  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.
