Expectation Propagation for Distributed Inference in Grant-Free Cell-Free Massive MIMO

Grant-free cell-free massive multiple-input multiple-output (GF-CF-MaMIMO) systems are anticipated to be a key enabling technology for next-generation Internet-of-Things (IoT) networks, as they support massive connectivity without explicit scheduling. However, the large amount of connected devices prevents the use of orthogonal pilot sequences, resulting in severe pilot contamination (PC) that degrades channel estimation and data detection performance. Furthermore, scalable GF-CF-MaMIMO networks inherently rely on distributed signal processing. In this work, we consider the uplink of a GF-CF-MaMIMO system and propose two novel distributed algorithms for joint activity detection, channel estimation, and data detection (JACD) based on expectation propagation (EP). The first algorithm, denoted as JACD-EP, uses Gaussian approximations for the channel variables, whereas the second, referred to as JACD-EP-BG, models them as Bernoulli-Gaussian (BG) random variables. To integrate the BG distribution into the EP framework, we derive its exponential family representation and develop the two algorithms as efficient message passing over a factor graph constructed from the a posteriori probability (APP) distribution. The proposed framework is inherently scalable with respect to both the number of access points (APs) and user equipments (UEs). Simulation results show the efficient mitigation of PC by the proposed distributed algorithms and their superior detection accuracy compared to (genie-aided) centralized linear detectors.