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 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 optimization problem, 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 envision that our technique for solving the challenging sum-of-ratios optimization can be applied to other optimization problems in wireless networks and mobile computing.

翻译：元宇宙作为一个新兴数字空间，有望提供与现实世界镜像的各类服务。面向移动元宇宙用户的无线通信需针对以下用户特征进行定制：1）强调应用特定效用而非单纯传输速率，2）因设备电池容量有限且部分应用能耗密集而关注能效，3）由于应用可能涉及敏感个人数据而重视安全性。为此，本文在面向元宇宙的无线网络优化中整合了应用特定效用、能效与物理层安全（PLS）三个维度。具体而言，在引入效用能效（UEE）表征各元宇宙用户在PLS下的应用特定目标后，我们构建了通过决策用户传输功率与通信带宽来最大化网络加权UEE和的优化问题。该问题属于和式比优化范畴，现有研究已证明其求解难度。尽管如此，本文提出的算法：1）通过转化为参数凸优化问题获得原优化问题的全局最优解，2）适用于所有凹函数、单调递增且二阶可微的效用函数，3）在用户数量上实现线性时间复杂度（渐进最优复杂度）。仿真实验验证了本算法相较其他方法的优越性。我们预期，所提出的和式比优化求解技术可推广应用于无线网络与移动计算领域的其他优化问题。