Mathematical Foundations for Signal Processing, Communications, and Networking

Introduction

Signal Processing Transforms, Serhan Yarkan and Khalid A. Qaraqe
Introduction
Basic Transformations
Fourier Series and Transform
Sampling
Cosine and Sine Transforms
Laplace Transform
Hartley Transform
Hilbert Transform
Discrete-Time Fourier Transform
The Z-Transform
Conclusion and Further Reading

Linear Algebra, Fatemeh Hamidi Sepehr and Erchin Serpedin
Vector Spaces
Linear Transformations
Operator Norms and Matrix Norms
Systems of Linear Equations
Determinant, Adjoint, and Inverse of a Matrix
Cramer’s Rule
Unitary and Orthogonal Operators and Matrices
LU Decomposition
LDL and Cholesky Decomposition
QR Decomposition
Householder and Givens Transformations
Best Approximations and Orthogonal Projections
Least Squares Approximations
Angles between Subspaces
Eigenvalues and Eigenvectors
Schur Factorization and Spectral Theorem
Singular Value Decomposition (SVD)
Rayleigh Quotient
Application of SVD and Rayleigh Quotient: Principal Component Analysis
Special Matrices
Matrix Operations
Further Studies

Elements of Galois Fields, Tolga Duman
Groups, Rings, and Fields
Galois Fields
Polynomials with Coefficients in GF(2)
Construction of GF(2^m)
Some Notes on Applications of Finite Fields

Numerical Analysis, Vivek Sarin
Numerical Approximation
Sensitivity and Conditioning
Computer Arithmetic
Interpolation
Nonlinear Equations
Eigenvalues and Singular Values
Further Reading

Combinatorics, Walter D. Wallis
Two Principles of Enumeration
Permutations and Combinations
The Principle of Inclusion and Exclusion
Generating Functions
Recurrence Relations
Graphs
Paths and Cycles in Graphs
Trees
Encoding and Decoding
Latin Squares
Balanced Incomplete Block Designs
Conclusion

Probability, Random Variables, and Stochastic Processes, Dinesh Rajan
Introduction to Probability
Random Variables
Joint Random Variables
Random Processes
Markov Process
Summary and Further Reading

Random Matrix Theory, Romain Couillet and Merouane Debbah
Probability Notations
Spectral Distribution of Random Matrices
Spectral Analysis
Statistical Inference
Applications
Conclusion

Large Deviations, Hongbin Li
Introduction
Concentration Inequalities
Rate Function
Cramer’s Theorem
Method of Types
Sanov’s Theorem
Hypothesis Testing
Further Readings

Fundamentals of Estimation Theory, Yik-Chung Wu
Introduction
Bound on Minimum Variance — Cramer-Rao Lower Bound
MVUE Using RBLS Theorem
Maximum Likelihood Estimation
Least Squares (LS) Estimation
Regularized LS Estimation
Bayesian Estimation
Further Reading

Fundamentals of Detection Theory, Venugopal V. Veeravalli
Introduction
Bayesian Binary Detection
Binary Minimax Detection
Binary Neyman-Pearson Detection
Bayesian Composite Detection
Neyman-Pearson Composite Detection
Binary Detection with Vector Observations
Summary and Further Reading

Monte Carlo Methods for Statistical Signal Processing, Xiaodong Wang
Introduction
Monte Carlo Methods
Markov Chain Monte Carlo (MCMC) Methods
Sequential Monte Carlo (SMC) Methods
Conclusions and Further Readings

Factor Graphs and Message Passing Algorithms, Ahmad Aitzaz, Erchin Serpedin, and Khalid A. Qaraqe
Introduction
Factor Graphs
Modeling Systems Using Factor Graphs
Relationship with Other Probabilistic Graphical Models
Message Passing in Factor Graphs
Factor Graphs with Cycles
Some General Remarks on Factor Graphs
Some Important Message Passing Algorithms
Applications of Message Passing in Factor Graphs

Unconstrained and Constrained Optimization Problems, Shuguang Cui, Man-Cho Anthony So, and Rui Zhang
Basics of Convex Analysis
Unconstrained vs. Constrained Optimization
Application Examples

Linear Programming and Mixed Integer Programming, Bogdan Dumitrescu
Linear Programming
Modeling Problems via Linear Programming
Mixed Integer Programming

Majorization Theory and Applications, Jiaheng Wang and Daniel Palomar
Majorization Theory
Applications of Majorization Theory
Conclusions and Further Readings

Queueing Theory, Thomas Chen
Introduction
Markov Chains
Queueing Models
M/M/1 Queue
M/M/1/N Queue
M/M/N/N Queue
M/M/1 Queues in Tandem
M/G/1 Queue
Conclusions

Network Optimization Techniques, Michal Pioro
Introduction
Basic Multicommodity Flow Networks Optimization Models
Optimization Methods for Multicommodity Flow Networks
Optimization Models for Multistate Networks
Concluding Remarks

Game Theory, Erik G. Larsson and Eduard Jorswieck
Introduction
Utility Theory
Games on the Normal Form
Noncooperative Games and the Nash Equilibrium
Cooperative Games
Games with Incomplete Information
Extensive Form Games
Repeated Games and Evolutionary Stability
Coalitional Form/Characteristic Function Form
Mechanism Design and Implementation Theory
Applications to Signal Processing and Communications
Acknowledgments

A Short Course on Frame Theory, Veniamin I. Morgenshtern and Helmut Bölcskei
Examples of Signal Expansions
Signal Expansions in Finite Dimensional Hilbert Spaces
Frames for General Hilbert Spaces
The Sampling Theorem
Important Classes of Frames

Index

Exercises and References appear at the end of each chapter.

Biography

Erchin Serpedin is a professor in the Department of Electrical Engineering at Texas A&M University. Dr. Serpedin has been an associate editor of several journals and has received numerous honors, including a National Science Foundation CAREER Award, a National Research Council Fellow Award, and an American Society for Engineering Education Fellow Award. His research focuses on statistical signal processing, wireless communications, and bioinformatics.

Thomas Chen is a professor of networks at Swansea University. Dr. Chen is technical editor for IEEE Press, editor-in-chief of IEEE Network, senior editor of IEEE Communications Magazine, and associate editor of International Journal of Security and Networks, Journal on Security and Communication Networks, and International Journal of Digital Crime and Forensics. His research areas encompass web filtering, web classification, traffic classification, smart grid security, privacy, cyber crime, and malware.

Dinesh Rajan is an associate professor in the Department of Electrical Engineering at Southern Methodist University. An IEEE senior member, Dr. Rajan has received several awards, including a National Science Foundation CAREER Award. His research interests include communications theory, wireless networks, information theory, and computational imaging.

"Here is a book providing the mathematical tools for a large range of researchers, more precisely for future researchers. First, we remark that the involved range is quite new, since many books give mathematical tools for signal processing, for communications or for networking. But this volume gives the tools for all three domains. In this way, a large group of students and researchers is addressed. Therefore the diversity of the subjects is larger. ... the chapters are written by well-known active workers in the domain. ... The included examples are interesting and suggestive. ... The book will be helpful for students and researchers to be acquainted with the recent trends in the areas included in the book. We think we are faced with an excellent book that will soon become a standard reference in the respective areas."
—Dumitru Stanomir (Bucureşti), Zentralblatt MATH, 1254 — 1