Network-Layer Performance Analysis of Multihop Fading Channels

Abstract

A fundamental problem for the delay and backlog analysis across multihop 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 paper, 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, 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 the algebra. Using this algebra, we derive the desired delay and backlog bounds. Using arguments from large deviations theory, we show that the bounds are asymptotically tight. An application of the analysis is demonstrated for a multihop network of Rayleigh fading channels with cross traffic at each hop.

Delay Analysis for Wireless Fading Channels with Finite Blocklength Channel Coding

“…The (min,×) network calculus approach developed in [2] was used for transmit power minimization for process automation under delay constraints [10]. However, the service was characterized by the infinite blocklength Shannon capacity model.…”

“…Furthermore, we assume that the transmitter has perfect estimates of the instantaneous SNR γi and adapts the coding rate Ri according to γi. A standard rate model that is often applied in wireless networking research, including in [2], assumes that the achievable rate Ri in bits per (complex-valued) symbol is equal to the Shannon capacity of the channel, and no errors occur:…”

“…(3). as in [2]. The ai data bits that are generated at the source correspond to the arrival process of the queueing system during time slot i.…”

“…In this section, we provide an overview of the results derived in [2], where stochastic network calculus in a transform domain was used to derive an upper bound for the delay. Even for coding at infinite blocklength, the major problem in deriving stochastic performance bounds for fading channels is the nonlinear mapping of SNR to achievable rate as R = log 2 (1 + SNR).…”

“…AlZubaidy et al [2] recently provided a methodology for wireless network performance analysis in fading channels with the Shannon capacity model. By applying stochastic network calculus in a transform domain, they were able to derive probabilistic delay bounds in closed form.…”