Green Wireless Network Scaling for Joint Deployment: Multi-BSs or Multi-RISs?

Abstract

The imminent emergence of sixth-generation (6G) networks faces critical challenges from spatially heterogeneous traffic and escalating energy consumption, necessitating sustainable scaling strategies for network infrastructure such as base stations (BSs) and reconfigurable intelligent surfaces (RISs). This paper presents a systematic scaling analysis of the Integrated Relative Energy Efficiency (IREE) metric under joint multi-BS and multi-RIS deployment in traffic-mismatched scenarios. Specifically, we propose an Alternating Directional Dual Radial Basis Function (ADD-RBF) framework that models the spatial capacity contributions of BSs and RISs through two separately parameterized RBF-type branches and maximizes IREE through accepted alternating optimization, with established representation expressiveness and stage-wise convergence properties. Theoretical analysis reveals distinct scaling behaviors: BS proliferation drives logarithmic capacity growth $\mathcal{O}(\log N^{BS})$ and polynomial large-scale mismatch reduction $\mathcal{O}\big((N^{BS})^{-t_g/2}\big)$, whereas RIS deployment provides a bounded passive capacity-gain correction and residual-structure-dependent mismatch reduction. Specifically, the RIS-side mismatch decreases polynomially as $\mathcal{O}\big((N^R)^{-t_\ell/2}\big)$ for spatially diffuse residuals and follows the stretched-exponential order $\mathcal{O}\big(\exp[-c_R\sqrt{N^R}]\big)$ for hotspot-dominated residuals. Simulation results show that RISs are effective in refining spatial traffic-capacity mismatch and alleviating hotspots, making them particularly attractive when mismatch dominates, while BSs are generally preferable under capacity shortages. These findings offer practical guidelines for green 6G network design.