This paper considers the problem of fully distributed channel allocation in clustered wireless networks when the propagation medium is random. We extend here the existing Trial and Error (TE) framework developed in the deterministic case and for which strong convergence properties hold. We prove that using directly this solution in the random context leads to unsatisfactory solutions. Then we propose an adaptation of the original Trial and Error Learning (TEL) algorithm, called Robust TEL (RTEL), assuming that the random channel effects translate into a bounded stochastic disturbance of the utility function. The solution consists in introducing thresholds in the transitions of the TEL’s Finite State Controller (FSC). We prove that this new solution restores the good convergence property inherited from the TEL. Furthermore, we provide analysis of the stochastic utilities in the Rayleigh fading case in order to check the bounded assumption. Finally, we develop an online algorithm that dynamically estimates the optimal threshold values to adapt to the instantaneous disturbance. Numerical results corroborate our theoretical claims.

Model-free decentralized optimizations and learning are receiving increasing attention from theoretical and practical perspectives. In particular, two fully decentralized learning algorithms, namely Trial and Error Learning (TEL) and Optimal Dynamical Learning (ODL), are very appealing for a broad class of games. Indeed, ODL has the property to spend a high proportion of time in an optimum state that maximizes the sum of the utilities of all players, whereas, TEL has the property to spend a high proportion of time in an optimum state that maximizes the sum of the utilities of all players if there is a pure Nash equilibrium, otherwise, it spends a high proportion of time in a state that maximizes a trade-off between the sum of the utilities of the players and a predefined stability function. On the other hand, estimating the mean fraction of time spent in the optimum state (as well as the mean time duration to reach it) is challenging due to the high complexity and dimension of the inherent Markov chains. In this article, under some specific system model, an evaluation of the above performance metrics is provided by proposing an approximation of the considered Markov chains, which allows overcoming the problem of high dimensionality. A comparison between the two algorithms is then performed which allows a better understanding of their performance.

This paper considers an orthogonal frequency division multiplexing system where the Effective Exponential SNR Mapping (EESM) is applied. We first present an approximate model in which the subcarriers grouped into one block are assumed to have the same channel coefficient and, subcarriers in different blocks have independent and identically distributed channel coefficients. Then, we present an algorithm based on a goodness of fit test to estimate the number of subcarriers to be grouped into one block. Building on this approximation model, we provide an approach to compute the statistics of the effective SNR obtained from the EESM mapping. This method is based on convolution technique. The approach presented in the paper is then validated through simulations.