Prerequisites & Notation

Before You Begin

This chapter builds on the forward model and radar signal processing fundamentals developed in earlier chapters. You should be comfortable with the following before proceeding.

The sensing operator $\mathbf{A}$ and the linear imaging model $\mathbf{y} = \mathbf{A}\mathbf{c} + \mathbf{w}$ (Review ch06)
Self-check: Can you explain what each row and column of $\mathbf{A}$ represents?
Ambiguity function and matched filtering from Chapter 09(Review ch09)
Self-check: Can you sketch the ambiguity function of an LFM chirp?
OFDM modulation: subcarrier spacing $\Delta f$ , cyclic prefix, DFT/IDFT
Self-check: Can you draw the OFDM transmit chain from frequency-domain symbols to time-domain waveform?
Fourier transform pairs: sinc, Dirichlet kernel, 2D-DFT
Self-check: Do you know that the DFT of a rectangular window is a Dirichlet kernel?

Notation for This Chapter

Key symbols introduced or heavily used in this chapter. See also the global notation table.

Symbol	Meaning	Introduced
$N_c$	Number of OFDM subcarriers	s01
$M$	Number of OFDM symbols in the coherent processing interval (CPI)	s01
$\Delta f$	Subcarrier spacing (Hz)	s01
$T_{\mathrm{sym}}$	OFDM symbol duration including cyclic prefix: $T_{\mathrm{sym}} = 1/\Delta f + T_{\mathrm{cp}}$	s01
$d[n,m]$	Data/pilot symbol on subcarrier $n$ , OFDM symbol $m$	s01
$\chi(\tau, \nu)$	Ambiguity function	s02
$X_{\mathrm{DD}}[l,k]$	OTFS delay-Doppler domain symbol at delay bin $l$ , Doppler bin $k$	s03
$\mathcal{Z}_x(\tau, \nu)$	Zak transform of signal $x(t)$	s03

← Ch 9 OFDM-Based Sensing