Grant-Free Random Access in Cell-Free Massive MIMO Systems With UE Detection Thresholds: A Stochastic Geometry Approach

In this paper, we analyze the grant-free random access (GFRA) in cell-free massive multiple-input multiple-output (CF-mMIMO) systems. Unlike previous works on GFRA that regard all user equipments (UEs) selecting the same pilot as undetectable, we give a more accurate model that the access point (AP) can detect the strongest UE when its signal-to-interference-plus-noise ratio (SINR) exceeds a threshold. On top of this, we also define the concept of effective access that a UE is successfully detected by APs around it within a limited area. With tools from stochastic geometry, the probability of UE effective access and the minimum required AP spatial density that satisfies UEs' access delay constraints are derived. It is found that increasing the AP antenna number from 1 to 2 can significantly improve the UE access probability and reduce the required AP number, while this improvement decays quickly as the antenna number keeps growing, which works more obviously when the access delay constraint is strict or the pilot length is short.