Distributed Opportunistic Scheduling With Two-Level Probing

Distributed opportunistic scheduling (DOS) is studied for wireless ad hoc networks in which many links contend for a channel using random access before data transmission. 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 must be backed off from the estimated rate in order to avoid transmission outages. Then, a natural question to ask is whether or not 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. By capitalizing on optimal stopping theory with incomplete information, it is shown 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, this 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. This study is also extended to the case with limited feedback, in which the feedback from the receiver to its transmitter takes the form of <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex Notation="TeX">$(0,1,e)$</tex></formula> .