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Wireless systems operating on the unlicensed part of the radio spectrum (e.g. WiFi and their evolutions) must share a (potentially large) number of frequency bands or channels in a decentralized manner. This task is complicated by fading and interference, i.e., the throughput achieved on each link depends on the quality and the level of congestion of the selected channel. In this paper, we propose and analyze decentralized protocols that aim at achieving utility-optimal allocations of spectrum resources. We first address the problem of finding an optimal static channel allocation (a classical channel assignment problem). We illustrate how optimal algorithms based on simple reversible Monte Carlo Markov Chain (MCMC) methods can be designed. We also evaluate the mixing time of these algorithms. We then consider scenarios where scheduling and channel selection algorithms operate at the same time-scale and have to be designed jointly. We formulate the corresponding optimization problem and combine CSMA protocols and MCMC methods to devise optimal decentralized scheduling and channel selection algorithms. The proposed algorithms differ from existing algorithms as they mimic centralized steepest coordinate ascent methods, yielding faster convergence.
Date of Conference: 21-23 March 2012