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.