Finite-state Markov modeling of fading channels - a survey of principles and applications <s> EARLY WORKS <s> The statistical characteristics of the fields and signals in the reception of radio frequencies by a moving vehicle are deduced from a scattering propagation model. The model assumes that the field incident on the receiver antenna is composed of randomly phased azimuthal plane waves of arbitrary azimuth angles. Amplitude and phase distributions and spatial correlations of fields and signals are deduced, and a simple direct relationship is established between the signal amplitude spectrum and the product of the incident plane waves' angular distribution and the azimuthal antenna gain. The coherence of two mobile-radio signals of different frequencies is shown to depend on the statistical distribution of the relative time delays in the arrival of the component waves, and the coherent bandwidth is shown to be the inverse of the spread in time delays. Wherever possible theoretical predictions are compared with the experimental results. There is sufficient agreement to indicate the validity of the approach. Agreement improves if allowance is made for the nonstationary character of mobile-radio signals. <s> BIB001 </s> Finite-state Markov modeling of fading channels - a survey of principles and applications <s> EARLY WORKS <s> This tutorial provides an overview of the basic theory of hidden Markov models (HMMs) as originated by L.E. Baum and T. Petrie (1966) and gives practical details on methods of implementation of the theory along with a description of selected applications of the theory to distinct problems in speech recognition. Results from a number of original sources are combined to provide a single source of acquiring the background required to pursue further this area of research. The author first reviews the theory of discrete Markov chains and shows how the concept of hidden states, where the observation is a probabilistic function of the state, can be used effectively. The theory is illustrated with two simple examples, namely coin-tossing, and the classic balls-in-urns system. Three fundamental problems of HMMs are noted and several practical techniques for solving these problems are given. The various types of HMMs that have been studied, including ergodic as well as left-right models, are described. > <s> BIB002 </s> Finite-state Markov modeling of fading channels - a survey of principles and applications <s> EARLY WORKS <s> A statistical characterization of transmission errors for digital mobile radio links at 910 MHz in different types of urban areas is presented. Error sequences for messages of 2-s duration at a nominal rate of 20-kb/s for binary-phase-shift-keying (BPSK) demodulated transmissions have been obtained and characterized by Fritchman's channel model, including one error state and two to four error-free states. In the data analyzed, no trend has been observed in the Fritchman parameter as a function of the type of area or of vehicle speed. Typical Fritchman's parameters are established for low and intermediate error rate channels (on the order of 10/sup -3/ and 10/sup -2/ error rates) and for higher error rate channels. Results are also presented for a limited sample of quadrature-phase-shift-keying (QPSK) demodulated 40-kb/s transmissions. > <s> BIB003 </s> Finite-state Markov modeling of fading channels - a survey of principles and applications <s> EARLY WORKS <s> An adaptive coding scheme for digital communication over time-varying channels is presented. The scheme is based on a finite-state Markov channel model. Emphasis is on the adaptation of the error protection to the actual channel state. The throughput gains that are achieved by the adaptive scheme relative to the conventional nonadaptive coding methods are demonstrated by several examples. Of special interest is the use of punctured convolutional codes with maximum-likelihood Viterbi algorithm to enable adaptive encoding and decoding without modifying the basic structure of the encoder and the decoder. > <s> BIB004 </s> Finite-state Markov modeling of fading channels - a survey of principles and applications <s> EARLY WORKS <s> A hidden Markov model for burst errors is specified by a probability transition matrix P, an initial probability vector p, and the state dependent probability of error matrix B. Several procedures are available for estimating P, p and B from a given error (observation) sequence. However, even with some restrictions on the structure of the underlying Markov models, the estimation procedures are computationally intensive particularly when the observation sequence contains long strings of identical symbols. We show that, under some mild assumptions, a Markov model with an arbitrary transition matrix P is equivalent to a Markov model with a unique "block diagonal" transition matrix /spl Lambda/. We also present a computationally very efficient algorithm for estimating /spl Lambda/ from a set of observation using a modified Baum-Welch (1972) algorithm. > <s> BIB005 </s> Finite-state Markov modeling of fading channels - a survey of principles and applications <s> EARLY WORKS <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> BIB006 </s> Finite-state Markov modeling of fading channels - a survey of principles and applications <s> EARLY WORKS <s> The finite-state Markov channel (FSMC) is a discrete time-varying channel whose variation is determined by a finite-state Markov process. These channels have memory due to the Markov channel variation. We obtain the FSMC capacity as a function of the conditional channel state probability. We also show that for i.i.d. channel inputs, this conditional probability converges weakly, and the channel's mutual information is then a closed-form continuous function of the input distribution. We next consider coding for FSMCs. In general, the complexity of maximum-likelihood decoding grows exponentially with the channel memory length. Therefore, in practice, interleaving and memoryless channel codes are used. This technique results in some performance loss relative to the inherent capacity of channels with memory. We propose a maximum-likelihood decision-feedback decoder with complexity that is independent of the channel memory. We calculate the capacity and cutoff rate of our technique, and show that it preserves the capacity of certain FSMCs. We also compare the performance of the decision-feedback decoder with that of interleaving and memoryless channel coding on a fading channel with 4PSK modulation. <s> BIB007
In 1991, Semmar et al. BIB003 used the Fritchman model  with a single error state and two to four error-free states to characterize error sequences in ultrahigh frequency (UHF) digital mobile radio channels at 910 MHz. In their work, the Fritchman model was fitted to measured data by determining suitable values for transition probabilities between channel states. In 1991, Vucetic BIB004 used a finite-state model for adaptive coding over time-varying radio channels. In BIB004 , each state represented a Rician fading channel with different Rician factors. In BIB005 , Sivaprakasam and Shanmugan developed a modified BaumWelch algorithm BIB002 to estimate the parameters of a hidden Markov model (HMM) based on the observation of actual error burst sequences in fading channels. It was the work by Wang and Moayeri in 1995 BIB006 that is widely viewed to have revived FSMC modeling of fading channels in mobile radio communications. One of the novelties of their work was to explicitly establish the link between the statistical Clarke's model for fading channels BIB001 and the FSMC states. In particular, each FSMC state in their model represented a range of received signal-to-noise ratio (SNR), which in turn determined the error probability in that state. Based on this assumption, Wang and Moayeri provided analytical expressions for states, state transition probabilities, and error probabilities in each state. The original FSMC modeling of fading channels as proposed in BIB006 or its variations are still widely used in the literature. Almost concurrently with Wang and Moayeri, Goldsmith and Varaiya proposed a new iterative method for computing the information rates and capacity of data-independent FSMC models with independent and identically distributed (i.i.d) inputs. They also introduced a maximum-likelihood (ML) decisionfeedback decoding technique for the receiver that took the inherent channel memory into account BIB007 . Their work was a generalization of an earlier study by Mushkin and Bar-David in  on the capacity and coding for the GEC.