Performance Limits of Neighbor Discovery in Wireless Networks

Neighbor Discovery (ND) is the procedure employed by wireless devices to establish a first contact. All ND protocols involve devices sending beacons, and also listening for them. Protocols differ in terms of how the beacon transmissions and reception windows are scheduled, and the device sleeps in between consecutive transmissions and reception windows in order to save energy. A successful discovery constitutes a sending device's beacon coinciding with a receiving device's reception window. The goal of all ND protocols is to minimize the discovery latency. In spite of the ubiquity of ND protocols and active research on this topic for over two decades, the basic question "Given a power budget, what is the minimum guaranteed ND latency?", however, has still remained unanswered. This paper is on the best-achievable ND latency for a given power budget between a pair of devices. In order to compute this lower bound, we introduce a concept called coverage maps, that allows us to analyze the ND procedure in a protocol-independent manner. Using it, we derive discovery latencies for different scenarios, e.g., when both devices have the same or different power budgets. We also show that some existing protocols can be parametrized such that they perform optimally. Our results are restricted to the case when a few devices discover each other at a time, as is the case in most real-life scenarios, while scenarios with large numbers of devices need further study.