# My pulsed bandwidth problem

1. Jan 7, 2012

### metiman

My application is a pulsed radio transmitter. Ideally I would like to be able to use 5 μs pulses spaced about 4 seconds apart. Each pulse would represent 1 bit. So my bit rate (and my symbol rate) would be around 0.25 bps. Just based on signal theory alone I think 0.25 bps would allow for a minumum bandwidth of 0.25 Hz for double sideband AM or as narrow as 0.125 Hz for single sideband or more efficient methods. I would either be using no modulation or pulse position modulation. The problem is that a 5 μs pulse has an instantaneous bandwidth of 200 kHz and this reduces my range to such an extent that the system is just not viable. My understanding is that this loss of range is due to the fact that the receiver has to listen to a much wider range of frequencies and this increases noise such that the weak signal from my transmitter is lost in a sea of noise.

Because of this I cannot just go out and buy the transmitter. The maximum pulse length in an appropriate commercial device is 5 μs. According to my link budget calcs I would need a pulse length of something like 500 ms, and no one makes anything like that. I would have to design and build it myself. I figure this will take me at least 5-10 years. So I am not too happy about it.

Nevertheless in a grasping at straws kind of way I am wondering if there is any conceivable method for getting around the short pulse induced bandwidth problem from the receiver side. The recent thread on amplitude modulation has got me wondering. Short pulses create a kind of OOK modulation. In the other thread it was pointed out that if a carrier is amplitude modulated with a simple sine wave that the sidebands will be virtually monochromatic. All the spectral energy from the transmitter would be concentrated in just 3 frequencies. With raised cosine or Gaussian pulse shaping I would hope to get close to this theoretical ideal of a sinusoidal baseband signal. Considering the simpler case of no pulse position modulation I have to wonder if it might be possible to design a receiver which only listens for those 3 frequencies and thus neutralizes the range penalty due to noise in the receiver. Why should the receiver have to listen to all that empty space between the sideband waves and the carrier wave? It would seem to just add noise. Adding in the PPM, as I would like to do, may complicate the situation of course. By increasing the bandwidth it would presumably add more sideband frequencies that the receiver has to detect.

So my question is whether there is any chance of this sort of scheme working. And if not, is it the kind of thing that is just impossible and will always be impossible? That is, what do you think the chances are of us finding a way around this limitation in the next century or millennium? Do you think we will still have this problem with short pulse transmissions in 2112 or 3012?

2. Jan 7, 2012

### Averagesupernova

I guess I'd like to know more about your project. In simpler terms, you need to transmit a pulse every now and then. Correct? What is it about this objective that is critical? Width of the pulse? Shape? Interval?

3. Jan 7, 2012

### vk6kro

As you might expect, there are plenty of schemes to achieve better range with less power for transmitters.

One the the QRSS system, where free computer programs like Spectrum and Argo are used to give an audio spectrum analyser to examine the output of a receiver. Then the transmitted signal is frequency shifted by just a few Hz and sent very slowly.

So, you might get a Morse code dot lasting 1 second and a dash lasting 3 seconds. This is very slow, but such a signal is visible using the programs above.
You can use very low bandwidth like this and get amazing range with very low power. A few milliwatts can be used to send a signal thousands of miles in some cases.

It is ideal for studying propagation effects, but not much good for long conversations.

You certainly can't transmit any 5 uS pulses like this, though. In fact, there are not many frequencies you could legally transmit such a pulse as it would cause massive interference to other users.

Would you consider getting an Amateur Radio licence?

4. Jan 8, 2012

### metiman

Are you sure you'd like to know more? The transmitter would be a 10 Ghz microwave device. Probably klystron based. Well, the device I would like to use, but apparently can't due to the short pulses is a magnetron, which is lovely because it is both an oscillator and an amplifier, and I can just buy the cute little thing off the shelf. Although it's not cheap.

Overall the intent of the project is METI aka active SETI. So I am calculating link budgets for distances of between 4.4 and 50 light years and at those distances receiver design becomes a major factor. I'm already assuming a receiver temperature of 5-10 degrees kelvin or less with a Helium-3 cooling system. Due to the unusual nature of the project I have the luxury of assuming that the receiver would be like a receiver that we might be able to build in 100 years, but more likely 1000 to 10,000 years from now. It's just so hard to predict future technology though. So there is a limit to what I can assume is possible and I'd prefer to be conservative and limit myself to likely tech advances in the next 100-500 years. I definitely don't want to violate any laws of physics. Those aren't too likely to change. The question is whether the range limitation of short pulse induced bandwidth is something that is due to an unavoidable law or just something that no one has bothered to figure out a way around because it hasn't been needed yet. Or because the limitations created by getting around the problem are too great for practical communication.

Short pulses have a number of benefits. Since I could buy an off the shelf part I could save myself 5-10 years of time and short pulses allow for insanely low duty cycles saving me a great deal of money on electricity. The klystron that I would be designing and building myself would have a pulse length of 250-500 ms with an (average if I use PPM) 4 second interval between pulses. This results in an (instantaneous) bandwidth between 2-4 Hz instead of 200 kHz, but the cost to run the device would be something like $25/day for just 4 hours of transmission time. Unless I could build my own power generation system I would be stuck transmitting only 1/8 of the time. The little green men may not be listening when I am transmitting or their planet may be on the opposite side of their sun or the receiving site may be partially blocked by a moon. The 5 μs pulsed device would only cost something like$20/year in electricity for 24/7 transmission. Another factor is the capacitor bank for the short pulses only needs to store about 5.4 joules whereas the longer pulses require a massive 350 kJ capacitor bank which is very expensive. If there is no way around the bandwidth problem my range would be no more than 2 light years or so before the short, wideband pulse was lost in a sea of noise. Also longer pulses require larger electron devices. The little magnetron is small and light enough to carry around in a backpack. The klystron would probably take up a large part of a room and weigh 500 kg or more. Needless to say the klystron would also be much more expensive to build than a little magnetron, although going DIY with the klystron may equalize the cost difference.

5. Jan 8, 2012

### metiman

It looks like they are using ultra narrow bandwidth, low bit rates, and atmospheric effects at low frequencies to transmit long distances with low power. Interesting project. In many ways it is similar to what I am trying to do on a larger scale. Since they are using narrow band transmission it does not apply to this issue though.

Well that depends how patient you are and how complex the conversation is.

This is an excellent point. Although now that you know the precise nature of the application you might see things a bit differently. None of the transmitting sites I am considering are in the northern hemisphere. There is only one target that interests me in the northern hemisphere compared to many in the southern hemisphere. My station site would either be in a somewhat remote area of Southern Argentina (Patagonia) or Northern Peru. Other than a few brief tests, possibly without an antenna, I would not be transmitting in the US.

Nevertheless RFI could be an issue. I wonder if I could filter the output with narrow passband filters so that only the carrier and upper and lower sideband channels are allowed through. I'm not sure if these kinds of systems can have their output filtered in that way. Also, remember that these pulses would be only 5 μs long with an interval of 4 seconds at 10 Ghz. I'm not sure how much trouble that could really cause. Perhaps overlapped chicken wire fencing could be used around the dish to further reduce stray signals in terrestrial directions. I'd just have to make sure the gaps were small enough to attenuate 3 cm waves.

Sure, but I don't see the point. My transmitter power would either be 350 kW for long pulses or 2 MW for short ones. So the FCC wouldn't be too happy with me, license or not. IIRC, even radio and TV stations are only allowed 50 kW. If I really wanted to transmit in the US I might look into getting some kind of specialized license for weather radar if that exists, but of course it's not really an issue. Argentine or Peruvian regulations might be relevant though, and I am unfamiliar with those at present.

So now that you have the full story, what do you think about the question? Do you think it is possible to use 3 narrow passband filters at the receiver to receive a transmission from a sinusiodally shaped wideband pulse with much less noise? That is, could all that empty spectral space be filtered out and would it result in greatly reduced noise at the receiver without greatly reducing the RF energy of the signal at the receiver? I certainly don't see any drawback to filtering it out even if it doesn't actually help with the SNR problem due to some TAINSTAFL issue of which I am currently unaware.

A distant receiver could presumably just tune to the carrier wave ignoring the sideband signals entirely or just tune to one of the sideband frequencies, but overall the signal would have much less power. How much power would the sidebands contain anyway compared to the carrier? Would the RF power be divided equally between the 3 frequencies? Why couldn't you just have 3 different receivers each listening to a very narrow band of frequencies? The first could listen at the lower sideband frequency. The second could listen to the carrier wave frequency. The third could listen to the upper sideband frequency. I presume this would result in 1/3 or less of the power you would get if you listened to all three frequencies at once, but the short pulses allow for a transmitter output power almost 6 times greater.

To be even more specific let's look at this case exactly. Assuming OOK equivalence and that a perfect sinusoidal pulse shape does in fact result in 3 essentially monochromatic or very narrow bands you would have a lower sideband EM wave at 9999800000 Hz, a central carrier wave at 10 Ghz, and an upper sideband EM wave at 10000200000 Hz. Why not just design a receiver to listen to any one of these frequencies or, through filtering, all of them simultaneously without also listening for signals in between 10 GHz and 9999800000 Hz or between 10 Ghz and 10000200000 Hz?

Last edited: Jan 8, 2012
6. Jan 8, 2012

### sophiecentaur

If you want to use such a narrow bandwidth at that high carrier frequency, you may have a serious problem with frequency stability, I think (in receiver and transmitter). Will the phase noise on a Magnetron allow you to lock on to the signal with your receiver?

7. Jan 8, 2012

### metiman

I'm not sure about the frequency stability issue. Magnetrons, even of the more stable coaxial variety, are infamous for their lack of frequency stability. So that is definitely a drawback compared to a klystron, which has orders of magnitude better frequency stability. I will probably have to use a klystron anyway. This thread is mostly about grasping at straws. I'm more curious about the theoretical possibility than I am expecting to be able to go back to the magnetron idea. At the moment I am just assuming that the aliens would have sufficiently good receiver technology to track a drifting frequency even without a CW carrier.

Going with wideband transmission to make it easier for them to follow a drifting frequency is not really an option anyway unless you are a government. I calculated the amount of power I would need for the 5 μs pulses assuming a standard receiver design and it came out to more than 20 GW. I think any amateur or even medium scale privately funded project really has no choice but to go narrow band. For large scale projects, like true galactic beacons, it has been demonstrated that short pulses in the nanosecond range are optimal, but that doesn't seem to scale down to amateur levels very well.

8. Jan 8, 2012

### fleem

There are several reasons a pulse-based UWB system yields profoundly higher capacity than a narrow-band system, when the same average transmit power is used:

1. Contrary to some common misconceptions, channel capacity increases with an increase in bandwidth (when transmit power is the same). See the Shannon-Hartley theorem. This occurs even in spite of the fact that the receiver is hearing more noise (because its listening to a wider bandwidth) and even if the transmit duty cycle is 100%.

2. Additionally, reducing the duty cycle (via strong, widely-spaced pulses or simply brief transmit cycles--which is possible even for a narrow band system) yields higher on-time SNR because transmit power is higher (to maintain the same average power) and the SNR is higher because the receiver need not hear the noise during the quiet time.

3. UWB is immune to multipath fading, assuming your receiver is smart enough to acquire one or more strong points in the multipathed pulse (which really is a requirement for a reasonable system)

There are several other advantages of pulse-based UWB depending on the application. The only real disadvantages are more complex receiver design and more difficult channelization (in theory even channelization can be better in a band that uses UWB rather than narrow-band signals, but putting it in to practice is a bit harder).

Last edited: Jan 8, 2012
9. Jan 8, 2012

### metiman

Let me do a more exact comparison. Using a rough online range calculator (less accurate than doing it by hand, but should suffice for comparison) a 350 kW 500 ms pulsed transmitter should get me a 9 dB SNR range of 45 light years using an average power of 38.88 kW (0.111 duty cycle x 350000). It would actually take a 35 GW 5 μs pulsed transmitter to give me an equal range under the same conditions and that would output an average power of 43.75 kW (1.25 x 10^-6 duty cycle x 35 x 10^9). So the average power is very close and you can obviously transmit a lot more data per unit time with a 200 kHz bandwidth than with a 2 Hz bandwidth. In fact I wonder if you could transmit live video with 200 kHz. You could definitely transmit voice and music with very high fidelity.

The problem is that the most powerful commercially available magnetron I can find is only 2 MW or 1/17500th the power I would need and each one of those 2 MW magnetrons costs about as much as a brand new BMW 1M. How difficult it would be to design and build a 35 GW short pulsed magnetron or klystron I'm not sure, but I think it would be very difficult. I've never even heard of a device that powerful. I think it's a lot easier to build a 350 kW long pulsed device even though the average power is almost the same. Another advantage to the 35 GW pulsed device is I think it would still be a lot smaller and lighter.

Definitely some interesting points about UWB that I hadn't considered before. Thanks, fleem. Nothing to say about the receiver design issue though? Being able to actually use all that bandwidth for sending information would be nice, but I think I'd rather use a less powerful transmitter and transmit information much more slowly. The most important message to send is just that we are here and interested in communicating. Saying anything else is just frosting on the cake.

10. Jan 8, 2012

### fleem

I just realized I missed an important consideration when talking about UWB for your case. A properly source coded (data compression) and channel coded (modulation that fills the channel) signal is indiscernible from noise in the eyes of someone unfamiliar with the data compression and modulation scheme used. Said another way, any predictability in the signal is a waste of energy as far as channel capacity goes--predictability means the receiver already knows what's being sent, and therefore it is a waste of channel. But in your case you want the signal to stand out with predictability so that it will be recognized as a product of intelligence, and maybe code a little information in it as an added benefit. So in your case the predictability itself is "information" and its the most important information. So the question becomes, "What source and channel coding is most likely to be recognizable to an alien race?". The answer is, of course, subjective. For all I know a CW signal is best.

11. Jan 8, 2012

### sophiecentaur

It is an immediate reaction so think that pulses or CW would be the most attention grabbing but any advanced bunch of Alien SETI freaks are likely to have the technology to recognise a signal format that is optimal for noise performance. The main point is that the signal should be recognisable within loads of noise. Secondary would be the information content, which could be at a very slow rate yet still be useful for them.

12. Jan 8, 2012

### metiman

As far as we know so far there are no naturally occurring narrow band signals in radio astronomy. Until and unless we discover some new stellar object that emits narrow band signals all narrow band carriers that are not terrestrial in origin are assumed to be from an ETI. In the entire history of SETI there has only been one signal that meets those criteria: the Wow! signal. So that is an advantage to narrow band. Regularly spaced wideband pulses tend to be from what we call pulsars, which are rapidly rotating neutron stars. But pulsars are really wideband and the pulse intervals decrease by very small amounts over time. Either pulse duration modulation or pulse position modulation would stand out quite nicely as being artificial I think and that's one reason why I want to use at least some kind of modulation. I don't want there to be any chance of my signal being mistaken for something naturally occurring.

13. Jan 8, 2012

### Antiphon

Your antenna will make or break your link budget given the distances involved.

Might I inquire as to why you are inviting disaster of a potentially apocalyptic scale to visit the human race?

14. Jan 8, 2012

### metiman

Actually the antenna size doesn't make quite as much difference as I had expected. And anyway the receiving antenna could make a much bigger difference. I'm planning to build a 20 meter antenna, and I'm assuming the receiving antenna will be at least 70 meters.

As far as inviting an invasion, I don't really think there are going to be any aliens within my 50 light year target radius. If there were it would imply that the galaxy would be brimming with intelligent life and there is no sign of that. The Wow! signal came from the direction of the galactic center (which is exactly what you would expect) and the closest star to that signal was Tau Sagittarii which is 120 light years away. I think that sort of distance is at least somewhat more plausible, although probably still too close. In any event I see it as worth the risk. I think it's pretty unlikely that an alien civilization would want to destroy us unless they thought we were a threat, which seems a bit silly considering how much more advanced they are likely to be. To us their technology would probably be indistinguishable from magic. An analogy that comes to mind is for you or I, through a combination of walking and rowing, to travel to the other side of the planet just to step on an ant. It just doesn't make sense.

15. Jan 8, 2012

### Antiphon

I would think a large high-gain parabolic would be in order. 20 meters is pretty big I suppose.

Perhaps their advanced technology and foreign culture will mesh nicely with ours. What could go wrong?

But if the ants lived in a gold mine and excreted diamonds, I'd be the first one there fashioning little ant shackles and making sure they did what I wanted them to. And I'm a nice guy!

16. Jan 9, 2012

### sophiecentaur

Are we not already pumping out non-random signals all day, every day, which are just as likely to be picked up by someone? And, before you point out the high peak power that's proposed, you need to consider the solid angle covered by the transmission and the probability of its being received by 'someone'. If your transmit beam is narrow enough to correspond to a high gain, then it's missing a lot of potential customers (you can't win) that the thousands TV and satellite up-link transmitters are getting to anyway.
Any civilisation that has spotted us will probably have named the source "50Hz60Hz" because that's the majority of the information that all the (analogue) TV transmissions have contained (alternating on a 24hour period). It will be only analogue transmissions that will have reached anywhere beyond say 20LY away.

17. Jan 9, 2012

### sophiecentaur

Bee keeping is a popular and lucrative pastime!

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