Prerequisites

Before You Begin

This chapter builds on probability and random variables (Chapter 2), signals and systems (Chapter 4), large-scale and small-scale fading (Chapter 6), detection and estimation theory (Chapter 9), and digital modulation (Chapter 10). A solid understanding of probability distributions, expectation, and logarithms is essential for the information-theoretic definitions. Familiarity with fading channel models is required for Sections 11.3-11.5.

Probability distributions, expectation, and random variables(Review ch02)
Self-check: Can you compute the expected value $E[g(X)]$ for a function $g$ of a discrete or continuous random variable $X$ ?
Logarithms, inequalities, and convexity(Review ch01)
Self-check: Can you verify that $\log_2(x)$ is a concave function and apply Jensen''s inequality $E[\log X] \leq \log E[X]$ ?
Fourier transforms and power spectral density(Review ch04)
Self-check: Can you relate bandwidth $B$ to the support of a signal''s power spectral density?
Rayleigh and Ricean fading models(Review ch06)
Self-check: Can you write the PDF of the instantaneous SNR $\gamma$ under Rayleigh fading and compute $E[\gamma]$ ?
SNR, BER, and modulation performance in AWGN(Review ch09)
Self-check: Can you compute the BER of BPSK as $Q(\sqrt{2E_b/N_0})$ and explain why higher-order modulations require more SNR?
Digital modulation and spectral efficiency(Review ch10)
Self-check: Can you define spectral efficiency $\eta = R_b/W$ and explain the bandwidth-power trade-off for $M$ -QAM?

Chapter 11 Notation

Key symbols introduced or heavily used in this chapter.

Symbol	Meaning	Introduced
$H$	Entropy of discrete random variable $X$ (bits)	s01
$H(X\|Y)$	Conditional entropy of $X$ given $Y$	s01
$I$	Mutual information between $X$ and $Y$	s01
$C$	Channel capacity (bits/s or bits/channel use)	s01
$B$	Channel bandwidth (Hz)	s02
$\text{SNR}$	Signal-to-noise ratio $P/(N_0 B)$	s02
$\gamma$	Instantaneous received SNR (random under fading)	s03
$\bar{\gamma}$	Average received SNR $E[\gamma]$	s03
$P_{\text{out}}$	Outage probability $P(\log_2(1+\gamma) < R)$	s03
$R$	Transmission rate (bits/s/Hz or bits/channel use)	s01
$C_{\text{erg}}$	Ergodic (average) capacity	s03
$C_\varepsilon$	$\varepsilon$ -outage capacity	s03
$\mu$	Water level in water-filling power allocation	s03
$N_r, N_t$	Number of receive and transmit antennas	s05
$\Gamma$	Gap to capacity (dB)	s06

← Ch 10 Entropy, Mutual Information, and Channel Capacity