Radar System Design: Reduce Power & Range for 1km Reach

[pyroartist]

I have been reading up on clear-air pulsed radars and am wondering if it is possible to scale down a large radar system to one with reduced power and gain, but also greatly reduced range.
Here are the specs for a large radar: Output power = 2.5 mega Watts Antenna gain = 47db. Range = 15km.
If I reduce the range maximum from 15km to 1km what is the equivalent required power? I believe there is a square root power reduction on EM energy propagation. But don't know if that affects this comparison.

Next, if I reduce the antenna gain from 47db to 15db what is the required power? I am assuming for the moment that the receiver will be unaffected by the change in gain. Thanks for any info on this. Math is not my forte'. Oh, and this is NOT homework. I have a possible application for this if it works out.

 

[berkeman]

The RF spectrum is regulated as a shared resource, so you can't just start transmitting at any old frequency you want without some power restrictions. What band are you considering for this "low power" radar system? What is the maximum allowable power you can transmit in that band without a license? Are there portions of that band that you could get a license to use?

 

[pyroartist]

For all the legal beagles out there... I will state that this is entirely legal. I am a licensed amateur radio operator and intend to operate in the 23 cm amateur band. I did not say this was a "low power" radar system and I will state now that it will be a medium power pulsed system with 100 nanosecond pulses. Amateur radio operators may transmit up to 1500 Watts PEP . Also, transmissions will last one second. Returned echos will be collected, processed, displayed and evaluated before proceeding with another transmission burst.This effort is similar to amateur moon bounce or asteroid bounce projects that amateurs often participate in.
I would like to concentrate on the technical problems only as this is currently only an idea in my head. Thanks.

 

[Baluncore]

If I reduce the range maximum from 15km to 1km what is the equivalent required power? I believe there is a square root power reduction on EM energy propagation.

For radar, the range is not the inverse square, but the inverse fourth power because the signal must go there and back. https://en.wikipedia.org/wiki/Radar#Radar_equation
A 15:1 range reduction would change signal needed by 1/(15^4) = 1/ 50625. That gives a power change of 10*Log(50625) = 47dB.

Next, if I reduce the antenna gain from 47db to 15db what is the required power?

Your antenna is used for transmit and receive also, so you have a reduction by 47 – 15 = 32dB twice = 64dB which is a disaster. It will also cost you all your directional resolution.

You might do better with this question by specifying your wavelength, maximum range, range resolution and directional resolution requirements. That will give you the required minimum antenna diameter.

For studies of Clear Air Turbulence up to about 1km you might find that sound ranging with a chirp gives better images. A distributed sparse array of low gain antennas can make up for the loss of directional resolution.

 

[pyroartist]

Thanks Balulncore. So it looks like I get a large benefit by reducing the required range but it all gets washed away because of the lower antenna gain. Does that mean that my relative system sensitivity would be 47 db - 64 db = -17db ?
Space, size and noise considerations make audio radar not feasible for this application. Lidar would work but pulsed lasers with sufficent power (> approx. 25 mJ.) are above $20K and tend to be very large. I can't afford that on a totally experimental budget.

 

[Baluncore]

Does that mean that my relative system sensitivity would be 47 db - 64 db = -17db ?

Yes, unfortunately you would be 17 dB down on the reference system.

But as an amateur you could try something different. With one transmit antenna you could transmit a short linear frequency sweep, an FM chirp in the band. At a separate receive antenna you mix = multiply the transmitted signal (attenuated), by the received RF signal using an RF mixer chip. The lower side-band, (difference frequency), from the mixer is an audio signal determined by the sweep rate in Hz/second and the return time or distance to and from the reflector. Record that audio with the sound input on your computer, take the FFT of the audio to get the audio power spectrum, you will then have made a plot of distance to all reflectors. Because the FFT is taken from all the data points recorded there is a conversion gain which will raise the reflected signals out of the noise, without needing high power or big antennas. You can accumulate power spectrums to lower the noise further.

 

[pyroartist]

Thanks for a very good idea! I have read about chirped signals and the fact that they improve the S to N ratio. Mathematically I don't understand how but if it works I may try it. The question is, do you think this method is likely to work detecting weak clear air refractive disturbances, maybe with insects and dust mixed in? At 1km?
Do you have any reference designs I could study? There are may questions here. How far apart must the Tx and Rx antennas be. Assume they are small yagis at 23cm. I will also need to build a chirp generator, transmit and receive circuits. Or maybe there are modules available somewhere at an amateur price.
Maybe asteroid bounce has done portions of this work already?

 

[Baluncore]

The question is, do you think this method is likely to work detecting weak clear air refractive disturbances, maybe with insects and dust mixed in? At 1km?

"weak clear air refractive disturbances” are by definition in the noise which is why you call them weak. With pulse radar, all the information about a particular range arrives at one time with an unknown lump of noise. With chirp radar the information about range arrives continuously, so the noise floor averages out. Another advantage of chirp radar is that the bandwidth of the signal is immediately reduced.

You might do better with this question by specifying your wavelength, maximum range, range resolution and directional resolution requirements.

Again, we do not know your application or specifications so it is difficult to say how best to meet the requirements.

Do the arithmetic. Speed of light is defined as c = 299,792,458. m/sec, let's call it about 300x10⁶ = 300e6
At 1km the return distance will be 2000 metre which will take 2e3 / 300e6 = 6.67 usec
To fit the audio of your sound card we set highest frequency to be from 1km = 10kHz.

Now we juggle the chirp rate, sweep time and band width to get range resolution.
A first estimate would sweep at a rate of 10kHz per 6.67 usec, which is 1.5kHz per usec. A chirp that lasts 1 millisec will sweep 1.5 MHz across the band. Digitising the LSB audio at 40KHz will gather only 40 samples. Half are lost in the FFT so our spectrum to 20kHz is represented by 20 values, only 10 of which are below 10kHz=1km. Note that the range resolution improves for wider sweeps.

We need more like 1024 samples for the FFT, so we need to sweep more like 40 MHz across the band. Range resolution will become about 300e6 / 40MHz = 7.5 metres.
But where can you find 40MHz of available amateur band that permits spread spectrum operation?
Some literature search into the best wavelengths for CAT radar reflection would help.

The sweep generator needs to be reasonably linear over the 40 MHz wide sweep. Minicircuits and others make UHF VCO modules that can be swept over 100MHz. I expect Analog Devices Inc make Direct Digital Synthesisers that can also sweep over that range.

 

[anorlunda]

The question is, do you think this method is likely to work detecting weak clear air refractive disturbances, maybe with insects and dust mixed in? At 1km?

If such a device existed, it would have important security and military applications as a long-range motion detector. Via disturbances in the air, you could detect someone hidden around the corner. As far as I know, such detectors don't exist yet.

As a glider pilot, I would also love to have such a device to remotely detect columns or rising or sinking clear air. Airliners would also like to avoid clear air turbulence. As far as I know, such detectors don't exist yet.

 

[pyroartist]

anorlunda:
I am a glider pilot too. So you guessed my application correctly. Yes, these devices do not exist in a usable form yet. However the technology of radar and lidar has been able to do this since the 1960s. If you search the scientific journals you will find many examples of this. I am just trying to make it practical and affordable.

 

[anorlunda]

I am a glider pilot too.

Very cool. Then you not only need it to work, you need small size, small mass, small energy consumption. In other words, a very refined design.

 

[pyroartist]

Yes, you understand all the problems this application demands.

 

[Klystron]

Good work! I assumed small aircraft application but overlooked gliders...

anorlunda:
I am a glider pilot too. So you guessed my application correctly. Yes, these devices do not exist in a usable form yet. However the technology of radar and lidar has been able to do this since the 1960s. If you search the scientific journals you will find many examples of this. I am just trying to make it practical and affordable.

Very cool. Then you not only need it to work, you need small size, small mass, small energy consumption. In other words, a very refined design.

Words to live by. Anorlunda's hypothesis, minus the mass, fits most software designs as well as "flyable radar".

Due to OP's limited funds and amateur status, I suggest a community approach to improving the design. Several pilots a/o gliding clubs pool resources to develop or redesign CAT -- clear air turbulence -- scanner similar to groups that use ground-based "scanners" to assist balloon pilots find clear air and avoid wind shear, etc. Payload and power on a passenger balloon is probably as restricted as on a glider. One solution includes ground support that trundles a mobile radar system powered by a generator and communicates with pilots via radio.

1) Develop your design to operate on the ground in your flight area including data analysis and telecast to the pilots.

2) Presuming a tow aircraft, mount your refined device in the powered craft taking advantage of the DC bus, and let the airplane guide the gliders suggesting optimum paths. This overcomes many of the limits of surface-based testing such as reduced line-of-sight and being stationery while allowing room for an operator aboard the tow.

3) Refine your design and operating parameters to fit the airborne version in a glider, perhaps leaving data processing or other components ground-based via radio link to reduce volume-mass-energy requirements. Even so, one or two airborne systems could assist a flock of gliders.

Interesting project. Storm chasers and weather scientists use combined data approaches including radar and other mobile devices that could be adapted.

 

[Baluncore]

I expect the radar wavelength best for seeing dust and insects will be 3cm or less, or optical lidar. To see clear air changes and turbulence will probably need longer wavelengths, say 30cm or more.

The doppler shift of rising thermals will be due to your airspeed at your flight level, but will be more significant looking up or down. That would suggest the upper and lower wing areas should house phased antenna arrays, separately looking up and down. The integration of that data would tie the above and below vertical velocity profiles to map the axis of thermals. Aircraft position and orientation changes would quickly devalue the data unless GPS position and gyro orientation were used to keep the display view right-way-up ahead of the aircraft. That makes for one big heap of Kalman Filters to integrate the multiple ageing data sources.

In some conditions, the integrated data approach could be spread between multiple aircraft in the local area along with ground based observations.

While not applicable to powered aircraft, there is maybe an alternative for gliders and balloons. A constellation of small solar powered gliding drones could surround a heavier manned glider, like wingmen or scouts, to provide a surrounding screen that reports on local variations in air temperature and differential air velocity. The algorithm needed to keep the constellation gradually circulating about the parent, without any drone being left behind would be quite interesting. That system would not need radar since GPS and a local area data network could gather all the information required. I would expect between 8 and 32 scouts would be needed.
That system might work well in calm conditions, but in rough conditions there is often a trailing string of ducklings doing their best to follow mother duck. When does a mother duck deviate, at a risk to herself and the rest of her brood, to protect one lost duckling?

 

[anorlunda]

The doppler shift of rising thermals will be due to your airspeed at your flight level, but will be more significant looking up or down. That would suggest the upper and lower wing areas should house phased antenna arrays, separately looking up and down.

I really like that thought. Very creative. Up/down differential. Time rate-of-change of that differential also provides an estimate of range. Horizontal airspeed and horizontal air motion could be ignored.

An onboard smart phone could do the data processing and display, and it already has the accelerometers to determine orientation. A phone is also small, light, and low power. The hard part is the radar's weight and power.

Edit: NASA does very good aeronautics research. Someone should put this thought in their heads. Gliders too could be the beneficiaries of research.

 

[trurle]

Actually i had some experience in past measuring these signals from air turbulence. Needed to make a non-random noise rejection model for these. The effective detection range for S/N=3dB was about ~50km with a 18kW at transmitter and ~46dBi gain per beam, in C-band.
For 15km range, you will likely still need about 150W, but C-band antenna for 46dBi is generally not flyable.
I would recommend to try something like 100-watt radar unit in X-band which is more practical for small radome. Generally, clear-air turbulence detector should be not the device on its own, but a software add-on to the existing weather radar. You should try to start from existing weather radar designs.

Finally, high-performance radars do use a sort of chirping, but not linear: actual chirp is split for multiple pulses, a "pulse train". This is so-called "Pulse-Doppler" design. This scheme allows to handle larger transmitter power and to have more fragile&sensitive receiver (because high-isolation switch between transmitter and receiver is now possible) compared to simple continuous-chirping design, while retaining S/N advantage of chirping.

P.S. By the way, 23cm band is likely not practical for this application. Return signal would be too weak and antenna is too cumbersome, even if conformal with airframe. Higher frequencies (~10GHz=3cm) may be optimal for the short range (~15km) you specified.