ArgMax and ArgMin: transitional probabilistic models in cognitive radio mesh networks

The erratic nature of spectrum availability and diversity imposes the use of a probabilistic framework for channel selection in cognitive radio networks protocol design. In this work, two probability distributions called ArgMax and ArgMin are proposed, which have broad applications in channel selection mechanisms, routing, and media access control protocols. The ArgMax probability distribution locates the maximum random variable among a set of random variables, while the ArgMin locates the minimum random variable. We show that the ArgMax probability distribution is a better candidate than the frequently used odds-on-mean probability distribution through theoretical analysis and simulation. The ArgMin probability distribution has a variety of applications and is shown to be useful in achieving a lower bound on the network's minimum spectral capacity. In simulation, we develop a probabilistic selection routing procedure (PSRP) that adopts the ArgMax probability distribution to guide packets throughout the network. The stochastic framework of probabilistic selection routing procedure is also an appropriate skeleton for building stochastic-based routing protocols for dynamic networks such as cognitive radio networks. The simulation results suggest that ArgMax enables the routing scheme to adapt to the network dynamic more quickly and to more accurately locate the best candidate to route to than the odds-on-mean probability distribution. The ArgMax enhances the network throughput and end-to-end delay by over 30% when network load increases. Copyright (c) 2013 John Wiley & Sons, Ltd.