Medium Access over Time-varying Channels with Limited Sensing Cost

This paper has been withdrawn because of some paper issues. Recent studies on MAC scheduling have shown that carrier sense multiple access (CSMA) can be controlled to be achieve optimality in terms of throughput or utility. These results imply that just a simple MAC algorithm without message passing is possible to achieve high performance guarantee. However, such studies are conducted only on the assumption that channel conditions are static. Noting that the main drive for achieving optimality in optimal CSMA is to let it run a good schedule for some time, formally referred to as the mixing time, it is under-explored how such optimal CSMA performs for time-varying channel conditions. In this paper, under the practical constraint of restricted back-off rates (i.e., limited sensing speed), we consider two versions of CSMAs: (i) channel-unaware CSMA (U-CSMA) and (ii) channel-aware CSMA (A-CSMA), each of which is characterized as its ability of tracking channel conditions. We first show that for fast channel variations, A-CSMA achieves almost zero throughput, implying that incomplete tracking of channel conditions may seriously degrade performance, whereas U-CSMA, accessing the media without explicit consideration of channel conditions, has positive worst-case guarantee in throughput, where the ratio of guarantee depends on network topology. On the other hand, for slow channel variations, we prove that A-CSMA is throughput-optimal for any network topology. Our results provide the precise trade-off between sensing costs and performances of CSMA algorithms, which guides a robust design on MAC scheduling under highly time-varying scenarios.