Finite-state Markov modeling of fading channels - a survey of principles and applications <s> APPLICATION THREE: THE MISMATCHED DECODING SETUP <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> BIB001 </s> Finite-state Markov modeling of fading channels - a survey of principles and applications <s> APPLICATION THREE: THE MISMATCHED DECODING SETUP <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> BIB002 </s> Finite-state Markov modeling of fading channels - a survey of principles and applications <s> APPLICATION THREE: THE MISMATCHED DECODING SETUP <s> The problem researched is the comparison of different finite-state Markov channel (FSMC) models used to approximate the Rayleigh fading channel. The criterion used to compare the Markov models is the error performance of receivers based on the FSMC, where the sufficient statistics are obtained from the Jakes-Clarke (1974) fading channel. The FSMC receivers perform joint maximum a posteriori (MAP) sequence detection and channel estimation using the Viterbi algorithm. Receiver outputs of bit decision and channel estimation error are used as the measure of comparison between various models and a well-developed reference receiver. For this research 1/sup st/ and 2/sup nd/ order models were implemented. Simulation results suggest that there can be a significant improvement in receiver performance when the receiver is based on a 2/sup nd/ order model over a 1/sup st/ order model. Likewise, an improvement in performance is observed when the number of Markov states is increased. <s> BIB003 </s> Finite-state Markov modeling of fading channels - a survey of principles and applications <s> APPLICATION THREE: THE MISMATCHED DECODING SETUP <s> In this paper we compare two different methods for receiver training in flat fading channels. The first method is the traditional way in which periodic training sequences are sent to the receiver (explicit training). In the second method, recently proposed, the information source emits bits with unequal probabilities of being '0' and '1'. This method is called implicit training, since the training is implied in the non-symmetrical source structure. BPSK signaling is used as the simplest example of constant-envelope phase modulations. We map the phase component of the flat fading channel response to a simple two-state Markov model. Then joint iterative trellis-based maximum a posteriori probability (MAP) method is used for channel state estimation and decoding. The results of computer simulations for the receiver bit error rate (BER) performance in various channel fading rates and information rates are presented. The results indicate superior performance of implicit training. In slow fading conditions, the gain is 4 dB at information rate of 0.15 bits/channel use and 1.2 dB for information rate of 0.25 bits/channel use. <s> BIB004 </s> Finite-state Markov modeling of fading channels - a survey of principles and applications <s> APPLICATION THREE: THE MISMATCHED DECODING SETUP <s> We study the effect of training method on the receiver bit error rate (BER) performance in constant envelope phase modulation schemes that are transmitted through flat fading channels. Here we propose a novel method for receiver training by sending information bits with unbalanced probabilities. We call this method implicit training and compare it with traditional (explicit) training scheme in which known periodic training sequences are sent to the receiver. The simulation results show superior performance of implicit training where the gain is 2 dB at information rate of 0.15 bits/channel use. <s> BIB005 </s> Finite-state Markov modeling of fading channels - a survey of principles and applications <s> APPLICATION THREE: THE MISMATCHED DECODING SETUP <s> The mismatch capacity of a channel is the highest rate at which reliable communication is possible over the channel with a given (possibly suboptimal) decoding rule. This quantity has been studied extensively for single-letter decoding rules over discrete memoryless channels (DMCs). Here we extend the study to memoryless channels with general alphabets and to channels with memory with possibly non-single-letter decoding rules. We also study the wide-band limit, and, in particular, the mismatch capacity per unit cost, and the achievable rates on an additive-noise spread-spectrum system with single-letter decoding and binary signaling. <s> BIB006 </s> Finite-state Markov modeling of fading channels - a survey of principles and applications <s> APPLICATION THREE: THE MISMATCHED DECODING SETUP <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> BIB007 </s> Finite-state Markov modeling of fading channels - a survey of principles and applications <s> APPLICATION THREE: THE MISMATCHED DECODING SETUP <s> In this paper, we consider an information-theoretic measure for the selection of effective memory order in time-varying flat-fading (FF) channels in the Jakes-Clarke’s model. The measure is based on how many past realisations of the fading channel actively contribute to an achievable information rate lower bound through the channel. The lower bound signifies the achievable information rate when the receiver is equipped with a sup-optimal mismatched decoding rule, which would have only been optimal for a finite-state Markov channel (FSMC) with a finite memory order. The sensitivity of the mismatched decoding rule to memory order is used to find the optimum channel memory order for decoding at the receiver side, with a negligible information rate loss. Our case study shows that the FF channel has an effective information-theoretic memory order of M = 1 for the normalised fading rates fDT . 0.01, where fD is the Doppler spread and T is symbol period. For faster fading rates, the use of first-order models at the receiver incurs a non-negligible information rate loss. The results are, generally, in accordance with our previous findings. <s> BIB008
The analysis in application two focused on optimized decoding as if the actual transmission had taken place through the FSMC model with disregard for its physical accuracy. Whereas, the decoding performance analysis in the third application assumes that the actual communication takes place over a physical communication channel, such as the TV-FFC, and it is only the decoding at the receiver that is based on a simplified and mismatched FSMC model. Mismatched FSMC-based decoding can be advantageous due to its mathematical tractability and promising FSMC-based decoding techniques that were described in the previous subsection. However, it should be noted that due to the mismatch between the channel and the decoder there is an immediate decrease in the achievable information rate BIB006 , even if the FSMC-based decoding were optimal for the FSMC model. Making the distinction between application two and three in the literature is not always easy. Although BIB007 have considered the FSMC modeling of underlying TV-FFC, whether the numerical BER results are provided by passing the transmitted data through the TV-FFC or through the obtained FSMC model is unknown to the authors of this article. Therefore, BIB007 has been classified in application two. Research work in the mismatched FSMC-based decoding setup for the TV-FFC includes BIB001 - BIB004 . Joint MAP sequence detection and channel state estimation are proposed or used in BIB001 , BIB003 , and BIB005 . Joint iterative channel state estimation and decoding using the BCJR algorithm are proposed or used in BIB002 , BIB004 , which is based on supertrellis or separate trellises of the turbo code and the FSMC model. In this application, the main design and performance criterion is not how the FSMC model can reproduce the statistical aspects of the real TV-FFC, but rather, the design criterion is the ability of the FSMC-based receiver to decode well and reliably in spite of receiver mismatch and the ability to minimize the gap between the information rates that are achievable. In BIB003 , the authors compared the BER performance of two receivers based on the first-and second-order Markov models, using joint MAP sequence detection and channel state estimation BIB001 . The actual communication channel was assumed to be a TV-FFC according to the Clarke's model. Interestingly, for a fixed number of channel states in two models, the BER performance of the first-order Markov receiver outperforms that of the second-order Markov receiver (even when a VQ method is used to obtain the second-order FSMC model). As a result, it is concluded in BIB003 that first-order FSMC models are adequate for decoding purposes and provide a good tradeoff between decoding complexity and error rate performance. From an information theoretic viewpoint, the lower bound on the achievable mismatched information rates BIB006 for first-order and second-order FSMC-based receivers were compared in BIB008 . It was concluded that first-order FSMC-based mismatched ML decoding incurs little information rate loss for normalized fading rates f D T s 0.01, whereas for the faster fading rate of f D T s 0.1, the use of second-order FSMC models is beneficial to achieve higher information rates.