The Throughput and Detectability Tradeoff in a Wireless Ad Hoc Network

In this work, we study the tradeoff between total throughput of a network and the cumulative emitted energy experienced by one or more external nodes that are not members of the network. We formulate the linear program to determine the routing and scheduling that maximizes the fair throughput for uplink and downlink traffic subject to the energy at each external node being below a threshold. Due to the spatial reuse with simultaneous transmitters and the multi-path routing approach, the number of variables in the linear program is exponential in the number of nodes in the network, so we solve this large linear program using an iterative approach known as column generation. We present numerical results in the form of energy heatmaps generated by the optimal schedule for individual network realizations, as well as the average energy heatmap over many Monte Carlo realizations, demonstrating the impact of the external node locations. We also present throughput results as a function of the node distance and the energy threshold for the single external node case. These results characterize the tradeoff between throughput and the distance and sensed energy sensitivity level, which provides a bound with which to compare the performance of practical routing and scheduling algorithms.