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

Device activity detection and channel estimation for grant-free massive access under frequency-selective fading have unfortunately been an outstanding problem. This paper aims to address the challenge. Specifically, we present an orthogo-nal frequency division multiplexing (OFDM)-based grant-free massive 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.