The range-resolution trade-off
A short pulse gives fine detail — you can tell two aircraft 30 metres apart are separate. But it contains so little energy that it vanishes into noise before it reaches a distant target. A long pulse travels farther but smears everything into a blur. You want long-pulse energy with short-pulse sharpness.
Chirp and linear FM
Instead of a single-frequency pulse, sweep the frequency linearly across the pulse duration — a chirp. On receive, pass the echo through a matched filter that does the inverse sweep. The result compresses the long pulse into a spike as short as the inverse of the bandwidth. A 10 µs pulse with 100 MHz bandwidth compresses to 10 ns — a 1,000-fold improvement.
Phase codes: Barker and beyond
Another way: divide the pulse into sub-pulses and flip their phase according to a code. Barker codes have ideal autocorrelation — sidelobes barely above noise. Longer Frank and Pn codes stretch to thousands of chips, giving enormous compression ratios. Military radars love them because they are harder to detect and jam.
Everywhere now
Pulse compression is in your car's adaptive cruise control (FMCW + chirp), in weather NEXRAD (clear-air mode), in every military phased array, and in SAR satellites imaging the ground from orbit. It is the single most important signal-processing innovation in radar since WWII.