The Earth Moon Earth (EME) station for Earth Venus Earth (EVE) testing effort continues! Let’s walk through the signal construction and explain how it’s received.
The challenge of EVE is to bounce a signal off Venus and receive it on Earth. Venus rotates (slowly) and it reflects back a small percentage of radio waves aimed in its direction. The amount reflected back to us is related to the reflectivity, or albedo, of the surface of the planet. This percentage ranges from 10 to 15 percent, depending on what part of the planet happens to be facing our radio transmitter. Since the surface of Venus has been mapped, and since we can calculate this in advance, we have a good idea of how much of our signal will be reflected back.
That reflected signal isn’t just weakened by a lossy reflective surface. Venus is very far away, so the path loss is immense. And, since Venus is rotating, the reflected signal is smeared from the rotation. This is called Doppler Spread, and it has a direct effect on how we design, contruct, transmit, and receive our signal. The enormous path loss and the Doppler Spread (low coherence time) of the signal are the two biggest challenges for a signal designer.
Pete Wyckoff tackled this problem by directly confronting the Doppler Spread. The signal design is based around this physical limitation of the channel. The reciprocal of Doppler Spread is coherence time, which is the amount of time we can coherently integrate the signal before we lose phase information. Integration is essentially gathering up energy over time and figuring out where the power appears. Higher power values at particular frequencies indicate a high probability of the presence of a transmitted signal. Most digital signal designs assume an infinite or very long coherence time. Dealing with Doppler Spread is not something that a typical radio signal designer has to face. When we deliberately bounce a signal off a reflector like Venus, then we have to account for this effect.
After this coherence time expires, we can still make use of the magnitude information for our signal integration, but we lose out on phase. This means we have a penalty to our receiver signal to noise ratio compared to a signal that doesn’t have any Doppler Spread.
Spiral, our recommended modulation and coding scheme, is a frequency shift keying design, with forward error correction. It’s a 4096-ary design, where each tone represents 12 bits of information. A symbol is a single tone. A frame is 11 tones. 11 symbols times 12 bits gives us 132 bit-slots. We set up 90 message bits and use 16 bits to give a cyclic redundancy check (CRC). This gives us 106 payload bits. We use BCH(127,106) forward error correction encoder. This adds 21 parity bits. We have 127 frame bits fill 132 slots, with 5 leftover slots zero-padded. A frame is 11 or 12 ASCII characters, depending on the type of ASCII encoding.
Doppler Spread is 1 Hz at 1299.5 MHz and 2.8 Hz at 2304 MHz. Coherence time is the reciprocal of Doppler Spread. We have a 0.5 second coherence time at 1299.5 MHz and 0.35 second coherence time at 2304 MHz. These two frequencies are the ones most commonly considered for EVE work.
Using the 0.35 second long receive window, we set our receiver tone bandwidth to 2.87 Hz. We set a tone spacing of 5.74 Hz, so that we have an entire “guard band” for each of our tones.
Using the 0.5 second long receive windows, we set our receiver tone bandwidth to 2 Hz. We set a tone spacing of about 4 Hz, and we run the symbol length as long as needed to get CNR in 1 Hz target.
We run the symbol length as long as needed to meet or exceed the CNR in 1 Hz target. If we’re at a station where we are receiving our own signal, then we send as long as we can without exceeding the round trip time. This is about four minutes for Venus.
The most straightforward way to do this (if you have to receive your own transmission) is to send one symbol per transmission. Send one symbol, which is one tone, for the entire round-trip time. Then turn the transmitter off, and receive the entire echo. If you have another station listening while you transmit, then you can send one tone after another. Each tone is sent as long as it takes to build up enough integrated signal power in order to recover the transmitted tone.
How do we receive? For each symbol, the receiver calculates coherent windows using the coherence time. For example, either 0.35 or 0.5 seconds long, depending on the transmission frequency used. Within each of these short windows, we coherently combine. Once all these individual windows are calculated, we non-coherently combine all of these results.
We determine the tone result. We collect a full frame of 11 tones. We determine the 12 bits indicated by each specific tone. We decode and then return the message.
Since Venus isn’t usually close enough to try things out, we decided to use the Moon as a test case. Althought the Moon appears to not be rotating, it is wobbling back and forth. This is called Libration, and it causes a Doppler Spread too. We thought this would be an excellent test bed for EVE signal design. We weren’t expecting it to be as interesting as it was!
The libration, or cyclic wobbling, is very much like a rotation. It causes Doppler Spread. Unlike a steady state rotation of a planet like Venus, the Moon’s Doppler Spread varies. The Libration cycle goes from fast to slow and back again, back and forth, over the course of a month. The amount of Libration can be tracked in the Python library Skyfield.
When we calculated the amount of Doppler Spread for EME tests of our EVE signal, we found that it varied above and below what we would be getting with Venus. For one particular date, sending EVE signals to the Moon to test would incur a penalty of over 5 dB, simply because the coherence time was much shorter than Venus! The effect varies depending on where you are on Earth. Higher latitudes don’t see as much Doppler Spread as lower latitudes. The Earth’s equator is the most challenging place to be.
In order to get the most performance out of EVE signals tested with the Moon, we adjust the tone spacing of our signal, and we adjust the duration of the coherently collected windows, based on the worst-case Doppler Spread for when the transmission was made. We round to the nearest hour, calculate the worst Doppler Spread a receiver would possible experience, and set the tones and coherence windows based on that Doppler Spread. That is how we adjust the Spiral communications protocol for EME.
Is this strictly necessary for EME communications? No. There are many ways to bounce a signal off the Moon. This scheme, where we adapt to varying Doppler Spread, provides a real-world case study of low coherence time signal theory. For very low SNR situations, where every dB counts, techniques like this can make the difference between copying a signal and receiving nothing.