CIF: Small: Stochastic Ordering of Wireless Systems

为各种应用（如数据通信、传感和推理）以低成本部署无线设备、系统和网络已经变得越来越可行。考虑到在随机衰落信道上运行的各种不同目的的复杂无线系统，如何比较这些系统的性能的问题就出现了。系统分析和设计可以受益于统一的方法来比较这些系统。本研究使用随机排序的概念来提供这样一种方法。结果有助于性能分析和无线系统的设计在广泛的随机传播条件。本研究的教育部分包括设计教育软件模块，通过随机顺序使用传感系统的性能比较来说明概率和通信的基本概念。统一的性能指标还可以对在衰落信道上运行的复杂无线系统进行比较。这样就可以根据性能度量的分析性质（如单调性、凸性或完全单调性）对大量系统进行性能比较。当系统组合时，我们可以确定在哪些条件下组成部分的顺序保持系统整体性能的顺序。具体的应用主题包括广义中继网络的随机排序，引入由无线系统的性能指标引起的新的随机顺序，将点过程的随机排序理论应用于无线传感器网络的性能排序，以及具有多个（可能相关的）随机信道系数的系统的随机排序，例如MIMO系统，或在频率选择信道上运行的系统。

It has become increasingly feasible to deploy wireless devices, systems, and networks at low cost for diverse applications such as data communications, sensing, and inference. Given the variety of complex wireless systems with different purposes operating over randomly fading channels, the question of how to compare the performance of these systems arises. System analysis and design can benefit from a unified approach to comparisons of such systems. This research uses the notion of stochastic ordering to provide such an approach. The results aid in performance analysis, and design of wireless systems across a wide range of random propagation conditions. The educational component of this research involves design of educational software modules to illustrate basic concepts in probability and communications using performance comparison of sensing systems through stochastic orders.Unifying performance metrics also enables comparisons of complex wireless systems operating over fading channels. This enables performance comparisons of a vast range of systems on the basis of the analytical properties of the performance metric such as monotonicity, convexity, or complete monotonicity. When systems are combined, we can determine the conditions under which ordering of the constituent parts preserves the ordering of overall system performance. Specific topics of application include stochastic ordering of generalized relay networks, introduction of new stochastic orders induced by performance metrics of wireless systems, applying the theory of stochastic ordering of point processes to order wireless sensor network performance, and stochastic ordering of systems with multiple (possibly correlated) random channel coefficients such as MIMO systems, or systems operating over frequency-selective channels.