# Low Power Signal Processing -- Bouncing an RF signal off the Moon

Gold Member

## Main Question or Discussion Point

I'm doing a project that has been done many times before, bouncing a signal off the moon, but I'm trying to do it with low power. I'm told the expected S/N ratio is -30dB. The problem I'm trying to figure out is whether or not it is theoretically possible to pull out the signal out from the noise, and if so, what is the best scheme for it?

I've done some minor investigation and it seems like cross correlation is somewhere to start. I'm imagining a process where I send out a signal with some random alterations in it and store it in the program, receive the signal a few seconds later, and phase shift it whatever amount to cross correlate. The thing is, I don't know whether this is actually effective enough for this situation, and I don't know how to implement this in code. I don't currently have MatLab, so I don't want to waste the money on it if it isn't even theoretically possible to do what I want to.

TLDR: I can find a bunch of info on the theory of signal processing but I don't know how to actually implement it or if it will work in this situation.

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berkeman
Mentor
I'm doing a project that has been done many times before, bouncing a signal off the moon, but I'm trying to do it with low power. I'm told the expected S/N ratio is -30dB. The problem I'm trying to figure out is whether or not it is theoretically possible to pull out the signal out from the noise, and if so, what is the best scheme for it?

I've done some minor investigation and it seems like cross correlation is somewhere to start. I'm imagining a process where I send out a signal with some random alterations in it and store it in the program, receive the signal a few seconds later, and phase shift it whatever amount to cross correlate. The thing is, I don't know whether this is actually effective enough for this situation, and I don't know how to implement this in code. I don't currently have MatLab, so I don't want to waste the money on it if it isn't even theoretically possible to do what I want to.

TLDR: I can find a bunch of info on the theory of signal processing but I don't know how to actually implement it or if it will work in this situation.
Can you say more about what you are doing? Are you intending to bounce RF off of the moon (and if so, at what frequency)? Or are you going to bounce a laser off of the retro-reflector array that is on the moon?

Gold Member
Can you say more about what you are doing? Are you intending to bounce RF off of the moon (and if so, at what frequency)? Or are you going to bounce a laser off of the retro-reflector array that is on the moon?
I'm going to use 2 meters, as that seems to be the best frequency for reflecting off the moon to most people.[citation needed] I'm not doing anything with lasers or the retro-reflector.

berkeman
Mentor
So you are going to use a frequency in the 2m HAM band? What are you going to use for your TX power, and what type (gain) antenna are you going to use? Are you wanting to send voice or data? What data rate do you want to achieve? What is the round-trip time for a signal bouncing off the moon (I'm being lazy not calculating it...)?

Gold Member
I guess I should have been more clear in the OP . The purpose is to measure the distance from the earth to the moon, essentially making a radar device I guess.
So you are going to use a frequency in the 2m HAM band?
Yes, and I have the licence for it, so it's all legal.
What are you going to use for your TX power, and what type (gain) antenna are you going to use?
The handheld I'm using is rated for 5 watts, and the antenna is going to be a four element yagi.
Are you wanting to send voice or data? What data rate do you want to achieve?
This is the part that mitigates the problem, as I just want to have a "blip" or just receive a signal. Just enough to tell how far away the moon is. It just has to have some resolution in terms of time.
What is the round-trip time for a signal bouncing off the moon (I'm being lazy not calculating it...)?
On average I guess it is ~2.706 seconds.

berkeman
Mentor
Yes, and I have the licence for it, so it's all legal.
Not if you aren't using one of the approved modulation schemes. We aren't allowed to just send "kerchunks" without some voice, CW or digital data content.

This is the part that mitigates the problem, as I just want to have a "blip" or just receive a signal. Just enough to tell how far away the moon is. It just has to have some resolution in terms of time.
So to stay legal, and optimize your SNR, you should consider sending CW (or digital, but slow CW will give you the best SNR), and correlating the TX and RX station times. Note that you will need two stations, one for TX and one for RX, and you will need to test locally to see what your TX-->RX delay is just getting through the radios.

Have you read through the wikipedia article or other articles about EME communication?

http://en.wikipedia.org/wiki/Earth-Moon-Earth_communication#

Pretty fun project, BTW... :-)

berkeman
Mentor
BTW, your 5W TX power may be a bit low. From the wikipedia article:

wikipedia said:
Recent advances in https://www.physicsforums.com/wiki/Digital_signal_processing [Broken] have allowed EME contacts, admittedly with low data rate, to take place with powers in the order of https://www.physicsforums.com/wiki/Orders_of_magnitude_(power) [Broken] and a single https://www.physicsforums.com/wiki/Yagi_antenna [Broken].

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davenn
Gold Member
2019 Award
BTW, your 5W TX power may be a bit low. From the wikipedia article
Agreed ... would be a waste of effort

From what a few of my fellow amateur friends are doing on 2m , you need to be looking at a minimum of ~ 1kW ERP = 100W into 10 elements
2 x 10 ele Yagi's phased will give another 3 dB = ~ 2kW and you are really starting to get somewhere

My mate in Christchurch is just starting his 1kW, 50MHz linear amplifier for EME
here's the heatsink for it .... it has to dissipate 500W of heat

The amp will draw 30A @ 50V = 1500W, 1000W RF and ~ 500W heat ;)

The return pathloss at 144MHz is ~ 251 dB and the reflected energy is only ~ 7% of what arrives at the moon ... it isn't a good reflector
You need hi gain in antennas, low loss coax, high power transmitter/amplifier, mast mounted high gain low noise GaAsFET preamps for receive

Dave

Gold Member
BTW, your 5W TX power may be a bit low. From the wikipedia article:
Yeah I was figuring that might be the case. Perhaps I will try 50 watts.

sophiecentaur
Gold Member
It would be a good idea to work out a detailed link budget (see this link for a way to approach it and there are many other articles on the subject). It's just a formalised way of working out the feasibility and performance of any link and forces you to get an appreciation of the overall effect of all the losses and gains involved in the chain. Just 'trying' an idea can give really disappointing results. Best to approach this with as much information as you can get. If you do it with a spreadsheet (putting in the 'dBs' for gain / loss of each element in the chain) you can get a final SNR in your total and see the result of spending on money / time on different arrangements. Only when you know all the details can you know the receiver bandwidth needed (and how complex your signal processing needs to be).
The good news is that you can use the same local oscillator source for transmit and receive so your bandwidth can be very narrow. A smart approach could save you a lot of money on high power amplifiers and a massive antenna.

Very intriguing! I wonder if you could do it at something much lower, say 10w.
Also do it on an ISM frequency so the hams don't line up at your door with tar, feathers, and a section of your fence...
Now, that should have everyone reading thinking I'm an entire nut case, lol...

Here's the magic.
Your correct regarding correlation. If you know what your signal looks like, and you continue to repeat it, then you can use correlation to pull it out from under the noise floor. My old business partner worked on this for the Pioneer space probe, and it worked out very well. This is also used for GPS and satallite radio.

Reviewing an online effort, http://physics.princeton.edu/pulsar/k1jt/Moonbounce_at_W2PU.pdf, I found that with their 25dB antenna and .4NF LNA, they could expect a 0 dB S/N at about 56 watts.

If they could squeek in an additional 15dB via the magic of correlation, they'd on need a 10 watt transmitter to reach 0dB S/N. With an additional 15dB, the noise would be 15dB down, and you could recognize your reflection with some ease. You wouldn't be measuring the dealy, but you would be able to point at the results and say "Hey, I bounced a signal off the moon!"

That said, if you average a known value in a Gaussian noise distribution, the noise will sink by 1 / sqrt (n), where in is the number of samples averaged. If you average 1000 samples, then the voltage S/N would bump up by about 32x, and you'd gt 30dB of S/N improvement.

Suppose you simply squawk a 100% modulation 1 kHz square burst from you transmitter for 2 seconds. Then record what you receive for 2 seconds. Take what you've received, and mix it with the same 1 kHz signal and look at the average. You've effectively averaged 2000 samples. By 1 / sqrt(n), you've pushed the noise down by 44x (voltage-wise) and gained 33dB.
You can do this in LTSpice. and get a feel for how it works :)

Now, banging it off the moon is more complicated because the any relative motion between you and the moon causes doppler shift. Thus, you cannot mix with the transmitted frequency, you have to mix with the returned returned frequency. Eeek! Of course, the information is still in your recording and as valid as ever, but you need to search for it and you don't know it's there until you get the correct beat frequency within about 25 Hz (based on a 15 degree phase shift from beginning to end).

Personally, I don't have much difficulty with the idea of making a 25 Hz step, checking, making another 25 Hz step, checking etc...

As to Matlab, I've never had it and taken plenty of product share from the fellows who do :) What you have between your ears will get you further. For example, you can build a "circuit" in LTSpice to generate your test signal then record it as an audio file on your drive using LTSpice's export command. For your experiement, you can transmit the audio file and record the return file. Again, using LTSpice, you can build a "circuit" to process the recording of your returned signal. You can go on to record more complex signals that have only one point of significant correllation (when totally ligned up) and use these as your burst. Bring them back in and use a correlation circuit to find your return signal and delay.

Standard microwave owen frequency is 2.45 Ghz. And it is a nice power ≈ 1 kW. Maybe one could use it, adjust it, make a waveguide and shoot the beam out of it to the moon :D

In addition, there are a lot of surplus dish antennas floating around from the 90's that can easily 35 - 40 dB at 2.5 GHz. That and LNAs.
I'd put two dishes up - one to transmit, and another to receive. That way I don't need an isolation device to keep from blowing the receiver.
In both cases, I'd try to align to mounted telescopes using a receiver and the incoming noise.

Standard microwave owen frequency is 2.45 Ghz. And it is a nice power ≈ 1 kW. Maybe one could use it, adjust it, make a waveguide and shoot the beam out of it to the moon :D
As I recall, these tubes had almost no filtering of the power supply, so they likely peaked out well over 1 kW. Since you only need ping with narrow pulses, I'm curious just how far one of these tubes could be pushed. Unfortunately, their frequency would swing all over as the tube changed temperature, so you'd need a way to either nail it down, or track with the receiver...

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Suppose you simply squawk a 100% modulation 1 kHz square burst from you transmitter for 2 seconds. Then record what you receive for 2 seconds. Take what you've received, and mix it with the same 1 kHz signal and look at the average. You've effectively averaged 2000 samples. By 1 / sqrt(n), you've pushed the noise down by 44x (voltage-wise) and gained 33dB.
I was planning on transmitting barker code 13, which should benefit me quite a bit, or so I read.

...but you need to search for it and you don't know it's there until you get the correct beat frequency within about 25 Hz (based on a 15 degree phase shift from beginning to end).

Personally, I don't have much difficulty with the idea of making a 25 Hz step, checking, making another 25 Hz step, checking etc...
It's a pretty cool effect IMO! I've had experience with it in the past when contacting satellites so this is all good.
I'll also be sure to check out LTSpice. Thanks for the informative post!

Baluncore
2019 Award
To recover the reflection of a low power signal you will require spread spectrum modulation techniques. SS can only be used legally above 400 MHz. A long pseudo-random sequence is predictable and so you do not have to record your transmitted signal. You will need a low noise pre-amplifier at your antenna. You will also need a precise clock so your transmit and receive data have the same regular time base.

Because the face of the moon is not flat, (it has a maximum depth equal to the Moon radius), your reflected signal will be multipath and so will sound very fluttery. When you perform the detection correlation you will get an estimate of the range to the reflective areas on the surface. The distance to the closest area of the face will give the fastest transit time.

Now the 2.5 second return time gives you a 5 second cycle time. You transmit a SS sequence for 2.5 seconds, then switch to receive, digitise and record for 2.5 seconds. That gives you 5 seconds to compute the correlation of the last data-set before the next data-set becomes available.

Fast correlation requires the product of the FFT of the Tx and Rx signals. You can pre-compute the FFT of the repeated Tx signal, so the 5 second cycle only requires the FFT of the Rx and computation of the product of the FFTs. That correlation can be accumulated over many cycles. Reverse transform the accumulated result to get the delay profile. Fast FFTs are available for PC clones that will do your computation in less than 5 seconds. You should widen your bandwidth and chip rate to get the maximum data that can be processed in 5 seconds.

A quick path loss analysis is here;
http://en.wikipedia.org/wiki/Earth–Moon–Earth_communication#EME_communications_technical_details

Your welcome. In the past, I found a shift register based PRN sequence that had few and small trivial correlations. As I recall, it was about 9 registers long. Anyway, I programmed it into two 22V10 PLDs and drove each from seperate 100 MHz clocks.
I passed the output of one PLD into the mixer input of an ancient Motorola front end IC, and drove the other V10 into a laser diode.
Using a PIN photodiode, I received a bit of leakage from the laser diode as well as the return echo. Inside my lab area, I could easily see the correlation when the PRNs lined up at the time of the leakage and again at the time of the the return signal.

Here's the fun part... Because the oscillators frequencies were fairly close, the PRN generators rolled into correlation once in ever so many 10's of ms. I could see the delay of light coming back from about 6 feet using a 1ms / division sweep rate :)

I respectfully disagree regarding the need for a spread spectrum signal. Most anything can be auto-correlated. You can transmit a chirp, burp, or a tone. The difficulty with the tone is that you find the reflection, but you lose any resolution since it auto-correlates all up and down the sequence. Since home-built ham rigs are notorious for chirping, I wonder how illegal it could be?
In any case, it's no fun to work below 400 MHz because 20 dB+ antennas become huge. It's also no fun to work above 2.5GHz, because losses and equipment become a nightmare.
That makes me think that 2.45GHz would be a sweet spot. You can get low quality LNAs and 20 watt power amplifiers right off the shelf, and the old TVRO satellite dishes would give reasonably good gain in these bands (better than 30dB). Of course, you'd need a signal generator, receiver, T/R equipment... Then, have to cobble the feed horn and align the things... Sounds like you need to convince a mob to help you :)

Also, you'd probably want to find a nice valley for this experiment - far from man made noise. I used to work in a lab that was buried in such a valley with nice 10-ft fences about a mile out. It was a wonderfully peaceful, clean RF environment.

Baluncore
2019 Award
I respectfully disagree regarding the need for a spread spectrum signal. Most anything can be auto-correlated. You can transmit a chirp, burp, or a tone.
A chirp or a burp is a Spread Spectrum signal. A PRBS has a minimum correlation with other inband signals and also does not need to be recorded.

Burps and chirps are qualified as spread spectrum. I guess it's time to start handing out fines to every other ham, lol.
I'm glad to hear that someone is personally wealthy enough to process the signal in real time. I suspect most of us would have to save the data and go for lunch while the PC crunched the numbers.

Baluncore