In this work, we study the optimal configuration of the physical layer in wireless networks by means of Semi-Markov Decision Process (SMDP) modeling. In particular, assume the physical layer is characterized by a set of potential operating points, with each point corresponding to a rate and reliability pair; for example, these pairs might be obtained through a now-standard diversity-multiplexing tradeoff characterization. Given the current network state (e.g., buffer occupancies), a Decision Maker (DM) needs to dynamically decide which operating point to use. The SMDP problem formulation allows us to choose from these points. A solution to the SMDP problem is an optimal selection of operating points, which is expressed by a decision rule as a function of the number of packets in the source’s finite queue, the channel state, and the size of the packet to be transmitted. We derive a general solution to the SMDP which covers various model configurations, packet size distributions and channel dynamics. For the specific case of exponential transmission times, we analytically prove the optimal policy has a threshold structure. Numerical results validate this finding, as well as depict muti-threshold policies for time varying channels such as the Gilbert-Elliott channel.

中文翻译：

---

无线网络中的最佳PHY配置

在这项工作中，我们通过半马尔可夫决策过程（SMDP）建模研究无线网络中物理层的最佳配置。特别是，假设物理层的特征在于一组潜在的工作点，每个点对应一个速率和可靠性对；例如，可以通过现在标准的分集复用权衡表征获得这些对。给定当前网络状态（例如，缓冲区占用），决策者（DM）需要动态地决定使用哪个操作点。SMDP问题的表述使我们可以从这些观点中进行选择。SMDP问题的一种解决方案是对工作点进行最佳选择，这由决策规则表示，取决于源有限队列中的数据包数量，信道状态，以及要传输的数据包的大小。我们得出了SMDP的通用解决方案，其中涵盖了各种模型配置，数据包大小分布和信道动态。对于指数传输时间的特定情况，我们分析证明了最优策略具有阈值结构。数值结果证实了这一发现，并描述了时变通道（如吉尔伯特-艾略特通道）的多阈值策略。