Why pulse compression works
Pulse compression, sometimes called matched filtering, is a technique for extracting information about a signal based on knowing what that…
Pulse compression, sometimes called matched filtering, is a technique for extracting information about a signal based on knowing what that signal is. Frequently used in radar, sonar, and photonics, pulse compression is particularly useful in suppressing noise and improving the accuracy of range finding.
In any active ranging system, whether it be radar, lidar, or sonar, a signal is broadcast from a transmitter and reflected off of objects in the far field. The return signal is then received, usually at the same site but sometimes elsewhere, and processed.
A common early method of range finding was to use pulses of a single frequency or tone. This is the well-known “ping” from submarine movies. In the early days of radar during the battle of Britain, for example, radar would be sent in pulses that swept across a circular area. In between pulses, the radar would listen for the echoes from distant objects and those echoes would be translated into blips on a cathode ray tube display. Many modern radars still mimic these old displays despite using vastly more advanced technology.
These single tones had to be relatively short in duration. Consider that if two objects, such as airplanes, were close together, the echoes from the two would overlap one another. This would make it look as though the aircraft were one large object instead of two.
To help count how many aircraft were on approach, pulses had to be kept short but that also meant that there was less energy sent out, meaning a higher chance of noise (either in the air or inside the electronic equipment which was full of noisy vacuum tubes) blotting out a legitimate echo.
The solution to the problem was not to use a single frequency or tone but to modulate it in some way. For example, there is the classic linear chirp where the frequency increases linearly across the pulse. There are also more complex encodings that modulate either frequency or the phase of the signal.
All of these share a common thread which is that the signal changes over time and that information becomes important when signal processing the echoes of distant objects.
Pulse compression is a way of extracting that information by comparing the received echoes to the signal that was transmitted.
In many articles on pulse compression, you will read that it helps improve range accuracy. This is false, and most articles gloss over exactly what is going on. Consider that a single tone, when it bounces off an object, bounces off at a particular distance, which translates into a particular delay from when the signal was transmitted. If you wanted to measure the precise range of this object, you would simply have to look at when exactly the rising (or falling) edge of the echo occurred after the pulse was sent. This would give the exact range to the accuracy of the receiver’s own time measurement equipment.
The problem comes in, as mentioned above, when you have many objects closely spaces together. You cannot resolve their ranges because their echoes overlap one another. Therefore, you can only detect the rising edge of the first object the signal encounters in a cluster of objects. The rest of them are lost inside the collective echo and look like one big blob on a screen.
Modulating the pulse resolves that problem because each echo generates its own distinct frequency (or phase) profile. So even a very long pulse, if it is appropriately modulated, bouncing off of many objects will generate an echo with many different overlapping frequencies.
That echo can be compared against the reverse of the pulse that was sent out, and all meaningful information extracted.
Consider it like this, if you were to make a chirp in a canyon full of rocks and listen for the echo, each rock it reflects off of would generate a mini-copy of that chirp. They could overlap one another but, because they would not overlap precisely in frequency, you could tease apart all the many objects contained therein.
This is the essence of pulse compression. Frequency modulation creates chords of return frequencies where the outgoing pulse was simply a rising tone. Chords can be dismantled by pulse compression, and so we get far greater resolution.
Likewise, pulse compression suppresses noise since noise rarely resembles the pulse that was sent out and so the comparison will generate a null result.
All this means that pulse compression is a means of improving range resolution, not range accuracy, and it does so by allowing the echoes of many different objects to overlap and later be broken apart.