  Device activity detection and channel estimation for massive grant-free
access under frequency-selective fading have unfortunately been an outstanding
problem. This paper aims to address the challenge. Specifically, we present an
orthogonal frequency division multiplexing (OFDM)-based massive grant-free
access scheme for a wideband system with one M-antenna base station (BS), N
single-antenna Internet of Things (IoT) devices, and P channel taps. We obtain
two different but equivalent models for the received pilot signals under
frequency-selective Rayleigh fading. Based on each model, we formulate device
activity detection as a non-convex maximum likelihood estimation (MLE) problem
and propose an iterative algorithm to obtain a stationary point using optimal
techniques. The two proposed MLE-based methods have the identical computational
complexity order O(NPL^2), irrespective of M, and degrade to the existing
MLE-based device activity detection method when P=1. Conventional channel
estimation methods can be readily applied for channel estimation of detected
active devices under frequency-selective Rayleigh fading, based on one of the
derived models for the received pilot signals. Numerical results show that the
two proposed methods have different preferable system parameters and complement
each other to offer promising device activity detection design for grant-free
massive access under frequency-selective Rayleigh fading.
