A Physical-Layer Scheduling Approach in Large-Scale Cooperative Networks

In a sensor, mesh, or ad hoc network, different transmissions take place between multiple source-destination pairs, which is referred to as <italic>data flows</italic>. In this paper, each data flow is associated with a certain duty cycle schedule to avoid collisions of multiple flows in an energy-efficient manner. Cooperative routes in the network are assumed to be linear and strip-shaped, where each hop or a level contains multiple nodes, and the distance between the nodes is kept constant. We assume all nodes in a cooperative route, which corresponds to one source-destination pair, follow the same duty cycle schedule, while schedules of different routes are orthogonal in time to avoid interference between routes. Therefore, when a new route is formed, it is important to select a duty cycle schedule that is not already in use by the nodes participating in the new route. As part of route set-up, an orthogonal frequency division multiplexing packet travels from the source to the destination, identifying the schedules in use by the nodes along the path. Our objective in this paper is to analyze the probabilities of detection for this method of detecting schedules, which is useful to gain insights into duty cycling-based medium access protocol design in the presence of multiple data flows. To this end, the successive transmissions in a linear network are modeled using an irreducible discrete time Markov chain. Also, three different approaches to detect a certain schedule are investigated, which are distinguished by the binary integration process with multiple sub-carriers corresponding to the schedule. We derive the probability transition matrix for the Markov chain based on different distributions of the received signal energy, the left eigenvector of which yields the probability of detection.