Joint Asynchronous Activity Detection and Delay Estimation for Grant-Free Random Access in Cell-Free Massive MIMO Systems

Device activity detection (DAD) is a key topic for massive grant-free random access (GFRA) in cell-free massive multiple-input multiple-output (CF-mMIMO) system. However, since the different distances between access points (APs) and different active devices, imperfect synchronization of internet of things devices with low-cost oscillators and the lack of strict synchronization procedure for cell free systems, they will lead to a severe distortion and interference for the received signals, which brings a serious challenge to DAD. So the asynchronous DAD remains an important research issue. In this paper, we investigate joint asynchronous activity detection and delay estimation for GFRA in CF-mMIMO systems. First, we formulate the DAD problem as a maximum likelihood estimation problem by exploiting the block diagonal property of the covariance matrix of the asynchronous received signals. And then, we propose two strategies to solve the reformulated optimization problem, i.e., coordinate descent enforcement and block coordinate descent. Furthermore, in order to leverage the macro diversity gain brought by the CF-mMIMO system to improve the activity detection performance, we propose adaptive AP selection-based asynchronous activity detection algorithms, which can achieve better detection accuracy and have better scalability. Finally, convincing simulations verify the effectiveness of our proposed asynchronous detection schemes.