Quantum-Behaved PSO-DE for Ubiquitous Connectivity in Space-Terrestrial Cell-Free Massive MIMO Systems

Abstract

To achieve ubiquitous connectivity over heterogeneous environments, we study a three-dimensional integrated architecture where a Low-Earth-Orbit (LEO) satellite complements a terrestrial cell-free Massive MIMO system. Under imperfect channel state information (CSI), we derive closed-form expressions for the uplink ergodic throughput using maximum-ratio combining (MRC) over spatially correlated Rician fading channels. To enhance user fairness, we formulate a max-min throughput optimization problem that jointly optimizes user association and transmit power allocation. The resulting mixed-integer nonlinear programming problem is NP-hard due to the coupling between binary association variables and continuous power control variables. To tackle this challenge, we propose a hybrid Quantum-Behaved Particle Swarm Optimization with Differential Evolution mutation (QPSO-DE) framework. Unlike classical particle swarm optimization, which relies on deterministic velocity updates, the proposed QPSO-DE adopts quantum-inspired probabilistic position sampling based on wave-function collapse, enabling non-local exploration of the solution space. Furthermore, when convergence stagnation is detected, a differential evolution-based mutation mechanism exploits population diversity to escape local optima. Numerical results demonstrate that the proposed space-terrestrial architecture substantially improves user fairness, while the QPSO-DE algorithm outperforms existing benchmark schemes across diverse network sizes and deployment scenarios.