Finite-state Markov modeling of fading channels - a survey of principles and applications <s> DESIGN TECHNIQUES AND ACCURACY CRITERIA <s> 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. > <s> BIB001 </s> Finite-state Markov modeling of fading channels - a survey of principles and applications <s> DESIGN TECHNIQUES AND ACCURACY CRITERIA <s> In this paper, we study the correlation properties of the fading mobile radio channel. Based on these studies, we model the channel as a one-step Markov process whose transition probabilities are a function of the channel characteristics. Then we present the throughput performance of the Go-Back-N and selective-repeat automatic repeat request (ARQ) protocols with timer control, using the Markov model for both forward and feedback channels. This approximation is found to be very good, as confirmed by simulation results. <s> BIB002 </s> Finite-state Markov modeling of fading channels - a survey of principles and applications <s> DESIGN TECHNIQUES AND ACCURACY CRITERIA <s> The throughput performance of a wireless media access protocol taking into account the effect of correlated channel fading, capture, and propagation delay is analyzed. For efficient access on the uplink (mobile-to-base-station link), the protocol makes use of the uplink channel status information which is conveyed to the mobiles through a busy/idle flag broadcast on the downlink (base-station-to-mobile link). A first-order Markov model is used to describe the correlation in the packet success/failure process on a Rayleigh-fading channel. The analytical results obtained through the first-order Markov approximation of the channel are compared to those obtained from an independent and identically distributed (i.i.d.) channel model. The Markovian-fading channel model is shown to provide better performance results than the i.i.d. channel model. Simulations show that a first-order Markov approximation of the Rayleigh-fading process is quite accurate. An enhanced version of the access protocol to take advantage of the memory in the fading channel behavior is proposed and analyzed. The effect of retransmission of erroneous data packets and propagation delay on the throughput is also analyzed. It is shown that the access protocol with an error detect (ED) feature is efficient in slow fading (e.g., pedestrian user speeds), whereas a retransmission protocol is more efficient in fast fading (e.g., vehicular user speeds). <s> BIB003 </s> Finite-state Markov modeling of fading channels - a survey of principles and applications <s> DESIGN TECHNIQUES AND ACCURACY CRITERIA <s> Finite-state Markov channel (FSMC) models are useful for analysing radio channels with nonindependent fading, which give rise to bursty channel errors. In the paper the FSMC model is constructed by partitioning the dynamic range of the fade amplitude into finite number of intervals and representing each interval as a ‘state’ in the model. Transitions between these channel states thus characterise the physical fading process. Based on the Nakagami-m distribution, a new analytical formulation for the state transition probability is presented and validated for channels with arbitrary degrees of time-interleaving. The resultant FSMC model is shown to be applicable to a wide range of practical fading channels, including diversity-combined channels and multicarrier channels. <s> BIB004 </s> Finite-state Markov modeling of fading channels - a survey of principles and applications <s> DESIGN TECHNIQUES AND ACCURACY CRITERIA <s> We form a finite-state Markov channel model to represent Rayleigh fading channels. We develop and analyze a methodology to partition the received signal-to-noise ratio (SNR) into a finite number of states according to the time duration of each state. Each state corresponds to a different channel quality indicated by the bit-error rate (BER). The number of states and SNR partitions are determined by the fading speed of the channel. Computer simulations are performed to verify the accuracy of the model. <s> BIB005 </s> Finite-state Markov modeling of fading channels - a survey of principles and applications <s> DESIGN TECHNIQUES AND ACCURACY CRITERIA <s> Previous models for the received signal amplitude of the flat-fading channel that use first-order finite-state Markov chains are examined. The stochastic properties of a proposed first-order model based on these models are examined. The limitations of using an information theoretic metric, which is sometimes used to justify a first-order Markov chain as a sufficient model for very slowly fading channels, are discussed. A simple method of qualitatively comparing autocorrelation functions is instead proposed. The usefulness of the first-order Markov chain in representing the flat-fading channel is examined by looking at two specific problems in wireless system applications that represent two disparate cases. The first case involves analysis over a short duration of time, relative to the inverse of the normalized Doppler frequency, while the second involves analysis over a long duration of time. Contrary to previous reports, the results indicate that first-order Markov chains are not generally suitable for very slowly fading channels. Rather, first-order Markov chains can be suitable for very slowly fading applications, which require analysis over only a short duration of time. <s> BIB006 </s> Finite-state Markov modeling of fading channels - a survey of principles and applications <s> DESIGN TECHNIQUES AND ACCURACY CRITERIA <s> This paper investigates the properties of a method for obtaining Markov models of unspecified order to be applied to narrow-band fading channels with additive white Gaussian noise. The models are obtained by applying the context tree pruning algorithm to experimental or simulated sequences. Fading environments are identified in which the extension from first-order to higher order models is justified. The paper presents, as examples, the evaluation of the covariance function and the packet error distribution. <s> BIB007 </s> Finite-state Markov modeling of fading channels - a survey of principles and applications <s> DESIGN TECHNIQUES AND ACCURACY CRITERIA <s> The performance studies of wireless systems often require a wireless channel model. A common one, for Rayleigh fading environments, is founded upon variations of the finite state Markov channel model (FSMC). This model partitions the received signal to noise ratio (SNR) into a finite number of intervals and represents each interval as a state of a Markov process. Previous studies have elaborated on the accuracy and appropriateness of the model under several assumptions. A key aspect that remains to be studied is the effect of the partitioning scheme. We study the effects of several proposed schemes and investigate the performance of a new scheme that takes into account the average fade duration at various SNR levels. <s> BIB008 </s> Finite-state Markov modeling of fading channels - a survey of principles and applications <s> DESIGN TECHNIQUES AND ACCURACY CRITERIA <s> We designed a multi-channel Nakagami fading simulator by modeling the received combined signal-to-noise ratio as a finite-state Markov chain, following a previously proposed approach. Our model generates directly the error process at the output of a diversity receiver and can emulate selection, maximal-ratio, and equal-gain combining. As the order of diversity increases, the savings in computational complexity improve linearly with respect to a traditional waveform simulator. The level crossing rates of the simulated envelope are shown to be very close to their theoretical values. The simulator's performance is also evaluated in terms of the accuracy of the obtained bit error rates, for both uncoded and coded systems. The simulator speeds up the performance evaluation of high-rate communication links where a high number of samples is needed. <s> BIB009 </s> Finite-state Markov modeling of fading channels - a survey of principles and applications <s> DESIGN TECHNIQUES AND ACCURACY CRITERIA <s> 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 Kth-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 Kth-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. <s> BIB010
Evidently, in order to evaluate and analyze a system performance measure, one needs to first design an FSMC model for the physical TV-FFC under consideration. For modeling channel error bursts, researchers have considered FSMC modeling of the fading channel amplitude a or the received SNR γ . In the literature, it is implicitly or explicitly assumed that channel phase is either estimated prior to coherent demodulation, or modulation and detection are not sensitive to phase distortions. This could be a reasonable assumption in very slow fading conditions with the normalized fading rate f D T s 1. A fundamental issue in the design of FSMC models is how accurate and reliable the resulting system performance measures are. 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 BIB006 packet error distribution BIB007  BIB010 , BER BIB009 , packet throughput BIB002 , BIB003 , and fade duration BIB006 ,  in the FSMC and in the reference TV-FFC models. 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 BIB006 , BIB007 , BIB010 , and BIB008 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 BIB001 , BIB004 , BIB005 , state duration or steady-state probabilities BIB005 , BIB008 . In summary, the authors above have aimed to optimize amplitude region thresholds and/or FSMC memory order in order to reproduce the closest performance measure or channel statistics, compared with the reference model, subject to complexity constraints on the FSMC model. The effect of Markov memory order in the FSMC model is discussed below in more detail.