IREE Oriented Green 6G Networks: A Radial Basis Function Based Approach

TL;DR

This work proposes an IREE-oriented green 6G design by marrying an SE-based radial-basis-function (RBF) network with Dinkelbach's fractional programming to maximize the integrated relative energy efficiency. The SE-based RBF approximates the continuous capacity distribution, enabling explicit computation of the Jensen-Shannon divergence with traffic, while the two-stage training addresses vanishing gradient issues and ensures convergence. The framework yields substantial IREE gains over traditional EE/SE designs and uncovers a JS-divergence constrained region in the IREE-SE trade-off, highlighting the value of balancing traffic distributions with network capacity. The approach provides practical design guidance for energy-efficient, traffic-aware 6G networks, particularly under spatially heterogeneous urban conditions.

Abstract

In order to provide design guidelines for energy efficient 6G networks, we propose a novel radial basis function (RBF) based optimization framework to maximize the integrated relative energy efficiency (IREE) metric. Different from the conventional energy efficient optimization schemes, we maximize the transformed utility for any given IREE using spectrum efficiency oriented RBF network and gradually update the IREE metric using proposed Dinkelbach's algorithm. The existence and uniqueness properties of RBF networks are provided, and the convergence conditions of the entire framework are discussed as well. Through some numerical experiments, we show that the proposed IREE outperforms many existing SE or EE oriented designs and find a new Jensen-Shannon (JS) divergence constrained region, which behaves differently from the conventional EE-SE region. Meanwhile, by studying IREE-SE trade-offs under different traffic requirements, we suggest that network operators shall spend more efforts to balance the distributions of traffic demands and network capacities in order to improve the IREE performance, especially when the spatial variations of the traffic distribution are significant.

Figures (11)

• Figure 1: An illustrative example of wireless networks and traffics within area $\mathcal{A}$. The $N_{BS}$ deployed BSs can be regarded as radial basis neurons, which are used to fit any continuous traffic distribution, thereby reducing JS divergence while increasing network capacity.
• Figure 2: An illustration of proposed scheme, where the blue gear is the driving gear and represents the forward and backward propagation through the RBF network to minimize $L_{err}^{(k)}$ and thus achieve better IREE. The green gear is the driven gear and 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: The norm of second-order gradient versus the norm of first-order gradient on the training trajectory of Adam for proposed RBF network. It can be observed that norm of second-order gradient and the norm of first-order gradient nearly satisfy an exponential relationship using one-shot training strategy while they satisfy a piece-wise linear relationship using the proposed two-stage training strategy.
• Figure 4: Comparison of loss function/IREE under different training strategies. The traffic and the network configuration is shown in Tab. \ref{['tab:simu_para']}. The number of samples $M = 1300$, and the number of epoch in each iteration $N_{epoch} = 2000$. It can be observed that under the one-shot training strategy, the VGP caused by the conflict between the gradient of the objective function and the gradient of the constraints will hinder the further convergence of IREE. While the proposed two-stage training strategy avoids the above problems by processing the gradient of the objective function and constraint conditions in two stages respectively.
• Figure 5: Numerical examples for the traffic and the network capacity distributions under $P_{\max} = 20$ dBW. With the powerful approximation ability of the RBF network, the proposed IREE maximization scheme is able to match the traffic with the network capacity and thus avoids potential resource wastage.

Theorems & Definitions (9)

• Definition 1: IREE Metric yu2022novel
• Lemma 1: Optimal Condition
• Theorem 1: Existence of RBF Network
• Theorem 2: Uniqueness of RBF Network
• Lemma 2: Optimal IREE Bound
• Remark 1: General Models
• Claim 1
• Theorem 3: Convergence Properties
• Lemma 3: Optimality IREE Gap of the Proposed Scheme