CSMA over Time-varying Channels: Optimality, Uniqueness and Limited Backoff Rate

TL;DR

This paper introduces a novel class of channel-aware CSMA algorithms that adapt to time-varying channels, achieving throughput optimality with exponential functions and providing insights into their performance relative to network topology and backoff rates.

Contribution

It proves that exponential functions are necessary for optimal rate regions in channel-aware CSMA and designs throughput-optimal updating rules for arbitrary network topologies.

Findings

Exponential functions are essential for achieving maximum rate regions in A-CSMA.

Designed updating rules achieve throughput optimality in time-varying channels.

Characterized throughput performance when backoff rates are restricted.

Abstract

Recent studies on MAC scheduling have shown that carrier sense multiple access (CSMA) algo- rithms can be throughput optimal for arbitrary wireless network topology. However, these results are highly sensitive to the underlying assumption on 'static' or 'fixed' system conditions. For example, if channel conditions are time-varying, it is unclear how each node can adjust its CSMA parameters, so-called backoff and channel holding times, using its local channel information for the desired high performance. In this paper, we study 'channel-aware' CSMA (A-CSMA) algorithms in time-varying channels, where they adjust their parameters as some function of the current channel capacity. First, we show that the achievable rate region of A-CSMA equals to the maximum rate region if and only if the function is exponential. Furthermore, given an exponential function in A-CSMA, we design updating rules for their parameters, which achieve throughput optimality for an arbitrary wireless network topology. They are the first CSMA algorithms in the literature which are proved to be throughput optimal under time-varying channels. Moreover, we also consider the case when back-off rates of A- CSMA are highly restricted compared to the speed of channel variations, and characterize the throughput performance of A-CSMA in terms of the underlying wireless network topology. Our results not only guide a high-performance design on MAC scheduling under highly time-varying scenarios, but also provide new insights on the performance of CSMA algorithms in relation to their backoff rates and the network topology.