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.
Analytical approaches for network-layer performance analysis of wireless networks include queueing theory, effective bandwidth and, more recently, network calculus. Since the service processes corresponding to the channel capacity of common fading channel models such as Rician, Rayleigh, or Nakagami- @math , require to take a logarithm of their distributions, researchers often turn to higher-layer abstractions to model fading channels, which lend themselves more easily to an analysis. A widely used abstraction is the two-state channel model developed by Gilbert @cite_29 and Elliott @cite_28 , and subsequent extensions to a finite-state Markov channel (FSMC) @cite_33 . Markov channel models are well suited to express the time correlation of fading channel samples. We refer to @cite_3 for a survey of the development and applications of FSMC models. @cite_37 evaluated the accuracy of first-order Markov channel models of fading channels, where the next channel sample depends only on the current state of the Markov process, and higher order processes that can capture memory extending further back in the process history. The authors found that a first-order Markov model is a good approximation of the fading channel, and that using higher order Markov processes does not significantly improve the accuracy of the model.
@cite_37 @cite_33 @cite_28 @cite_29 @cite_3
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The authors first study the behavior of a finite-state channel where a binary symmetric channel is associated with each state and Markov transitions between states are assumed. Such a channel is referred to as a finite-state Markov channel (FSMC). By partitioning the range of the received signal-to-noise ratio into a finite number of intervals, FSMC models can be constructed for Rayleigh fading channels. A theoretical approach is conducted to show the usefulness of FSMCs compared to that of two-state Gilbert-Elliott channels. The crossover probabilities of the binary symmetric channels associated with its states are calculated. The authors use the second-order statistics of the received SNR to approximate the Markov transition probabilities. The validity and accuracy of the model are confirmed by the state equilibrium equations and computer simulation. > In this paper, we develop a method for analyzing time-varying wireless channels in the context of the modern theory of the stochastic network calculus. In particular, our technique is applicable to channels that can be modeled as Markov chains, which is the case of channels subject to Rayleigh fading. Our approach relies on theoretical results on the convergence time of reversible Markov processes and is applicable to chains with an arbitrary number of states. We provide two expressions for the delay tail distribution of traffic transmitted over a fading channel fed by a Markov source. The first expression is tighter and only requires a simple numerical minimization, the second expression is looser, but is in closed form. The multipath-rich wireless environment associated with typical wireless usage scenarios is characterized by a fading channel response that is time-varying, location-sensitive, and uniquely shared by a given transmitter-receiver pair. The complexity associated with a richly scattering environment implies that the short-term fading process is inherently hard to predict and best modeled stochastically, with rapid decorrelation properties in space, time, and frequency. In this paper, we demonstrate how the channel state between a wireless transmitter and receiver can be used as the basis for building practical secret key generation protocols between two entities. We begin by presenting a scheme based on level crossings of the fading process, which is well-suited for the Rayleigh and Rician fading models associated with a richly scattering environment. Our level crossing algorithm is simple, and incorporates a self-authenticating mechanism to prevent adversarial manipulation of message exchanges during the protocol. Since the level crossing algorithm is best suited for fading processes that exhibit symmetry in their underlying distribution, we present a second and more powerful approach that is suited for more general channel state distributions. This second approach is motivated by observations from quantizing jointly Gaussian processes, but exploits empirical measurements to set quantization boundaries and a heuristic log likelihood ratio estimate to achieve an improved secret key generation rate. We validate both proposed protocols through experimentations using a customized 802.11a platform, and show for the typical WiFi channel that reliable secret key establishment can be accomplished at rates on the order of 10 b s. In this paper, we introduce an analytical framework to compute the average rate of downlink heterogeneous cellular networks. The framework leverages recent application of stochastic geometry to other-cell interference modeling and analysis. The heterogeneous cellular network is modeled as the superposition of many tiers of Base Stations (BSs) having different transmit power, density, path-loss exponent, fading parameters and distribution, and unequal biasing for flexible tier association. A long-term averaged maximum biased-received-power tier association is considered. The positions of the BSs in each tier are modeled as points of an independent Poisson Point Process (PPP). Under these assumptions, we introduce a new analytical methodology to evaluate the average rate, which avoids the computation of the Coverage Probability (Pcov) and needs only the Moment Generating Function (MGF) of the aggregate interference at the probe mobile terminal. The distinguishable characteristic of our analytical methodology consists in providing a tractable and numerically efficient framework that is applicable to general fading distributions, including composite fading channels with small- and mid-scale fluctuations. In addition, our method can efficiently handle correlated Log-Normal shadowing with little increase of the computational complexity. The proposed MGF-based approach needs the computation of either a single or a two-fold numerical integral, thus reducing the complexity of Pcov-based frameworks, which require, for general fading distributions, the computation of a four-fold integral.