The Range Resolution Dilemma
In simple pulsed radar, range resolution equals c·τ/2 — shorter pulses give finer resolution but carry less energy, reducing detection range. A 1 μs pulse resolves targets 150 m apart but carries 1/100th the energy of a 100 μs pulse. Pulse compression breaks this trade-off: by modulating a long pulse with a frequency sweep (chirp) and applying matched filtering on receive, the radar achieves the resolution of a short pulse with the energy of a long one.
The Linear Frequency Modulated Chirp
The most common waveform sweeps frequency linearly across bandwidth B during pulse duration τ. On receive, a matched filter (whose impulse response is the time-reversed transmitted waveform) compresses the energy into a spike of width ~1/B. The compression ratio τ·B can exceed 10,000 in modern systems — a 100 μs pulse with 100 MHz bandwidth compresses to 10 ns, achieving 1.5 m resolution while maintaining the full energy of the long pulse.
Matched Filter Processing
The matched filter maximizes output SNR by correlating the received signal with a replica of the transmitted waveform. For a chirp, this is efficiently implemented using the FFT: multiply the received spectrum by the conjugate of the transmitted spectrum, then inverse-FFT. The result is a compressed pulse with peak SNR improved by exactly the time-bandwidth product — a 30 dB gain for TBP = 1000.
Sidelobes and Windowing
The compressed pulse has range sidelobes at -13.3 dB (for a rectangular window) that can mask weak targets near strong ones. Window functions (Hamming, Taylor, Kaiser) reduce sidelobes to -40 dB or below at the cost of slightly broadened main lobe (~20% wider). Modern radars often use mismatched filters or nonlinear frequency modulation to achieve very low sidelobes with minimal resolution loss — critical for detecting small targets near large clutter returns.