OFDM-Based Massive Grant-Free Transmission Over Frequency-Selective Fading Channels

In massive grant-free transmission, joint user activity detection (UAD) and channel estimation (CE) is essential for data recovery at the receiver, which has been extensively researched in frequency-flat fading scenarios. However, in practical orthogonal frequency division multiplexing (OFDM)-based systems, frequency-selective fading (FSF) leads to a significant increase in the number of channel coefficients to be estimated, imposing new challenges for the design of joint UAD and CE algorithms. Therefore, this paper investigates joint UAD and CE for OFDM-based massive grant-free transmission over FSF channels. Firstly, by employing the discrete cosine transform (DCT), the joint estimation problem is formulated as the compressed sensing (CS) problem with the reduced dimension of the DCT-domain channel response vector. Then, based on the low-dimension sparse channel model, we develop a hybrid message passing (HMP) algorithm under the constrained Bethe free energy (BFE) minimization framework to achieve efficient joint UAD and CE. To deal with the lack of the DCT-domain prior information in practical scenarios, we parameterize it as the Cauchy distribution or the Laplacian distribution and learn their parameters by the proposed HMP algorithm. Numerical results confirm the superior joint UAD and CE performance of the proposed algorithm over FSF channels.