Distributed Opportunistic Scheduling With Two-Level Probing

Distributed opportunistic scheduling (DOS) is studied for wireless ad-hoc networks in which many links contend for the channel using random access before data transmissions. Simply put, DOS involves a process of joint channel probing and distributed scheduling for ad-hoc (peer-to-peer) communications. Since, in practice, link conditions are estimated with noisy observations, the transmission rate has to be backed off from the estimated rate to avoid transmission outages. Then, a natural question to ask is whether it is worthwhile for the link with successful contention to perform further channel probing to mitigate estimation errors, at the cost of additional probing. Thus motivated, this work investigates DOS with two-level channel probing by optimizing the tradeoff between the throughput gain from more accurate rate estimation and the resulting additional delay. Capitalizing on optimal stopping theory with incomplete information, we show that the optimal scheduling policy is threshold-based and is characterized by either one or two thresholds, depending on network settings. Necessary and sufficient conditions for both cases are rigorously established. In particular, our analysis reveals that performing second-level channel probing is optimal when the first-level estimated channel condition falls in between the two thresholds. Numerical results are provided to illustrate the effectiveness of the proposed DOS with two-level channel probing. We also extend our study to the case with limited feedback, where the feedback from the receiver to its transmitter takes the form of (0,1,e).