Prerequisites

Before You Begin

This chapter builds on mathematical foundations (Chapter 1), large-scale fading and path-loss models (Chapter 5), cellular architecture basics (Chapter 6), and the information-theoretic capacity of fading channels (Chapter 11). The reader should be comfortable with path-loss exponents, log-normal shadowing, ergodic capacity expressions, and basic probability theory including order statistics and Poisson processes.

Probability theory, order statistics, and Poisson processes(Review ch01)
Self-check: Can you state the probability mass function of a Poisson random variable $N \sim \text{Poisson}(\lambda A)$ and compute $\Pr[N = k]$ ? Can you explain why the number of points in a region of area $A$ under a homogeneous PPP with intensity $\lambda$ follows this distribution?
Path-loss models and large-scale fading(Review ch05)
Self-check: Can you write the simplified path-loss model $\ell(d) = d^{-\alpha}$ and explain why the path-loss exponent $\alpha$ typically ranges from 2 (free space) to 6 (dense urban)? Can you describe the effect of log-normal shadowing on coverage?
Cellular system fundamentals and frequency reuse concepts(Review ch06)
Self-check: Can you explain the concept of frequency reuse in a cellular system and why it enables spatial reuse of spectrum? Can you state the relationship between the reuse factor $N$ and the number of available channel groups per cell?
Ergodic and outage capacity of fading channels(Review ch11)
Self-check: Can you write the ergodic capacity $C = \mathbb{E}_h[\log_2(1 + \text{SNR}\,|h|^2)]$ for a Rayleigh fading channel and explain the difference between ergodic capacity and $\varepsilon$ -outage capacity?

Chapter 21 Notation

Key symbols introduced or heavily used in this chapter.

Symbol	Meaning	Introduced
$R$	Cell radius (hexagonal model)	s01
$N$	Frequency reuse factor (cluster size)	s01
$D$	Co-channel reuse distance: $D = R\sqrt{3N}$	s01
$\alpha$	Path-loss exponent	s01
$\lambda$	Spatial intensity (density) of base stations in a PPP (BSs per unit area)	s02
$\Phi$	Homogeneous Poisson point process modelling BS locations	s02
$p_c(\tau, \alpha)$	Coverage probability: $\Pr[\text{SINR} > \tau]$	s02
$\tau$	SINR threshold for coverage	s02
$B$	Range expansion bias (dB) for small-cell association in HetNets	s03
$\mathcal{A}$	Area spectral efficiency (bits/s/Hz/km $^2$ )	s04
$H_{\text{hys}}$	Handover hysteresis margin (dB)	s05
$T_{\text{TTT}}$	Time-to-trigger for handover (ms)	s05
$S$	Number of sectors per cell site	s06

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