Prerequisites & Notation

This chapter applies electromagnetic theory and signal-processing tools to model how radio waves propagate over large distances.

Fourier transform and frequency-domain analysis(Review ch04)
Self-check: Can you compute $X(f) = \mathcal{F}\{x(t)\}$ and interpret the magnitude spectrum?
Complex baseband representation(Review ch04)
Self-check: Can you write a bandpass signal in terms of its complex envelope $\tilde{x}(t)$ ?
Logarithms and decibel (dB) conversions
Self-check: Can you convert between linear power ratios and dB? $P_{\text{dB}} = 10\log_{10}(P/P_{\text{ref}})$
Gaussian random variables and the Q-function(Review ch02)
Self-check: Can you compute $P(X > x) = Q((x - \mu)/\sigma)$ ?
Basic electromagnetics: plane waves, wavelength, frequency
Self-check: Do you know the relation $c = f\lambda$ and that $\lambda \approx 0.15$ m at 2 GHz?

Symbols introduced in this chapter. See also the NGlobal Notation Table master table.

Symbol	Meaning	Introduced
$P_t, P_r$	Transmitted and received power	s01
$G_t, G_r$	Transmit and receive antenna gains	s01
$\lambda$	Wavelength ( $c/f$ )	s01
$d$	Transmitter–receiver separation distance	s01
$PL(d)$	Path loss (dB) at distance $d$	s03
$n$	Path-loss exponent	s03
$X_\sigma$	Shadow fading (dB), $X_\sigma \sim \mathcal{N}(0, \sigma^2)$	s05
$d_c$	Breakpoint (crossover) distance	s03
$h_t, h_r$	Transmit and receive antenna heights	s01