User Activity Detection and Channel Estimation in Frequency-Selective Faded Grant-Free Access

In grant-free multiple access, active users transmit without requesting permission and the base station must perform user activity detection (UAD), a problem associated with compressive sensing. However, most UAD solutions consider a flat fading channel model. In this work, we propose a solution to the UAD problem for frequency-selective fading channels through the embedding of a polynomial approximation which renders the system block-sparse. We then propose a block orthogonal matching pursuit (BOMP) algorithm which jointly performs UAD and channel estimation, having as advantages a low complexity and an excellent performance under short pilot sequences, as demonstrated by simulation results.