Stochastic methods and their applications to communications : stochastic differential equations approach / Serguei Primak, Valeri Kontorovich, Vladimir Lyandres.

Format:

Book

Author/Creator:

Primak, Serguei.

Contributor:

Kontorovich, V. I︠A︡. (Valeriĭ I︠A︡kovlevich)

Lyandres, Vladimir.

Language:

English

Subjects (All):

Telecommunication--Mathematics.

Telecommunication.

Stochastic differential equations.

Physical Description:

1 online resource (448 p.)

Edition:

1st ed.

Place of Publication:

Chichester ; Hoboken, NJ : Wiley, c2004.

Language Note:

English

Summary:

Stochastic Methods & their Applications to Communications presents a valuable approach to the modelling, synthesis and numerical simulation of random processes with applications in communications and related fields. The authors provide a detailed account of random processes from an engineering point of view and illustrate the concepts with examples taken from the communications area. The discussions mainly focus on the analysis and synthesis of Markov models of random processes as applied to modelling such phenomena as interference and fading in communications. Encompassing both theory

Contents:

Stochastic Methods and Their Applications to Communications; Contents; 1. Introduction; 1.1 Preface; 1.2 Digital Communication Systems; 2. Random Variables and Their Description; 2.1 Random Variables and Their Description; 2.1.1 Definitions and Method of Description; 2.1.1.1 Classification; 2.1.1.2 Cumulative Distribution Function; 2.1.1.3 Probability Density Function; 2.1.1.4 The Characteristic Function and the Log-Characteristic Function; 2.1.1.5 Statistical Averages; 2.1.1.6 Moments; 2.1.1.7 Central Moments; 2.1.1.8 Other Quantities; 2.1.1.9 Moment and Cumulant Generating Functions

2.1.1.10 Cumulants2.2 Orthogonal Expansions of Probability Densities: Edgeworth and Laguerre Series; 2.2.1 The Edgeworth Series; 2.2.2 The Laguerre Series; 2.2.3 Gram-Charlier Series; 2.3 Transformation of Random Variables; 2.3.1 Transformation of a Given PDF into an Arbitrary PDF; 2.3.2 PDF of a Harmonic Signal with Random Phase; 2.4 Random Vectors and Their Description; 2.4.1 CDF, PDF and the Characteristic Function; 2.4.2 Conditional PDF; 2.4.3 Numerical Characteristics of a Random Vector; 2.5 Gaussian Random Vectors; 2.6 Transformation of Random Vectors

2.6.1 PDF of a Sum, Difference, Product and Ratio of Two Random Variables2.6.2 Probability Density of the Magnitude and the Phase of a Complex Random Vector with Jointly Gaussian Components; 2.6.2.1 Zero Mean Uncorrelated Gaussian Components of Equal Variance; 2.6.2.2 Case of Uncorrelated Components with Equal Variances and Non-Zero Mean; 2.6.3 PDF of the Maximum (Minimum) of two Random Variables; 2.6.4 PDF of the Maximum (Minimum) of n Independent Random Variables; 2.7 Additional Properties of Cumulants; 2.7.1 Moment and Cumulant Brackets; 2.7.2 Properties of Cumulant Brackets

2.7.3 More on the Statistical Meaning of Cumulants2.8 Cumulant Equations; 2.8.1 Non-Linear Transformation of a Random Variable: Cumulant Method; Appendix: Cumulant Brackets and Their Calculations; 3. Random Processes; 3.1 General Remarks; 3.2 Probability Density Function (PDF); 3.3 The Characteristic Functions and Cumulative Distribution Function; 3.4 Moment Functions and Correlation Functions; 3.5 Stationary and Non-Stationary Processes; 3.6 Covariance Functions and Their Properties; 3.7 Correlation Coefficient; 3.8 Cumulant Functions; 3.9 Ergodicity; 3.10 Power Spectral Density (PSD)

3.11 Mutual PSD3.11.1 PSD of a Sum of Two Stationary and Stationary Related Random Processes; 3.11.2 PSD of a Product of Two Stationary Uncorrelated Processes; 3.12 Covariance Function of a Periodic Random Process; 3.12.1 Harmonic Signal with a Constant Magnitude; 3.12.2 A Mixture of Harmonic Signals; 3.12.3 Harmonic Signal with Random Magnitude and Phase; 3.13 Frequently Used Covariance Functions; 3.14 Normal (Gaussian) Random Processes; 3.15 White Gaussian Noise (WGN); 4. Advanced Topics in Random Processes; 4.1 Continuity, Differentiability and Integrability of a Random Process

4.1.1 Convergence and Continuity

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

Description based on metadata supplied by the publisher and other sources.

ISBN:

9786610275212

9781280275210

1280275219

9780470021187

0470021187

9780470021170

0470021179

OCLC:

57597810