# How well can Voyager 1 separate Earth signals from Solar noise these days?

This is a follow-up question to Can Voyager 1 receive signals from Earth? and this and this answer. UPDATED: see additional information and discussion below.

As it continues to move farther from the Sun, the angular separation between the Earth and Sun continues to decrease, can its antenna actually resolve the two and limit the noise from the sun? (seems to be about 0.4 degrees at opposition now) For that matter, how strong IS the noise from the sun relative to earth transmissions, considering the passband of Voyager's electronics - is is it a serious issue to begin with? As earth oscillates in its orbit - is there a seasonal effect?

Besides the mind-boggling large distances an weak signal, the problem I'm talking about here is that - as seen from Voyager 1 (and 2), the earth is only a small fraction of 1° away from the sun, which is a powerful and noisy radio source.

Voyager receives at around 2 GHz1, so its 3.7m diameter dish can not separate the two. Even a quiet sun is almost $$\text{10}^6$$ Jy. The electronics is circa 1970, if it has an input bandwidth presented to the front-end of 10MHz, the sun will be a million times stronger than the 20kW Deep Space Network DSN signal.

above: data for the Sun, planets, Pluto, Voyager 1 and Voyager 2, from January 1, 1969 (a good year to start things) until now. Dots are now. Data is from NASA JPL Horizons.

above: Angular separation between the earth and the sun in degrees, as seen from Voyager 1 (heavy, blue) and Voyager 2 (light, green). The dips to near-zero stop happening once the spacecraft left the plane of the ecliptic.

above: example of the type of settings I used to get the data in ecliptic coordinates.

above: Partial screen shots from DSN Now: https://eyes.nasa.gov/dsn/dsn.html, just for fun because this is downlink at 8 GHz rather than uplink at 2 GHz.

1 from All About Circuits' Communicating Over Billions of Miles: Long Distance Communications in the Voyager Spacecraft (a fun read!):

The uplink carrier frequency of Voyager 1 is 2114.676697 MHz and 2113.312500 MHz for Voyager 2. The uplink carrier can be modulated with command and/or ranging data. Commands are 16-bps, Manchester-encoded, biphase-modulated onto a 512 HZ square wave subcarrier.

from DESCANSO Design and Performance Summary Series Article 4: Voyager Telecommunications as discussed in this answer.

• This has been on the back burner in my mind since you posted. I't starting to bug me so I'll do some research and post an answer when i get some free time. Mar 7, 2016 at 18:48
• @AndrewW. I wouldn't want you to leave Voyager 1 on the back burner too long! If you can just add a short answer with some kind of a link. Am I right - about 0.4 degrees max at opposition? Yikes! Is the sun actually very noisy?
– uhoh
Jun 4, 2016 at 14:59
• I inquired about this at JPL's Space Flight Operations Facility, and they said that they can, and do, still talk with the Voyager probes, usually on a daily basis, and that they still have clear communication with both. Jul 19, 2016 at 19:59
• @uhoh I'm not sure about every day, but I see one or both of them on there fairly often, labeled as VGR1 and VGR2. Voyager 1 is talking right now. Jul 20, 2016 at 1:21
• Woops, I forgot path loss in the DSN signal the received signal is P.G.A.4.pi/d^2. Here's a link showing an example of link budget from the DSN: propagation.gatech.edu/ECE6390/project/Fall2010/Projects/group7/… Jul 21, 2016 at 19:05

According to this source, the quiescent Sun produces about 10-20 Watts per square meter per Hertz at 2 GHz at Earth's orbit. At a distance of 152 AU, it will be a factor of 1522 weaker or about 4 x 10-25 W/m2/Hz. Collected with a 12 foot dish (~10 square meters) gives 4 x 10-24 W/Hz for solar noise.

Thermal noise in the front end is kT W/Hz. Assuming a noise temperatue of, say, 250K, this is 1.4 x 10-23 x 250 = 3.5 x 10-21 W/Hz

So the solar noise is much less than the thermal noise from Voyager's front-end amplifier. The fact that the antenna provides no discrimination doesn't matter.

The radio noise from the Sun can be over 1000 times larger during a solar storm. It would then be comparable to the front-end noise and could be a problem.

• This sounds pretty conclusive, and surprisingly low, thanks! Related: What exactly is the interaction that blocked Juno's data downlink near solar conjunction? and pointing out that Stars are not particularly "loud" in radio are answers to: How far have individual stars been seen by radio telescopes?
– uhoh
Apr 9, 2021 at 7:47
• @uhoh Yes, the situation is very different the other way round. The downlink antenna has more than 100x the area of Voyager and the cryogenic receiver noise is probabably 10x less. Plus the sun is now at 1 AU, so there's that reduction by152^2 also missing. I have no idea what the plasma around the sun does to the transmission, but it can't be good. The only positive thing is that the directivity of the big down-link antenna is much better, especially at X-band. Apr 9, 2021 at 19:21
• @uhoh It is remarkable to think that, within that narrow beamwidth and that narrow bandwidth, the Goldstone DSN antenna is much more luminous than the Sun. Apr 9, 2021 at 19:25
• Yes indeed, the world looks very different in radio! Luckily, while Earth always appears close to the Sun from the Voyagers, they don't usually appear close to the Sun from Earth.
– uhoh
Apr 9, 2021 at 19:28

I was fortunate to have worked on Voyager, and other projects at JPL from 1970 to 1975. I was also fortunate to have had Solomon Golomb, PhD, as my advisor and mentor in Electrical Engineering graduate school at USC in the late 1960's. I wanted to study communications theory, and Dr. Golomb was the only professor at USC who was involved in that area. According to information from USC published at the time of his death, Dr. Golomb's research when I was his research assistant is the reason NASA can separate faint radio signals sent from spacecraft from much stronger background noise. (Incidentally, this research is given the credit for us having CD's, DVD's, and cell phones.) I really did not and do not really understand the research that I helped this reknowned mathematician who was a full professor of Electrical Engineering perform. I do know that without him, we would not be able to decipher Voyager's signals.

I believe that the Voyager receiver uses a PLL, phase locked loop to acquire the signal and filter out the solar noise. Also, the solar radiation is different to the transmitted signal which Voyager can use to differentiate between the noise with a band pass filter and some other electronics.

• Can you tell how you know this, and what it implies? Aug 13, 2016 at 13:53

The separation is still not too hard, for two reasons. One, the sun emits incoherent noise, while the DSN signal is carefully designed for coherent detection and processing by the spacecraft receivers. Two, the sun is a broadband source, which divides its power in the band roughly equally across the whole thing, while the DSN signal occupies only a tiny fraction of the band, so its power density is comparable. However, as the Voyagers continue to get farther away, the data rates they can comfortably support continue to decrease.

The main reference text for what follows is the DSN Telecommunications Link Design Handbook (Module 202), to which the DESCANSO document linked above directs the reader who wants even more detail than that contained. The DESCANSO text is also useful, answering parts of this question starting about five pages after the beam width graphic posted above, but I'll get to that a bit later.

Phase Coherence

The uplink signal carrier phase is tracked with the classic Costas variant of the digital phase locked loop. Costas, John P., "Synchronous communications", Proceedings of the IRE 44 (12) 1713–1718, 1956, doi:10.1109/jrproc.1956.275063.

The frequency which the PLL tracks measures the Doppler shift caused by the spacecraft motion (for deep space, always receding very rapidly). The beauty of this scheme is that the whole point of a phase-locked loop is to search the input spectrum for anything that might be coherent, and latch onto it while discarding everything else. There are comments below about what happens when the sun gets very close to the line of sight back to Earth, but the problem is not the total power output of the sun; it is the scintillation $$-$$ the variation of power with time $$-$$ that forces the PLL to run with so large a tracking bandwidth that it can't lock up properly.

Since the frequency of a carrier equals the rate-of-change of carrier phase, the Downlink Channel supports Doppler measurement by extracting the phase of the downlink carrier (Reference 1).

The Receiver and Ranging Processor (RRP) accepts the signal from the IDC and extracts carrier phase with a digital phase-locked loop (Reference 2). The loop is configured to track the phase of a phase-shift keyed signal with residual carrier, a suppressed carrier, or a QPSK signal.

There is an additional loss to the carrier loop signal-to-noise ratio when tracking a residual carrier with non-return-to-zero symbols in the absence of a subcarrier. This loss is due to the presence of data sidebands overlaying the residual carrier in the frequency domain and therefore increasing the effective noise level for carrier synchronization. In this case, $$\rho_L$$ must be calculated as (Reference 3)

$$S_L$$ = squaring loss of the Costas loop (Reference 4),

The one-sided, noise-equivalent, carrier loop bandwidth is denoted $$B_L$$. The user may choose to change $$B_L$$ during a tracking pass, and this can be implemented without losing phase-lock, assuming the change is not too large. There are limits on the carrier loop bandwidth. $$B_L$$ can be no larger than 200 Hz. The lower limit on $$B_L$$ is determined by the phase noise on the downlink. In general, the value selected for $$B_L$$ should be small in order to maximize the carrier loop signal-to-noise ratio. On the other hand, $$B_L$$ must be large enough that neither of the following variables becomes too large: the static phase error due to Doppler dynamics and the contribution to carrier loop phase error variance due to phase noise on the downlink. The best $$B_L$$ to select will depend on circumstances. Often, it will be possible to select a $$B_L$$ of less than 1 Hz. A larger value for $$B_L$$ is necessary when there is significant uncertainty in the downlink Doppler dynamics, when the downlink is one-way (or two-way non-coherent) and originates with a less stable oscillator (such as an Auxiliary Oscillator), or when the Sun-Earth-probe angle is small (so that solar phase scintillations are present on the downlink).

The user may select either a type 2 or type 3 carrier loop. Both loop types are perfect, meaning that the loop filter implements a true accumulation. In the presence of a persistent Doppler acceleration, a type 2 loop will periodically slip cycles.

They don't have a reference for explaining type 2 versus type 3 filters. A recent one I found interesting was P. Kanjiya, V. Khadkikar and M. S. E. Moursi, "Obtaining Performance of Type-3 Phase-Locked Loop Without Compromising the Benefits of Type-2 Control System," IEEE Transactions on Power Electronics 33(2) 1788-1796, 2018, doi: 10.1109/TPEL.2017.2686440.

References they did put in the above are:

1. P. W. Kinman, "Doppler Tracking of Planetary Spacecraft", IEEE Transactions on Microwave Theory and Techniques 40(6) 1199-1204, 1992.

2. J. B. Berner and K. M. Ware, "An Extremely Sensitive Digital Receiver for Deep Space Satellite Communications", Eleventh Annual International Phoenix Conference on Computers and Communications, pp. 577-584, Scottsdale, Arizona, April 1-3, 1992.

3. J. Lesh, "Tracking Loop and Modulation Format Considerations for High Rate Telemetry", DSN Progress Report 42-44, Jet Propulsion Laboratory, Pasadena, CA, pp. 117-124, April 15, 1978.

4. M. K. Simon and W. C. Lindsey, "Optimum Performance of Suppressed Carrier Receivers with Costas Loop Tracking", IEEE Transactions on Communications 25(2) 215-227, 1977.

Power Density

10 MHz is the full range of the RF spectrum allocated for the use of deep space research satellite communication, from 2010 MHz to 2020 MHz. However, the DSN does not fill that uniformly, and the spacecraft do not pay close attention to all channels at once. This is like your radio, which picks up the entire 20 MHz FM band (88.7 to 108.7 MHz), but only listens to one 200 kHz channel at a time. The difference is that, in order for this to work with the Voyagers, the channel instantaneous bandwidth needs to be very small.

The central result of communication theory is the channel capacity formula (Shannon 1948), which relates the theoretical maximum bit rate, $$C$$, to the occupied signal bandwidth, $$B$$ (though giving a rigorous theoretical definition of bandwidth is tricky), and the relative power of signal, $$S$$, and noise, $$N$$, as

$$C=B\log_2\left(1+\frac{S}{N}\right)$$

Note this uses the ratio $$S/N$$ not expressed in decibels, so 20 dB SNR means plug in $$S/N$$ = 100 to obtain $$C=B\log_2(101)\approx 6.66 B$$. If $$S = N$$, so $$S/N = 1$$, then $$C = B\log_2(2)=B$$. The quantity $$1 + S/N$$ equals $$(S+N)/N$$, which is what the display on a spectrum analyzer actually shows when you look at the amplitude of the Fourier transform as a function of offset frequency. If the "hill" you see on the screen is 3 dB high, that means $$(S+N)/N=2$$, so $$S=N$$. This statistic is sometimes called the Lawson-Uhlenbeck deflection ratio, in honor of the classic textbook Lawson, J. L., & Uhlenbeck, G. E., Threshold Signals, MIT Radiation Lab Series, Volume 24, New York, McGraw Hill (1950).

The data rates actually used in DSN for Voyager seem ridiculously tiny by near-Earth standards, but channel capacity and power spectral density tell us why it needs to be like that. Voyager Telecommunications on page 60 says

the command processor assembly (CPA) and the command modulator assembly (CMA) clock out the command bit stream, modulate the command subcarrier, and provide the modulated subcarrier to the station’s exciter for modulation of the RF uplink carrier. The command bit rates, the command subcarrier frequency, and the command modulation index (suppression of the uplink carrier) are controlled through standards and limits tables.

...directs the station to turn command modulation on and selects the 16-bps command rate and a calibrated “buffer” in the station’s CMA. The CMA produces the command subcarrier, which produces a 512-Hz square wave to match the subcarrier tracking-loop best-lock frequency in the Voyager CDU.

Exact numbers from here on depend on how exactly you prefer to define "bandwidth", and just how much of the DSN signal's power fits inside each one. The basic idea is the sun spreads its power nearly uniformly across the whole 10 MHz, as a blackbody in a narrow band is probably the closest nature gets to the theoretically-beloved "additive white Gaussian noise" (AWGN). When you view that on a power spectral density display, you get the result of dividing by bandwidth.

That is, since each bin in your histogram shows, for example, 1 Hz of bandwidth, then only one ten-millionth of the sun's power falls in each bin. If the whole DSN signal falls entirely within one such bin $$-$$ which is entirely possible if it is operating as an unmodulated carrier $$-$$ its SNR in that one bin is ten million times what its average SNR is over the whole 10 MHz.

Even when somewhat wider than that, there is still a considerable advantage; for example, if we use 512 Hz as the nominal bandwidth, then in those 512 of your 10 million bins, the DSN SNR will be 10,000,000/512 = 19,500 times higher than its average over all 10 million bins. The "actual" bandwidth of a square wave depends strongly on the author's preference, since it is a sum of all the odd harmonics, which gives the classic $$\sin(x)/x$$ shape in the frequency domain, with sidelobes that fall rather slowly. However, if we take 512 Hz at face value for $$B$$, then using 16 bps for $$C$$ means we only need $$1/32 = C/B = \log_2(1+S/N)$$, so SNR could theoretically be as low as -16.5 dB and DSN could still get the message through, even before considering things like error-correction coding gain.

Different tasks performed with different modulation schemes require different levels of SNR for equivalently acceptable performance, but explaining what they all are is quite complicated. Instead, I refer you to pages 64 and 65 of Voyager Telecommunications, which shows plots of how the ratio of telemetry power to background noise varies by year and day of year (the curves) versus SNR needed for certain bit rates to provide desired performance (the horizontal dashed and dotted lines). In those plots (which are actually for X band, not S band, but the idea is the same and they're the only ones I could find), variation based on time of year is as large as the difference between 2020 and 2005, but less than the difference between 2005 and 1995 (earlier years have bigger gaps than later ones).

Since you "modified" your question: The purpose of an antenna is to receive a signal not to filter noise. The Power voyager receives, could be sun + earth, earth - sun, sun - earth or only sun. The Modulation used is still unknown, so i cant calculate the needed SNR for it to work.

But the normal radiation level shouldn't be a problem for the voyager probe. Think of the sun as a constant emitter. Only flares create spikes. The spectrum of these radio waves will have a Gaussian bell curve (Watts/ Hz). The Engineers of Nasa will probably have picked a Frequency spectrum that is on one of the lower ends of this bell curve. The radio power of the sun decreases faster per Meter away from its origin then that of earth. Since earth uses directional communication and the sun is just a big ball of energy. So the true problem will be, to always point at voyager correctly.

• I'm pretty sure that it depends on many things. If you search for words like Voyager 1, high gain antenna, uplink (means from DSN to Voyager) and start reading, there's a lot there. The sun is pretty noisy at ~2GHz and the high gain antenna can not separate the earth from the sun. It transmits at ~8GHz but (if I read correctly) uplink is always at the lower frequency. There is a lot of work the 1970's space-hardened electronics has to do before demodulation. It's really incredible stuff!
– uhoh
Jul 20, 2016 at 13:38
• You cant calculate the Signal to Noise ratio without the energy put into the signal. Yes they state the Hertz and the kb/s, but these numbers dont help calculating the actual Watts the probe gets to use to decide what a signal means. The work you are referring is probably the signal transformation to a bit stream. (Demodulating the signal -> deciding what bit / byte that is -> checking against check sum)Again, without the used technique it is for me impossible to say what the signal to noise ratio is or, what the actual needed ratio is.
– Git
Jul 20, 2016 at 13:53
• That's a downlink signal, just to illustrate the "...mind-boggling large distances an weak signal...". So far I haven't seen an uplink. I'll add that to the label, Any receiver system has some frequency limitation before the first active stage. I read somewhere that the feed horn has a 20MHz bandpass for example, but there may also be a tuned circuit. Since the sun is broadband, the wider the frequency range exposed to the front-end (first active amplification state) the more chance of overloading it, especially if the sun is active. It's a real-world problem, not just a demodulation problem
– uhoh
Jul 22, 2016 at 0:15
• The frequency of the sun does not pose a problem, since it always stays the same. So you just have to use a Filter for these Frequencies, their Amplitudes. So you tune to your specific frequency, add a low high pass filter to get just the amplitudes you are interested, and then transform your signal back to lose the carrier. Then all the nice digital stuff takes place. The signal does not lose so much strength over distance since it originated from a dish not just a wire. But the sun does.
– Git
Jul 22, 2016 at 8:19
• @Git 1) the sun is a broadband source including some energy at the uplink frequency. 2) The inverse quare law applies just as much to the transmit antenna as it does to the sun. . Apr 9, 2021 at 6:30