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Device activity detection and channel estimation for massive grant-freeaccess under frequency-selective fading have unfortunately been an outstandingproblem. This paper aims to address the challenge. Specifically, we present anorthogonal frequency division multiplexing (OFDM)-based massive grant-freeaccess scheme for a wideband system with one M-antenna base station (BS), Nsingle-antenna Internet of Things (IoT) devices, and P channel taps. We obtaintwo different but equivalent models for the received pilot signals underfrequency-selective Rayleigh fading. Based on each model, we formulate deviceactivity detection as a non-convex maximum likelihood estimation (MLE) problemand propose an iterative algorithm to obtain a stationary point using optimaltechniques. The two proposed MLE-based methods have the identical computationalcomplexity order O(NPL^2), irrespective of M, and degrade to the existingMLE-based device activity detection method when P=1. Conventional channelestimation methods can be readily applied for channel estimation of detectedactive devices under frequency-selective Rayleigh fading, based on one of thederived models for the received pilot signals. Numerical results show that thetwo proposed methods have different preferable system parameters and complementeach other to offer promising device activity detection design for grant-freemassive access under frequency-selective Rayleigh fading.

Device Activity Detection for Massive Grant-Free Access Under Frequency-Selective Rayleigh Fading