Channel Calibration for Cell-Free Massive MIMO Systems Using Diffusion Model

Cell-free massive multiple-input multiple-output (MIMO) systems have emerged as a transformative architecture for sixth generation (6G) communication networks, where distributed access points (APs) collaborate to simultaneously serve all user equipments (UEs). However, in time division duplex (TDD) systems, the reciprocity of uplink channel and downlink channel is disrupted by hardware imperfections in radio frequency (RF) chains, leading to significant degradation in system performance. This paper begins with a theoretical analysis of the downlink performance under a conjugate beamforming scheme, considering scenarios with and without channel calibration. A key theoretical insight highlights the limitation of conventional least squares (LS) calibration method, which fails to achieve high calibration accuracy even with an unlimited number of pilot observations. To overcome this limitation, we propose a novel channel calibration approach based on a diffusion model, designed to successively refine the calibration vector obtained from the LS calibration method. Furthermore, to address the shortcomings of conventional denoising diffusion probabilistic model (DDPM) training architectures, we introduce an innovative bridge-based diffusion model that maps the distribution of LS calibration vectors to their perfect counterparts. The proposed diffusion neural network architecture employs a conditional generative process, integrating a message passing neural network (MPNN) to incorporate domain-specific calibration insights. Numerical results demonstrate the superior performance of our proposed calibration method compared to existing methods, with supplementary experiments and in-depth analyses confirming the efficacy of the proposed successive refinement design.