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Key	Meaning	Default
pmf	Probability mass function of discrete RV $X$	$P$
gauss	Real Gaussian distribution	$\mathcal{N}$
cgauss	Circularly symmetric complex Gaussian	$\mathcal{CN}$
covmat	Covariance matrix	$\boldsymbol{\Sigma}$
entropy	Shannon entropy	$H$
hd	Differential entropy	$h$
mi	Mutual information	$I$
kldiv	Kullback-Leibler divergence	$D$
cap	Channel capacity	$C$
rate	Code rate (bits/symbol or bits/channel use)	$R$
rd	Rate-distortion function	$R$
wf_lvl	Waterfilling level (channel coding)	$\nu$
rwf_lvl	Reverse waterfilling level (source coding)	$\gamma$
markov	Markov chain relation	$X \multimap Y \multimap Z$
typ_set	Strongly typical set	$\mathcal{T}_\epsilon^{(n)}$
ch	Channel matrix (MIMO, OFDM, general)	$\mathbf{H}$
snr	Signal-to-noise ratio	$\text{SNR}$
es	Energy per transmitted symbol	$E_s$
n0	One-sided noise power spectral density	$N_0$
bw	Signal bandwidth (Hz)	$W$
noise_rv	Noise random variable (theoretical)	$Z$
noisevar	Noise variance / noise power	$\sigma^2$

Universal Conventions

Fixed conventions used throughout this book. These are standard across all telecommunications literature and are not customizable.

General Mathematics

Symbol	Meaning
$\mathbb{R}, \mathbb{C}$	Real and complex number fields
$\mathbb{R}^n, \mathbb{C}^n$	Real/complex $n$ -dimensional vector spaces
$\mathbb{R}^{m \times n}, \mathbb{C}^{m \times n}$	Spaces of real/complex $m \times n$ matrices
$j = \sqrt{-1}$	Imaginary unit (engineering convention)
$\Re\{\cdot\}, \Im\{\cdot\}$	Real and imaginary parts
$\|\cdot\|$	Absolute value (scalar) or cardinality (set)
$\lceil \cdot \rceil, \lfloor \cdot \rfloor$	Ceiling and floor functions
$\triangleq$	Defined as
$\propto$	Proportional to
$\mathcal{O}(\cdot)$	Big-O asymptotic notation

Symbol	Meaning
$\mathbf{x}, \mathbf{y}, \mathbf{z}$	Column vectors (always boldface lowercase)
$\mathbf{A}, \mathbf{B}, \mathbf{H}$	Matrices (always boldface uppercase)
$(\cdot)^T$	Transpose
$(\cdot)^*$	Complex conjugate
$(\cdot)^H$	Conjugate transpose (Hermitian)
$(\cdot)^{-1}$	Matrix inverse
$(\cdot)^{\dagger}$	Moore-Penrose pseudoinverse
$\\|\cdot\\|$ or $\\|\cdot\\|_2$	Euclidean (l_2) norm
$\\|\cdot\\|_p$	$\ell_p$ norm
$\\|\cdot\\|_F$	Frobenius norm
$\langle \mathbf{x}, \mathbf{y} \rangle$	Inner product $\mathbf{y}^H \mathbf{x}$
$\text{tr}(\cdot)$	Matrix trace
$\det(\cdot)$	Matrix determinant
$\text{rank}(\cdot)$	Matrix rank
$\text{diag}(\cdot)$	Diagonal matrix from vector, or diagonal of matrix
$\text{vec}(\cdot)$	Column-wise vectorization
$\otimes$	Kronecker product
$\odot$	Hadamard (element-wise) product
$\mathbf{I}_n$	$n \times n$ identity matrix
$\mathbf{0}_{m \times n}$	$m \times n$ zero matrix
$\mathbf{A} \succ 0$ , $\mathbf{A} \succeq 0$	Positive definite, positive semidefinite
$\lambda_i(\mathbf{A})$	$i$ -th eigenvalue of $\mathbf{A}$
$\sigma_i(\mathbf{A})$	$i$ -th singular value of $\mathbf{A}$