Finite-State Markov Modeling of Correlated Rician-Fading Channels

Abstract

Abstract-Stochastic properties of the binary channel that describe the successes and failures of the transmission of a modulated signal over a time-correlated flat-fading channel are considered for investigation. This analysis is employed to develop th-order Markov models for such a burst channel. The order of the Markov model that generates accurate analytical models is estimated for a broad range of fading environments. The parameterization and accuracy of an important class of hidden Markov models, known as the Gilbert-Elliott channel (GEC), are also investigated. Fading rates are identified in which the th-order Markov model and the GEC model approximate the fading channel with similar accuracy. The latter model is useful for approximating slowly fading processes, since it provides a more compact parameterization.

Finite-state Markov modeling of fading channels - a survey of principles and applications

“…In other words, the CP method performs sample-by-sample partitioning of the individual fading channel gain or its components to D regions according to the methods described in the previous section and then inflates the state space to K = D M . Therefore, in the CP method, the number of FSMC states grows exponentially with memory order M. The authors in [18], [19], and [36] have considered constructing Mth-order FSMC models using the CP method. The Linde-Buzo-Gray (LBG) algorithm (see [64, p. 117] for the original LBG reference) is a widely used iterative technique to obtain the codevectors and their associated regions in the VQ method.…”

“…For Rayleigh fading, the pdf f A (a) was given in (2). Other statistical models used for the FSMC modeling of the fading amplitude include Rician [16], [17], [19], [49] and Nakagami m [23], [24]. Having an analytical expression for f A (a) is not necessary for obtaining FSMC steady-state probabilities.…”

“…In the first-order FSMC models considered in the literature (either in the developed theory or in provided numerical examples), the number of considered FSMC states K ranges from 2-4 [13], [20], [21], [27], [28], [38], [47], [50] to 1,000-2,000 [15], [23]. However, the middle range of K = 8 to K = 64 states is more widely used [14], [18], [19], [23], [24], [26], [33], [35]- [37], [59] and is generally accepted to have a better balance between accuracy and model complexity than FSMC models with smaller number of states. The number of input symbols P in the FSMC model is also a factor for the physical layer analysis of fading channels.…”

“…A natural criterion for accuracy would be how the obtained performance measures in the FSMC model compare with those in the reference model for the TV-FFC (such as the Clarke's model or the AR model) or with those obtained through field measurements. Examples, include comparison of packet error rates [15] packet error distribution [17][18][19], BER [23], packet throughput [20], [21], and fade duration [15], [22] in the FSMC and in the reference TV-FFC models. The other criterion is how accurately the FSMC model can reproduce channel statistics.…”

“…The other criterion is how accurately the FSMC model can reproduce channel statistics. Comparison of the ACF in the TV-FFC with that in the FSMC model is the widely accepted statistical measure and has been studied in [15], [17], [19], and [26] in order to verify the FSMC design technique. Other statistical measures include comparison of state transition probabilities between the FSMC model and simulated Clarke's fading model [14], [24], [25], state duration or steady-state probabilities [25], [26].…”