A fundamental problem for 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, 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, ×) 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. The network-layer performance analysis seeks to provide estimates on the delays experienced by traffic traversing the elements of a network, as well as the corresponding buffer requirements. For wireless networks, a question of interest is how the stochastic properties of wireless channels impact delay and backlog performance. Wireless channels are characterized by rapid variation of channel quality caused by the mobility and location of communicating devices. This is due to fading, which is the deviation in the attenuation experienced by the transmitted signal when traversing a wireless channel. The term fading channel is used to refer to a channel that experiences such effects. In this paper we explore the network-layer performance of a multi-hop network where each link is represented by a fading channel. We model the wireless network by tandem queues with variable capacity servers, where each server expresses the random capacity of a fading channel. We ignore the impact of coding by assuming that transmission rates over the fading channels are equal to their information-theoretic capacity limit, C, which is expressed as a function of the instantaneous signal-to-noise ratio (SNR) at the receiver, γ, by C(γ) = W log(1 + γ), where W is the channel bandwidth (in Hz). Numerous models are available to describe the gain of fading channels depending on the type of fading (slow or fast), and the environment (e.g., urban or rural). The instantaneous, information-theoretic channel capacity of a fading channel can be represented as the logarithm of γ by (see Chp. 14.2 in [30]) C(γ) = c log g(γ) ,
Paper REF proposes an SNR domain approach to analyze the performance of multihop fading channels.
A Network Calculus Approach for the Analysis of Multi-Hop Fading Channels
ArXiv
ArXiv
Computer Science