Bounded Deep Unfolding for Joint Beamforming and Scheduling in Multi-Cell MIMO Networks

Abstract: This paper investigates the joint resource block group (RBG) scheduling and beamforming optimization problem for weighted sum-rate (WSR) maximization in multi-cell multiple-input multiple-output (MIMO) downlink networks. While the Fast Fractional Programming (FastFP) framework provides a reliable model-driven solution, it suffers from conservative continuous beamforming updates and prohibitive computational overhead during the discrete RBG matching phase. To address these bottlenecks, we propose a joint deep unfolding framework comprising two core modules: P-Net and K-Net. For continuous beamforming, P-Net learns an adaptive relaxation factor along the analytical FastFP update direction. By strictly constraining this factor within an ascent-preserving interval, P-Net accelerates the optimization trajectory while rigorously retaining monotonic improvement and stationary-point convergence guarantees. For discrete RBG scheduling, K-Net learns a long-horizon priority policy that guides a low-complexity greedy assignment, effectively preserving the assignment quality while bypassing the high complexity of Hungarian matching. Both networks leverage analytical algorithmic priors and utilize recurrent parameter sharing, enabling flexible inference beyond the training horizon. Extensive simulations demonstrate that the proposed joint framework achieves higher WSR and faster execution times than conventional model-driven baselines, while generalizing robustly across unseen network scales, antenna configurations, and channel conditions without retraining.