Prerequisites & Notation

Before You Begin

This chapter builds on NumPy arrays (Chapter 5), linear algebra tools (Chapter 6), statistics and random processes (Chapter 9), and the digital modulation framework from Chapter 20.

NumPy arrays, complex arithmetic, and random number generation (Chapter 5)(Review ch05)
Self-check: Can you generate complex Gaussian random vectors with rng.standard_normal?
Linear algebra: Cholesky, SVD, eigendecomposition (Chapter 6)(Review ch06)
Self-check: Can you compute the Cholesky factor of a correlation matrix?
Distributions: Rayleigh, Rice, Nakagami (Chapter 9)(Review ch09)
Self-check: Do you know that $|h| \sim \text{Rayleigh}$ when $h \sim \mathcal{CN}(0,1)$ ?
3GPP channel model concepts (optional)
Self-check: Are you familiar with large-scale and small-scale fading?

Notation for This Chapter

Symbols and conventions for channel modeling.

Symbol	Meaning	Introduced
$PL(d)$	Path loss at distance $d$ (in dB)	s01
$X_\\sigma$	Log-normal shadow fading, $X_\sigma \sim \mathcal{N}(0, \sigma^2)$ dB	s01
$h$	Complex channel fading coefficient	s02
$K$	Ricean $K$ -factor (LOS-to-NLOS power ratio)	s02
$\\mathbf{H}$	MIMO channel matrix ( $N_r \times N_t$ )	s03
$\\mathbf{R}_r, \\mathbf{R}_t$	Receive and transmit spatial correlation matrices	s03
$f_d$	Maximum Doppler frequency	s02
$\\tau_{\\mathrm{rms}}$	RMS delay spread	s04
$J_0(\\cdot)$	Zeroth-order Bessel function of the first kind	s02

← Ch 20 Path Loss and Shadowing