Prerequisites & Notation

Prerequisites for This Chapter

This chapter develops radar signal processing from the radar equation through matched filtering, range-Doppler processing, detection theory, and spatial filtering. It assumes familiarity with the following topics.

Electromagnetic scattering and far-field approximation(Review ch06)
Self-check: Can you write down the scattered field for a point target in the far field of a transmit/receive array?
The sensing operator and its Kronecker structure(Review ch07)
Self-check: Can you explain why $\mathbf{A} = \mathbf{A}_{\text{freq}} \otimes \mathbf{A}_{\text{Rx}} \otimes \mathbf{A}_{\text{Tx}}$ ?
Fourier transforms and power spectral density(Review ch04)
Self-check: Can you compute the Fourier transform of a rectangular pulse and state Parseval's theorem?
Antenna arrays and beamforming fundamentals(Review ch07)
Self-check: Can you write the steering vector $\mathbf{a}(\theta)$ for a ULA and explain how beamforming suppresses interference?
Neyman-Pearson detection and the likelihood ratio test(Review ch01)
Self-check: Can you state the Neyman-Pearson lemma and derive the threshold for a given false alarm probability?

Notation for This Chapter

Symbols introduced or heavily used in this chapter. See also the NGlobal Notation Table master table.

Symbol	Meaning	Introduced
$P_t$	Transmit power	s01
$G^{\text{tx}}, G^{\text{rx}}$	Transmit and receive antenna gains	s01
$\sigma$	Radar cross-section (RCS) in m $^2$	s01
$R$	Range (distance to target) in meters	s01
$f_d = 2v/\lambda$	Doppler frequency shift	s02
$s(t)$	Transmitted waveform (complex baseband)	s02
$\chi_A(\tau, \nu)$	Ambiguity function of waveform $s(t)$	s02
$h_{\text{MF}}(t) = s^*(-t)$	Matched filter impulse response	s03
$W$	Signal bandwidth	s03
$P_{\text{fa}}, P_d$	Probability of false alarm and detection	s05
$\mathbf{a}(\theta)$	Array steering vector at angle $\theta$	s06
$\mathbf{R}_{cn}$	Clutter-plus-noise covariance matrix	s06

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