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Together with the fundamentals of probability, random processes and statistical analysis, this insightful book also presents a broad range of advanced topics and applications. There is extensive coverage of Bayesian vs. frequentist statistics, time series and spectral representation, inequalities, bound and approximation, maximum-likelihood estimation and the expectation-maximization (EM) algorithm, geometric Brownian motion and Itô process. Applications such as hidden Markov models (HMM), the Viterbi, BCJR, and Baum–Welch algorithms, algorithms for machine learning, Wiener and Kalman filters, and queueing and loss networks are treated in detail. The book will be useful to students and researchers in such areas as communications, signal processing, networks, machine learning, bioinformatics, econometrics and mathematical finance. With a solutions manual, lecture slides, supplementary materials and MATLAB programs all available online, it is ideal for classroom teaching as well as a valuable reference for professionals.

Abstract-A new statistical model, in the form of a hidden bivariate Markov chain observed through a Gaussian channel, is developed and applied to spectrum sensing for cognitive radio. We focus on temporal spectrum sensing in a single narrowband channel in which a primary transmitter is either in an idle or an active state. The main advantage of the proposed model, compared to a standard hidden Markov model (HMM), is that it allows a phase-type dwell time distribution for the process in each state. This distribution significantly generalizes the geometric dwell time distribution of a standard HMM. Measurements taken from real data confirm that the geometric dwell time distribution characteristic of the HMM is not adequate for this application. The Baum algorithm is used to estimate the parameter of the proposed model and a forward recursion is applied to online estimation and prediction of the state of the cognitive radio channel. The performance of the proposed model and spectrum sensing approach are demonstrated using numerical results derived from real spectrum measurement data.Index Terms-Cognitive radio, spectrum sensing, hidden Markov model, bivariate Markov chain, Baum algorithm.

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Abstract-We develop analytical models to evaluate the performance of optical-burst switch (OBS) architectures employing fiber delay lines (FDLs) as optical buffers to reduce burst-loss probability. The performance of such architectures cannot be captured accurately using traditional queueing models, since FDLs behave fundamentally differently from conventional electronic buffers. We formulate a Markovian model to evaluate the system performance when the burst-arrival process is Poisson and the burst lengths are exponentially distributed under an idealized model of FDL behavior. The model accurately captures both the balking and deterministic delay properties of FDLs, but the complexity of the model makes it infeasible for solving problems of practical interest. By considering approximations of the model in the regimes of short and long FDLs, we develop relatively simple closed-form expressions that can be used for dimensioning OBS architectures. We also extend the approximate model to include the impact of FDL delay granularity. We present numerical results that validate our modeling approach and demonstrate that significant performance gains in optical-burst switching are achievable when FDLs are employed as optical buffers.