Finite-state Markov modeling of fading channels - a survey of principles and applications <s> CTP METHOD <s> Fading is modeled by applying context tree pruning (CTP) to the sequence of fading states that results from quantizing a sequence of real-valued fading measurements. There results a family of finite state Markov chains of increasing order that represent the channel with increasing fidelity. A fading state may be the union of chain states. A particular model may be chosen from that family according to an application-specific criterion. The resulting models facilitate analysis and simulation of wireless systems that exploit channel memory. An example criterion compares each model's fading state sojourn time statistics with those of the original sequence. <s> BIB001 </s> Finite-state Markov modeling of fading channels - a survey of principles and applications <s> CTP METHOD <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> BIB002
CTP is the third technique for obtaining higher-order FSMC models for fading channels, proposed in BIB002 and BIB001 . Let us first assume that a sample-by-sample quantization of the fading channel gain sequence of length N is available and the discrete-valued fading channel gain sequence is denoted by u N 1 , The CTP method is an algorithm to estimate the contexts from the training sequence u N 1 and to simplify the full tree by merging contexts. By applying more aggressive thresholds within the CTP state merging strategy, it is possible to generate a hierarchy of CT-based models for the TV-FFC with decreasing levels of complexity (parameter size), but with lower fidelity than the best model at the top of hierarchy. Fidelity can be selected according to the application and is a goodness-of-fit criterion that judges model quality. Therefore, the model designer can choose an appropriate balance between Markov model accuracy and complexity. In BIB002 , a maximum CT depth of M = 7 was imposed when obtaining the context set and it was found that the actual context length for fading channels with f D T s ≥ 0.01 was always strictly less than seven in all constructed models.