Distributed URLLC Beamforming for Partially Connected Cell-Free Massive MIMO Systems with Scalable Graph Neural Networks

In this paper, we investigate the downlink distributed transmit beamforming problem in partially connected cell-free massive multiple-input multiple-output (CF mMIMO) systems, specifically designed to satisfy the stringent requirements of ultra-reliable and low-latency communication (URLLC) services. First, we propose a scalable framework that incorporates partial access points (APs) to serve active user equipment (UE), with a reduced energy consumption and computational complexity. To this end, a min-max optimization problem is formulated for minimizing the decoding error probability (DEP) among URLLC services. Then, a graph neural network (GNN)-based strategy called G4PCF is proposed for partially connected CF mMIMO, which takes into account the underlying characteristics of the problem. Furthermore, by leveraging the temporal correlation in channel state information acquired from the previous frame, we develop a parallel G4PCF (P-G4PCF) scheme that significantly reduces both the signaling overhead and computation delay for minimizing DEP of the worst UE. Simulation results demonstrate that the proposed G4PCF and P-G4PCF architectures exhibit excellent scalability for CF mMIMO networks, offering superior performance over existing methods in terms of quality of service outage probability. Notably, P-G4PCF excels in supporting URLLC services with short frame durations and highly correlated channels, while G4PCF performs better under lower channel correlation. Moreover, the proposed algorithms can significantly enhance the application of GNNs into CF mMIMO systems with a reduced complexity compared with the classical weighted minimum mean-squared error algorithm, especially with delay sensitive services.