A fundamental problem in the delay and backlog analysis across multi-hop paths in wireless networks is how to account for the random properties of the wireless channel. Since the usual statistical models for radio signals in a propagation environment do not lend themselves easily to a description of the available service rate on a wireless link, the performance analysis of wireless networks has resorted to higher-layer abstractions, e.g., using Markov chain models. In this work, we propose a network calculus that can incorporate common statistical models of fading channels and obtain statistical bounds on delay and backlog across multiple nodes. We conduct the analysis in a transfer domain, which we refer to as the SNR domain', where the service process at a link is characterized by the instantaneous signal-to-noise ratio at the receiver. We discover that, in the transfer domain, the network model is governed by a dioid algebra, which we refer to as (min,x)-algebra. Using this algebra we derive the desired delay and backlog bounds. An application of the analysis is demonstrated for a simple multi-hop network with Rayleigh fading channels and for a network with cross traffic.
Queue-based channel (QBC) @cite_22 is an alternative model for fading channels, which models a binary additive noise channel with memory based on a finite queue. Here, a queue with size @math contains the last @math noise symbols, and the noise process is an @math -order Markov chain. The model was found to provide a better approximation to the Rayleigh and Rician slow fading channels compared to the Gilbert-Elliot model @cite_18 . An extension of the QBC model, called Weighted QBC @cite_18 permit queue cells (i.e., channel samples) to contribute with different weights to the noise process.
@cite_18 @cite_22
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A new channel model for binary additive noise communication channel with memory, called weighted queue-based channel (WQBC), is introduced. The proposed WQBC generalizes the conventional queue-based channel (QBC) such that each queue cell has a different contribution to the noise process, i.e. the queue cells are selected with different probabilities. Suitably selecting the modeling function, the generalization introduced by the WQBC does not increase the number of modelling parameters required compared to the QBC. The statistical and information-theoretical properties of the new model are derived. The WQBC and the QBC are compared in terms of capacity and the accuracy in modeling a family of hard decision frequency-shift keying demodulated correlated Rayleigh and Rician fading channels. It is observed that the WQBC requires a much smaller Markovian memory than the QBC to achieve the same capacity, and provides a very good approximation of the fading channels as the QBC for a wide range of channel conditions. A model for a binary additive noise communication channel with memory is introduced. The channel noise process, which is generated according to a ball sampling mechanism involving a queue of finite length M, is a stationary ergodic Mth-order Markov source. The channel properties are analyzed and several of its statistical and information-theoretical quantities (e.g., block transition distribution, autocorrelation function (ACF), capacity, and error exponent) are derived in either closed or easily computable form in terms of its four parameters. The capacity of the queue-based channel (QBC) is also analytically and numerically compared for a variety of channel conditions with the capacity of other binary models, such as the well-known Gilbert-Elliott channel (GEC), the Fritchman channel, and the finite-memory contagion channel. We also investigate the modeling of the traditional GEC using this QBC model. The QBC parameters are estimated by minimizing the Kullback-Leibler divergence rate between the probability of noise sequences generated by the GEC and the QBC, while maintaining identical bit-error rates (BER) and correlation coefficients. The accuracy of fitting the GEC via the QBC is evaluated in terms of ACF, channel capacity, and error exponent. Numerical results indicate that the QBC provides a good approximation of the GEC for various channel conditions; it thus offers an interesting alternative to the GEC while remaining mathematically tractable.