Finite-state Markov modeling of fading channels - a survey of principles and applications <s> HISTORICAL BACKGROUND ON APPLICATIONS OF FSMC MODELS FOR FADING CHANNELS <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> HISTORICAL BACKGROUND ON APPLICATIONS OF FSMC MODELS FOR FADING CHANNELS <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> BIB002 </s> Finite-state Markov modeling of fading channels - a survey of principles and applications <s> HISTORICAL BACKGROUND ON APPLICATIONS OF FSMC MODELS FOR FADING CHANNELS <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> BIB003 </s> Finite-state Markov modeling of fading channels - a survey of principles and applications <s> HISTORICAL BACKGROUND ON APPLICATIONS OF FSMC MODELS FOR FADING CHANNELS <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> BIB004 </s> Finite-state Markov modeling of fading channels - a survey of principles and applications <s> HISTORICAL BACKGROUND ON APPLICATIONS OF FSMC MODELS FOR FADING CHANNELS <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> BIB005 </s> Finite-state Markov modeling of fading channels - a survey of principles and applications <s> HISTORICAL BACKGROUND ON APPLICATIONS OF FSMC MODELS FOR FADING CHANNELS <s> A useful model for general time-varying channels is a finite state Markov chain. In this paper, maximum likelihood sequence estimation (MLSE) for signals over finite state Markov channels (FSMCs) is studied. Also studied is the maximum a posteriori (MAP) channel state estimation. When coded signals with interleaving are transmitted, the channel estimates can be used to make soft-decision decoding. The error performance of the proposed sequence and channel state estimation schemes are evaluated through computer simulations. The effect of channel modeling error is also discussed. <s> BIB006 </s> Finite-state Markov modeling of fading channels - a survey of principles and applications <s> HISTORICAL BACKGROUND ON APPLICATIONS OF FSMC MODELS FOR FADING CHANNELS <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> HISTORICAL BACKGROUND ON APPLICATIONS OF FSMC MODELS FOR FADING CHANNELS <s> This paper addresses the design and performance evaluation with respect to capacity of M-PSK turbo-coded systems operating in frequency-flat time-selective Rayleigh fading. The receiver jointly performs channel estimation and turbo decoding, allowing the two processes to benefit from each other. To this end, we introduce a suitable Markov model with a finite number of states, designed to approximate both the values and the statistical properties of the correlated flat fading channel phase, which poses a more severe challenge to PSK transmission than amplitude hiding. Then, the forward-backward algorithm determines both the maximum a posteriori probability (MAP) value for each symbol in the data sequence and the MAP channel phase in each iteration. Simulations show good performance in standard correlated Rayleigh fading channels. A sequence of progressively tighter upper bounds to the capacity of a simplified Markov-phase channel is derived, and performance of a turbo code with joint iterative channel estimation and decoding is demonstrated to approach these capacity bounds. <s> BIB008 </s> Finite-state Markov modeling of fading channels - a survey of principles and applications <s> HISTORICAL BACKGROUND ON APPLICATIONS OF FSMC MODELS FOR FADING CHANNELS <s> We describe parallel concatenated codes for communication over finite-state binary Markov channels. We present encoder design techniques and decoder processing modifications that utilize the a priori statistics of the channel and show that the resulting codes allow reliable communication at rates which are above the capacity of a memoryless channel with the same stationary bit error probability as the Markov channel. These codes outperform systems based on the traditional approach of using a channel interleaver to create a channel which is assumed to be memoryless. In addition, we introduce a joint estimation/decoding method that allows the estimation of the parameters of the hidden Markov model when they are not known a priori. <s> BIB009 </s> Finite-state Markov modeling of fading channels - a survey of principles and applications <s> HISTORICAL BACKGROUND ON APPLICATIONS OF FSMC MODELS FOR FADING CHANNELS <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> BIB010 </s> Finite-state Markov modeling of fading channels - a survey of principles and applications <s> HISTORICAL BACKGROUND ON APPLICATIONS OF FSMC MODELS FOR FADING CHANNELS <s> We propose a modified algorithm for decoding of low-density parity-check codes over finite-state binary Markov channels. The proposed approach clearly outperforms systems in which the channel statistics are not exploited in the decoding, even when the channel parameters are not known a priori at the decoder. <s> BIB011 </s> Finite-state Markov modeling of fading channels - a survey of principles and applications <s> HISTORICAL BACKGROUND ON APPLICATIONS OF FSMC MODELS FOR FADING CHANNELS <s> Density evolution analysis of low-density parity-check (LDPC) codes in memoryless channels is extended to the Gilbert-Elliott (GE) channel, which is a special case of a large class of channels with hidden Markov memory. In a procedure referred to as estimation decoding, the sum-product algorithm (SPA) is used to perform LDPC decoding jointly with channel-state detection. Density evolution results show (and simulation results confirm) that such decoders provide a significantly enlarged region of successful decoding within the GE parameter space, compared with decoders that do not exploit the channel memory. By considering a variety of ways in which a GE channel may be degraded, it is shown how knowledge of the decoding behavior at a single point of the GE parameter space may be extended to a larger region within the space, thereby mitigating the large complexity needed in using density evolution to explore the parameter space point-by-point. Using the GE channel as a straightforward example, we conclude that analysis of estimation decoding for LDPC codes is feasible in channels with memory, and that such analysis shows large potential gains. <s> BIB012 </s> Finite-state Markov modeling of fading channels - a survey of principles and applications <s> HISTORICAL BACKGROUND ON APPLICATIONS OF FSMC MODELS FOR FADING CHANNELS <s> This paper proposes a novel successive decoding paradigm for fading channels. K independent codewords of different rates and lengths are interleaved at the transmitter according to a pattern, and successively decoded at the receiver. This enables progressively better channel estimates for the receiver, at a minimal cost of pilot symbols. At each decoding stage, channel estimation and decoding are performed separately, or iteratively if the residual channel correlation within a codeword can be exploited. The flexible interleaver pattern, after some level of optimization, achieves near-capacity system performance with only a small number of codewords K, as demonstrated numerically by a finite state Markov modelled flat fading channel. <s> BIB013
Traditionally, FSMCs have been used to model error bursts in fading channels during the design stages of wireless communication systems. This helps system designers analyze and improve performance measures in the physical or media access control layers. Since 1997, FSMC models have enabled closed-form or simulation-based analysis of system-level performance measures, such as packet throughput BIB003 , BIB004 , packet error distribution (PED)  , and packet error rate (PER) BIB007 through bursty wireless channels. The bit error rate (BER) in more sophisticated communications systems that include receiver diversity has been studied using FSMC models in BIB010 and BIB005 . The potential benefits of incorporating FSMC memory into decoding algorithms at the receiver to achieve higher information rates has been known as early as 1989  . Since the late 1990s, an active area of research has been to develop practical decoding techniques at the receiver using FSMC models for fading channels. FSMC models enable implementation of mathematically tractable channel estimation and data decoding algorithms for time-varying fading channels BIB006 , BIB008 . Decoding algorithms for conventional turbo codes and low-density parity-check (LDPC) codes have been modified in BIB009 , BIB011 , and BIB012 , respectively, to take into account FSMC state estimation, and it is shown that information rates higher than the memoryless channel capacity become possible. More recently, successive decoding is proposed for fading channels modeled by FSMCs that takes channel memory into account BIB013 . In a later section on FSMC applications, we will provide a more in-depth categorization of the FSMC applications for fading channels. Since 1995 BIB002 , first-order FSMC models for fading channels have been the models of choice due to their computational simplicity and the ease with which model parameters can be determined. A first-order Markovian assumption in the FSMC model means that given the previous fading channel state, the current state is statistically independent of all other past and future fading channel states. Ever since, the accuracy of first-order FSMC models for fading channels, compared with higher-order FSMC models, has been the subject of research. One main research aim has been to find channel fading rates over which low-order FSMC models are a sufficiently good match with other widely accepted statistical fading models, such as the Clarke's model BIB001 . While it is generally accepted that first-order FSMC models are more accurate for slow fading channels than for medium-rate or fast-fading channels, still today, there is no consensus about exact fading rates over which first-order FSMC models are accurately applicable for fading channels. In a later section on FSMC applications, we will provide a detailed examination of the literature on the accuracy of first-order and higher-order FSMC models for fading channels. This study will take into account the FSMC application and the criterion used for accuracy analysis. A summary of the history of FSMC and its applications is shown in Table 1 .