which iteratively performs the estimation of <inline-formula> <tex-math notation="LaTeX">$K$ </tex-math></inline-formula> 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.