The Metaverse, an emerging digital space, is expected to offer various services mirroring the real world. Wireless communications for mobile Metaverse users should be tailored to meet the following user characteristics: 1) emphasizing application-specific perceptual utility instead of simply the transmission rate, 2) concerned with energy efficiency due to the limited device battery and energy intensiveness of some applications, and 3) caring about security as the applications may involve sensitive personal data. To this end, this paper incorporates application-specific utility, energy efficiency, and physical-layer security (PLS) into the studied optimization in a wireless network for the Metaverse. Specifically, after introducing utility-energy efficiency (UEE) to represent each Metaverse user's application-specific objective under PLS, we formulate an optimization to maximize the network's weighted sum-UEE by deciding users' transmission powers and communication bandwidths. The formulated problem belongs to the sum-of-ratios optimization, for which prior studies have demonstrated its difficulty. Nevertheless, our proposed algorithm 1) obtains the global optimum for the weighted sum-UEE optimization, via a transform to parametric convex optimization problems, 2) applies to any utility function which is concave, increasing, and twice differentiable, and 3) achieves a linear time complexity in the number of users (the optimal complexity in the order sense). Simulations confirm the superiority of our algorithm over other approaches. We explain that our technique for solving the sum-of-ratios optimization is applicable to other optimization problems in wireless networks and mobile computing.

翻译：元宇宙作为一种新兴数字空间，有望提供与现实世界镜像的多样化服务。面向移动元宇宙用户的无线通信需适配以下用户特征：1）强调特定应用场景的感知效用而非单纯传输速率；2）受限于设备电池容量及部分应用的高能耗特性，需关注能效优化；3）由于应用可能涉及敏感个人数据，需保障安全性。为此，本文将应用特定效用、能效及物理层安全（PLS）共同纳入元宇宙无线网络的优化研究。具体而言，在引入效用-能效（UEE）作为PLS约束下各元宇宙用户应用层优化指标后，我们通过决策用户传输功率与通信带宽构建了最大化网络加权总UEE的优化问题。该问题属于比值和优化范畴，已有研究证实其求解难度。然而，本文提出的算法：1）通过参数化凸优化变换实现加权总UEE优化的全局最优解；2）适用于任意凹性、单调递增且二阶可微的效用函数；3）在用户规模上达到线性时间复杂度（阶次最优复杂度）。仿真实验验证了本算法相较于其他方法的优越性。我们进一步阐明，所提出的比值和优化求解技术可推广至无线网络与移动计算领域的其他优化问题。