Prerequisites & Notation

This chapter builds on FFT/IFFT operations (Chapter 7), digital modulation (Chapter 20), and channel models (Chapter 21).

FFT and IFFT operations (Chapter 7)(Review ch07)
Self-check: Can you compute np.fft.ifft and np.fft.fft and understand their normalization?
QAM constellations and BER simulation (Chapter 20)(Review ch20)
Self-check: Can you generate 16-QAM symbols and compute BER?
Multipath channel models and delay spread (Chapter 21)(Review ch21)
Self-check: Do you know what coherence bandwidth and cyclic prefix mean?

OFDM-specific symbols used throughout the chapter.

Symbol	Meaning	Introduced
$N$	Number of OFDM subcarriers (FFT size)	s01
$N_{\\text{CP}}$	Cyclic prefix length in samples	s01
$\\Delta f$	Subcarrier spacing ( $\Delta f = 1/T_u$ )	s01
$T_u$	Useful OFDM symbol duration (without CP)	s01
$T_s$	Total OFDM symbol duration ( $T_s = T_u + T_{\text{CP}}$ )	s01
$X[k]$	Frequency-domain data symbol on subcarrier $k$	s01
$x[n]$	Time-domain OFDM sample after IFFT	s01
$H[k]$	Channel frequency response on subcarrier $k$	s02
$\\hat{H}[k]$	Estimated channel frequency response	s02