Chapter Summary

Chapter 9 Summary: Radar Signal Processing Fundamentals

Key Points

• 1.
  The Radar Equation

  The monostatic radar equation $P_r = P_t G^2 \lambda^{2} \sigma / (4\pi)^3 R^4$ establishes the $R^{-4}$ power law that determines maximum detection range and per-voxel $\text{SNR}$ in the imaging forward model.

• 2.
  Ambiguity Function and Waveform Design

  The ambiguity function $\chi_A(\tau, \nu)$ characterizes a waveform's joint range-Doppler resolution. The volume constraint $\iint|\chi_A|^2 = 1$ is the radar uncertainty principle. LFM chirps achieve pulse compression ($W T \gg 1$); phase codes approach thumbtack ambiguity.

• 3.
  Matched Filtering and Pulse Compression

  The matched filter $h(t) = s^*(-t)$ maximizes $\text{SNR}$ and achieves range resolution $\Delta R = c/(2W)$. Pulse compression gives $W T$ processing gain. Windowing suppresses range sidelobes with 1-2 dB mismatch loss.

• 4.
  Range-Doppler Processing

  The 2D FFT (fast-time matched filter + slow-time DFT) produces the range-Doppler map. Coherent integration provides $N_p$ gain. Range-Doppler coupling in LFM waveforms requires keystone transform correction.

• 5.
  Detection Theory

  Neyman-Pearson gives the optimal LRT; CFAR detectors maintain constant $P_{\text{fa}}$ by adaptive noise estimation. Swerling models characterize target fluctuations. For Swerling I, $P_d = P_{\text{fa}}^{1/(1+\bar{\gamma})}$.

• 6.
  Space-Time Adaptive Processing

  STAP jointly filters in angle and Doppler via $\mathbf{w} = \mathbf{R}_{cn}^{-1}\mathbf{v}$, suppressing airborne clutter that occupies a sinusoidal ridge in the angle-Doppler plane. The space-time steering vector has Kronecker structure $\mathbf{v} = \mathbf{b} \otimes \mathbf{a}$.

• 7.
  Direction Finding

  MUSIC and ESPRIT achieve super-resolution DOA estimation by exploiting subspace structure. The CRB scales as $N_a^{-3}$. These subspace methods generalize directly to the imaging problem as adaptive beamforming (Ch 13).