Prerequisites & Notation

Before You Begin

This chapter pivots from OTFS as a communications waveform to OTFS as a radar sensing waveform. The DD-domain machinery of Chapters 1-10 is the same; we now interpret the channel's DD structure as a target scene to be estimated. Classical radar theory (range-Doppler processing, ambiguity function) provides the analysis framework.

The DD channel as a sum of targets(Review OTFS Ch. 1)
Self-check: Can you identify that $h(\tau, \nu)$ encodes the scatterers' range-velocity coordinates?
OTFS transmit waveform(Review OTFS Ch. 6)
Self-check: Do you know that the OTFS signal is a Gabor expansion on the critical DD lattice?
Fractional Doppler and BEM(Review OTFS Ch. 10)
Self-check: Can you explain why fractional Doppler is the signal of interest in radar?
Classical radar: range and Doppler from matched filter(Review Telecom Ch. 29)
Self-check: Do you recall that range resolution is $c/(2W)$ and Doppler resolution is $1/T$ ?
Ambiguity function basics(Review Telecom Ch. 29)
Self-check: Can you state the definition of the ambiguity function for a pulse $s(t)$ ?

Notation for This Chapter

Symbols introduced in this chapter.

Symbol	Meaning	Introduced
$A_s(\tau, \nu)$	Ambiguity function of the waveform $s(t)$	s01
$R, v$	Target range (meters) and velocity (m/s)	s01
$\Delta R, \Delta v$	Range and velocity resolution: $\Delta R = c/(2W), \Delta v = c/(2 T f_0)$	s03
$R_{\max}, v_{\max}$	Unambiguous range and velocity: $R_{\max} = c M/(2 W), v_{\max} = c N/(2 T f_0)$	s05
$\sigma_R, \sigma_v$	Range and velocity estimation errors (CRLB)	s03
$\text{PSL}$	Peak sidelobe level — ambiguity function's largest non-zero-lag value	s02

← Ch 10 The Ambiguity Function