Thompson Sampling-Based Channel Selection Through Density Estimation Aided by Stochastic Geometry

Abstract

We propose a sophisticated channel selection scheme based on multi-armed bandits and stochastic geometry analysis. In the proposed scheme, a typical user attempts to estimate the density of active interferers for every channel via the repeated observations of signal-to-interference power ratio (SIR), which demonstrates the randomness induced by randomized interference sources and fading effects. The purpose of this study involves enabling a typical user to identify the channel with the lowest density of active interferers while considering the communication quality during exploration. To resolve the trade-off between obtaining more observations on uncertain channels and using a channel that appears better, we employ a bandit algorithm called Thompson sampling (TS), which is known for its empirical effectiveness. We consider two ideas to enhance TS. First, noticing that the SIR distribution derived through stochastic geometry is useful for updating the posterior distribution of the density, we propose incorporating the SIR distribution into TS to estimate the density of active interferers. Second, TS requires sampling from the posterior distribution of the density for each channel, while it is significantly more complicated for the posterior distribution of the density to generate samples than well-known distribution. The results indicate that this type of sampling process is achieved via the Markov chain Monte Carlo method (MCMC). The simulation results indicate that the proposed method enables a typical user to determine the channel with the lowest density more efficiently than the TS without density estimation aided by stochastic geometry, and $\epsilon $ -greedy strategies.