Distributed Penalty Nesterov Gradient Algorithm For Extremely Large-Scale MIMO Systems

In this paper, we propose the distributed penalty Nesterov gradient (DPNG) detection algorithm for uplink extremely large-scale multiple-input multiple-output (XL-MIMO) systems, to address the performance limitations of conventional linear detectors. Instead of directly solving the maximum likelihood (ML) detection problem, we introduce a convex relaxation by incorporating a tailored penalty function that enforces alignment between the estimates and the constellation set. By integrating the diffusion strategy into reformulated detection problem, the DPNG algorithm enables efficient distributed computation. According to theoretical analysis, we prove this reformulated detection problem to be strongly convex and Lipschitz continuous. Leveraging these properties, the optimal solution of the reformulated problem achieves better performance than traditional linear detection. Furthermore, theoretical result demonstrates that the proposed DPNG algorithm efficiently finds this solution with a sublinear convergence rate, precisely quantifying the trade-off between detection performance and computational complexity. Extensive simulations confirm that DPNG achieves notable BER improvements with lower complexity and bandwidth, thereby providing practical advantages over prior methods in distributed XL-MIMO detection.