Oulu, May 2021
Acknowledgments
We are thankful to our colleagues, collaborators, friends, and family for their constant support and encouraging words throughout the writing of this book.
We thank Richard Demo Souza and Samuel Montejo Sánchez for their detailed comments and insightful ideas. These discussions kept us pushing toward further exploration of our research both in breadth and depth.
We thank Pedro H. J. Nardelli, Dick Carrillo Melgarejo, Nelson J. Mayedo Rodríguez, Dian Echevarría Pérez, Osmel M. Rosabal, Jean de Souza Sant’Ana, Richard Demo Souza and Samuel Montejo Sánchez for their valuable feedback on specific chapters.
We thank Sarah Lemore (Associate Managing Editor, Wiley) for the assistance provided and for putting up with our requests for extensions, which were granted and all were duly appreciated and well used.
We thank our families for their patience, support, and occasionally taking the blame for our lack of skills in time management. Even then, they were always there for us.
O. A. L. & H. A.
Mathematical Notation
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indicator function. It is equal to 1(0) if A is true(false) |
| [x]+ | max(x,0) |
| [x]× | min(x]+, ref), where ref refers to certain reference level according to the application scenario, e.g., Bmax |
| ~ | distributed as |
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set of natural numbers |
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real coordinate space of dimension is omitted when equals to 1 |
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set ofpositive real numbers |
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complex coordinate space ofdimension d. d is omitted when equals to 1 |
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denotes cardinality or absolute value operation in case of a set or a scalar as input, respectively |
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lp norm. The value ofp may or may not be specified when p = 2 expected value with respect to random variable X. When X is not specified, the expected value is with respect to all random variables |
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probability of occurrence of event A |
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Laplace transform of random variable X |
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inverse Laplace transform operator |
| fX(x) | PDF of random variable X |
| FX(x) | CDF of random variable X |
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CCDF of random variable X |
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gamma function |
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upper incomplete gamma function |
| Kv(·) | modified Bessel function of the second kind and order v |
| erf(·) | error function |
| Tr(·) | matrix trace operator |
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big-O notation |
| diag(x) | diagonal matrix with the main diagonal from entries of x |
| (·)T | transpose operator |
| (·)H | Hermitian transpose operator |
| rank(·) | rank operator |
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generalized greater-than-or-equal-to inequality: between vectors, it represents component-wise inequality; between symmetric matrices, it represents matrix inequality |
| inf · | infimum operator |
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imaginary unit, i.e.,  |
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variance with respect to random variable X. When X is not specified, the variance is with respect to all random variables |
| Jn(·) | Besselfunction of first kind and order n |
| det(·) | determinant operation |
| mod(a, b) |
a modulo b operation
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