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

TL;DR

This paper tackles the sustainability of 6G networks facing spatio-temporal traffic heterogeneity by introducing Integrated Relative Energy Efficiency (IREE) to jointly optimize capacity and traffic-capacity alignment under joint multi-BS and multi-RIS deployments.It proposes the Alternating Directional Dual-Radial Basis Function (ADD-RBF) framework, which models BS and RIS channels as two distinct types of RBF neurons and optimizes them via alternating training, with universal approximation guarantees and convergence analysis.The authors derive fundamental scaling laws showing a dichotomy: base stations provide logarithmic capacity growth with polynomial mismatch reduction, whereas RISs yield exponential mismatch mitigation with sub-logarithmic capacity gains, a finding validated by comprehensive simulations in urban and rural traffic profiles.The results yield concrete deployment guidelines: prioritize BS densification to address capacity shortages, then shift to RIS-centric scaling to mitigate spatial mismatch with minimal energy overhead, enabling energy-efficient, scalable 6G network design.

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 establishes fundamental scaling laws for 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 channels of BSs and RISs as two type of spatially decoupled RBF neurons to maximize IREE through alternative optimization, with proven universal approximation capability and convergence guarantees. Theoretical analysis reveals a scaling dichotomy: BS proliferation drives logarithmic capacity growth $\mathcal{O}(\log N^{BS})$ but only polynomial mismatch reduction $\mathcal{O}(1/\sqrt{N^{BS}})$, whereas RIS deployment achieves exponential mismatch mitigation $\mathcal{O}(δ_{\text{err}}^{-(N^R+1)})$ despite its sub-logarithmic capacity gains. Simulation results validate that RISs excel in capturing spatial traffic correlations and alleviating hotspots, making them particularly effective when mismatch dominates, while BSs are preferable under capacity shortages. These findings offer practical guidelines for green 6G network design.

Figures (7)

• Figure 1: An illustrative example of target area $\mathcal{A}$ with $N^{BS}$ BSs and $N^R$ RISs. The active beamforming vectors, the bandwidths and the locations of BSs, as well as the passive beamforming matrices and the locations of RISs shall be optimized to maximize the energy efficiency of the network.
• Figure 2: Overview of the proposed ADD-RBF scheme. The black dashed line represent the forward propagation while the orange and blue dashed line represent the backward propagation processes for the LoS channel of the RISs and BSs, respectively. The green dashed line represents to obtain the optimized IREE through a series of $L_{err}^{(k)}$ minimization problems, where $L_{err}^{(k)}$ is constructed through IREE in current iteration $\eta_{IREE}^{(k)}$.
• Figure 3: Proposed ADD-RBF scheme vs End-to-end training. The end-to-end training fails to converge due to the highly non-concave loss landscape while the proposed ADD-RBF scheme avoid this problem by quasi-concavity decomposition.
• Figure 4: An illustration of the urban & rural traffic profiles, both of which follow a normalized log-normal model lee2014spatial.
• Figure 5: Comparative evaluation across four network deployment configurations. The top row displays the performance achieved by baseline scheme, while the bottom row corresponds to results from the proposed ADD-RBF scheme. From left to right, the first column depicts deployments utilizing solely BS with unoptimized locations; the second column shows joint BS and RIS deployment where the positions are not optimized; the third column represents joint deployments featuring optimized RIS placements alongside unoptimized BS locations; and the fourth column showcases the scenario with both BS and RIS locations optimized. Red triangles indicate BS positions, and orange diamonds denote RIS placements.

Theorems & Definitions (8)

• Definition 1: IREE Metric yu2022novel
• Lemma 1: Dual-RBF Architecture
• Theorem 1: Universal Approximation Property for $C_S(\mathcal{L}^U)$
• Lemma 2: Quasi-concavity Decomposition in Alternating Training
• Theorem 2: Convergence property of ADD-RBF Scheme
• Lemma 3: Order-wise Analysis of JS Divergence
• Theorem 3: EE Scaling Law for Multi-BSs & Multi-RISs Deployment
• Theorem 4: IREE Scaling Law for Multi-BSs & Multi-RISs Deployment