Sure. But the ambiguity issue must be understood first
In the 60s the phantom and the sparrow was introduced. The Phantom’s radar used a LPRF( LOW Pulse Repetition Frequency) to detect and track targets. LPRF allow us to detect targets based on the time it takes for a pulse to go and return. Simple.
The Aim-7D/E instead of tracking the signal from the plane in a time manner like the Phantom’s radar, it looked for the target in the frequency spectrum. An approaching target will stand out against the clutter if its coming in hot, under the horizon and chaffing. The problem with the AIM-7/Phantom’s radar mix is due to the range/doppler ambiguity which comes from the PRF selection from the radar.
This essentially covers the issue but I’ll try to explain it shortly.
Look at the range column on the picture above. If you send a signal every 1 millisecond ( 0.001s), your max instrumented range is 150km. Your PRF is 1kHz. But what happens if your radar is powerful and there’s a targets at 170km? The signal of this target will be coming
1.2 ms(0.0002s) after you sent your first signal, as you send a pulse every 1ms, it’ll look like you are getting a return signal 0.2ms after your pulse and the target will appear at 30km on your scope, a ghost target as it really is at 170km. The solution, use a lower PRF. Lets take 0.5 kHz, meaning a signal every 2ms. Now your Max instrumented range is 300km. Good enough.
For the sparrow, we switch from the time domain to the frequency domain of the doppler shift. Here its important to know that the returns repeat every multiple of PRF.
Above you see the doppler shift domain, fo is 0 closure rate( ex. the target is going at my same velocity and direction), the signals comes back at the same frequency.
On a a head on scenario, the faster the target is coming towards us, the higher the doppler shift will be. Lets say a target is approaching us a x speed and the frequency shift we see is +750Hz. On the previous case we had 2 PRFs, at 500 Hz and 1000 Hz. If our PRF had been set at 500Hz, on our scope it look like the target is going away, a negative closure velocity. A False target. So we set our PRF at 1 kHZ. Now, solved the second problem but we have our initial problem! Our range is limited to 150km. This known as the doppler dilemma
We can’t know both at the extremes, one must be sacrificed. You can see it on the first pic.
Radars operate at 8-10 Ghz. Lets put an engagement, 2 planes approaching each other at Mach 2 for a combined MACH 4 closure rate and the frequency is 9GHz.
The doppler shift is 82.4 kHz. Using the analysis we did above, we would need that our PRF to be 82.4 kHz. Our max instrumented range falls down to a poor 1.8km. No Bueno! But atleast you can see target below you clearly.
But what about targets going away? Targets with a negative doppler shift will appear left (RED BARS) to the PRF, in a similar way closing targets will appear to the right(Big BLUE BARS). This means that the negative targets will appear on our positive side and closing targets will appear to the negative side(negative). And if the targets is going away fast enough, it may even get just besides the same closing + target. So what radar engineers did is only study a small bandwith. On the example above -PRF/2 to +PRF/2 to prevent ghost targets. On the engagement above, that would mean that the minimum PRF required we found above doubles to 164 kHz. And now our Maximum instrumented range falls down to 910 meters!
Now, make the interceptor fire a sparrow. The sparrow can reach Mach 4. We would require an even higher PRF. So what did radars engineers did. They put 2 antennas, 1 for the main radar, LPRF, and another one for the sparrow to guide in. This second antenna instead of using a pulsed waveform, it uses a Continuous Wave( CW). In the frequency domain, CW doesn’t have PRF lines that repeat, meaning there’s no PRF/ doppler dilemma. But you cannot measure range directly. (There are other methods like Frequency Modulation and measuring with using several PRFs). This is what is called the CWI( CW illuminator). Here’s the F4Js radar, and the horn to the left is the CW illuminator.
There are things to note:
-
RWRs could tell if you are being fired upon by detecting a CW in your direction. As the CWI only got turned on when you fired and guided the missile.
-
The beamwidth of the horn is big compared to that of the antenna, energy gets sent in a 15° cone basically compared to 3.5° of a main radar. Energy gets wasted, it that could be used for longer ranges and as you illuminate a big cone there can be many more targets you are inadvertently illuminating that the missile could go after instead of the one you want.
As technology progressed, things got smaller and computer power increased. Better radars got into service like the AWG 9( pulse and HPRF) and APG 63(HPRF and MPRF). More complex waveforms could be used. The 7F introduced the ability the guide on pulsed signals, PD guidance. You need a high PRF so MPRF can’t be used. The awg-9 can fire the sparrow with a CW illuminator or in HPRF. The F15-F18 can only do it in HPRF.
The illuminator on phantoms worked at 200Watts, this gave the AIM-7F’s seeker 22 Nautical miles range for a 2m^2 target. When guiding in HPRF(PD - 440 W avg power), the range got increased respectively. The eagle has ~5 kW of peak power, as it works in roughly 30-50% duty ratio, the average power falls down to like 1.5kW-2.5kW average power. Do the math and seeker range range increases( 33-38NM )a lot more for the same target, now mix the sparrow M doing all digitally( compared to 7F which is analogue and has more internal noise which deteriorates the signal) and you get more range.
Green line is the 22NM figure under 200W of CW. Red line is 440W under PD and then you have the envelope of what I would say it the Mike sparrow
And as a bonus of using the same HPRF tracking signal to guide your missile nor changing it, the target cannot know he’s being fired upon!
There’s other stuff like conical/monopulse tracking and the choice between time difference and doppler shift for tracking. Hope this helped a bit to explain.
I rose this CW/HPRF more than a year ago, yet nothing is done. Same with the F15 radar which has a report on the DEV. Community Bug Reporting System @k_stepanovich
