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
set of natural numbers
real coordinate space of dimension is omitted when equals to 1
set ofpositive real numbers
complex coordinate space ofdimension d. d is omitted when equals to 1
denotes cardinality or absolute value operation in case of a set or a scalar as input, respectively
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
probability of occurrence of event A
Laplace transform of random variable X
inverse Laplace transform operator
fX(x)
PDF of random variable X
FX(x)
CDF of random variable X
CCDF of random variable X
gamma function
upper incomplete gamma function
Kv(·)
modified Bessel function of the second kind and order v
erf(·)
error function
Tr(·)
matrix trace operator
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
generalized greater-than-or-equal-to inequality: between vectors, it represents component-wise inequality; between symmetric matrices, it represents matrix inequality
inf ·
infimum operator
imaginary unit, i.e.,
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
atan2(c)
returns the angle in the Euclidean plane between the positive x axis and the ray to the point c
derivative ofsingle-variable function f
partial derivative ofmulti-variable function f with respect to x Hessian offunction f
Q(·)
Q-function, the tail distribution function of the standard normal distribution
Distributions
Exp(x)
exponential random variable with mean x
N(m, R)
Gaussian real random vector with mean vector m and covari-ance matrix R
