CIF: Small: Stochastic Ordering of Wireless Systems

以低成本部署无线设备、系统和网络以用于诸如数据通信、感测和推理的各种应用已经变得越来越可行。由于各种复杂的无线系统具有不同的目的，在随机衰落信道上工作，如何比较这些系统的性能的问题出现。系统分析和设计可以受益于一个统一的方法来比较这样的系统。本研究使用随机排序的概念来提供这样一种方法。结果有助于在性能分析和设计的无线系统在广泛的随机传播条件。本研究的教育部分涉及教育软件模块的设计，以说明概率和通信的基本概念，通过随机orders.Unifying性能指标的传感系统的性能比较也使复杂的无线系统在衰落信道上运行的比较。这使得性能比较的基础上的分析性能指标，如单调性，凸性，或完全单调性的系统范围广泛。当系统被组合时，我们可以确定组成部分的排序保持整个系统性能的排序的条件。具体的应用主题包括广义中继网络的随机排序，引入无线系统的性能指标引起的新的随机订单，应用点过程的随机排序的理论来订购无线传感器网络的性能，和随机排序的系统与多个（可能相关的）随机信道系数，如MIMO系统，或系统在频率选择性信道上操作。

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.