This paper studies optimal linear power control for battery-limited energy harvesting communications. It provides a systematic analysis of linear power control policies, covering the greedy and fixed-fraction policies as special cases. Three optimality notions are introduced: the maximin optimal linear policy for a given battery capacity and mean-to-capacity ratio (MCR), and two capacity-agnostic policies that minimize the nominal additive gap and maximize the nominal multiplicative factor, respectively. Except the capacity-agnostic additive-gap optimal linear policy, which coincides with the fixed-fraction policy, the other two optimal linear policies are novel and constitute the main contributions of this paper. It is shown, among others, that the worst nominal multiplicative factor for both novel policies is approximately 0.6530, a substantial improvement over the fixed-fraction policy's value of 0.5. Simulations show that under quasi-static fading, the maximin optimal linear policy performs comparable to the maximin optimal policy (the top-performing policy), while the capacity-agnostic multiplicative-factor optimal linear policy performs slightly worse; nevertheless, both novel policies significantly outperform the fixed-fraction policy in the low-to-medium signal-to-noise ratio (SNR) regime. Moreover, this paper also investigates the optimality of the greedy policy for certain families of energy-arrival distributions, and establishes the tightest semi-universal bounds on the battery-capacity threshold for greedy optimality.

翻译：本文研究电池受限的能量收集通信中的最优线性功率控制问题。文章对线性功率控制策略进行了系统性分析，其中贪婪策略和固定比例策略作为特例被涵盖。文中引入了三种最优性概念：针对给定电池容量和均值容量比（MCR）的最大最小最优线性策略，以及两种容量无关策略——分别最小化名义加性间隙和最大化名义乘性因子。除与固定比例策略重合的容量无关加性间隙最优线性策略外，其余两种最优线性策略均为本文首次提出，构成了主要贡献。研究结果表明，两种新策略的最差名义乘性因子均约为0.6530，较固定比例策略的0.5值有显著提升。仿真显示在准静态衰落信道下，最大最小最优线性策略的性能与最优策略（性能最佳策略）相当，而容量无关乘性因子最优线性策略性能稍逊；但两种新策略在低至中等信噪比（SNR）区间均显著优于固定比例策略。此外，本文还针对特定能量到达分布族研究了贪婪策略的最优性，并建立了贪婪最优性所需电池容量阈值的紧致半普适界。