Chapter Summary

Chapter Summary

Key Points

• 1.

  Matched filtering maximizes detection SNR. The chirp matched filter compresses a long pulse ($T_p$) into width $1/B$, providing $BT_p$ processing gain. Range resolution is $\Delta R = c/(2B)$, independent of pulse length.

• 2.

  Range-Doppler processing uses 2D FFT. Fast time (matched filter) resolves range; slow time (FFT across pulses) resolves Doppler. Coherent integration of $M$ pulses adds $10\log_{10}(M)$ dB of SNR gain.

• 3.

  CFAR maintains constant false alarm rate. The threshold adapts to local noise: $\alpha = N(P_{\text{fa}}^{-1/N} - 1)$. Guard cells prevent target self-masking; more training cells improve the noise estimate.

• 4.

  OFDM radar reuses the communication signal. Element-wise division by TX data, IFFT for range, FFT for Doppler. This enables ISAC with the same waveform used in 5G NR.

• 5.

  The ambiguity function characterizes waveform quality. Chirps have a ridge (range-Doppler coupling); OFDM has a thumbtack (independent resolution). Choose the waveform based on the application.