  Existing works on grant-free access, proposed to support massive machine-type
communication (mMTC) for the Internet of things (IoT), mainly concentrate on
narrow band systems under flat fading. However, little is known about massive
grant-free access for wideband systems under frequency-selective fading. This
paper investigates massive grant-free access in a wideband system under
frequency-selective fading. First, we present an orthogonal frequency division
multiplexing (OFDM)-based massive grant-free access scheme. Then, we propose
two different but equivalent models for the received pilot signal, which are
essential for designing various device activity detection and channel
estimation methods for OFDM-based massive grant-free access. One directly
models the received signal for actual devices, whereas the other can be
interpreted as a signal model for virtual devices. Next, we investigate
statistical device activity detection under frequency-selective Rayleigh fading
based on the two signal models. We first model device activities as unknown
deterministic quantities and propose three maximum likelihood (ML)
estimation-based device activity detection methods with different detection
accuracies and computation times. We also model device activities as random
variables with a known joint distribution and propose three maximum a posterior
probability (MAP) estimation-based device activity methods, which further
enhance the accuracies of the corresponding ML estimation-based methods.
Optimization techniques and matrix analysis are applied in designing and
analyzing these methods. Finally, numerical results show that the proposed
statistical device activity detection methods outperform existing
state-of-the-art device activity detection methods under frequency-selective
Rayleigh fading.
