You have to know that Galileo Galilei is among my top 5 best inspirational personalities, and the inevitable consequence of such admiration is being a space nerd. But this equation won't be complete if I don't mention that software engineering is my home and my background lays in electronics and telecommunications.
Having said that, a few weeks ago I thought I wanted to start writing a series of articles about the Apollo AGC (Automatic Guidance Computer)— maybe more specifically about the Apollo Lunar Lander AGC — to tribute these passions I have: Software, Space, and Electronics & Telecommunications.
Now, I can see the question mark on top of your head asking “but man, what does the Apollo Lunar Lander AGC has to do with interplanetary communications? Is this phishing?”, and the question is one hundred percent legit. The answer is that each space program for each nation would count for nothing without telecommunications.
So yes, all Apollo’s AGCs were on top of a spaceship cruising into space at 40233 Km/h and communicating telemetry back to Earth. It was between 1968 and 1972, and the understanding of the AGC will first go through the understanding of how Earth-Space telecommunications works.
Guglielmo Marconi and Heinrich Hertz
The term telecommunications comes from the greek tèle, which means far, hence, communicating (sharing) with something (or someone) far away. The man, during his history, evolved this technology from beacons, pigeons (not a joke), telegraph, telephone, to radio, television, and eventually the current internet. We can easily categorize the above-mentioned technologies into wired and wireless, for instance, the pigeon was definitely wireless (also slow and unreliable), but the telegraph was wired until 1894 when the Italian inventor and electric engineer Guglielmo Marconi made the first long-distance radio-telegraph communication.
Heinrich Hertz (a German physicist), indeed, discovered in 1886 the physical phenomenon described as radio waves, and Guglielmo Marconi has first created a physical radio transmitter. It was a complete game-changer, probably the most important in the history of telecommunications, because since 1894 men are able to communicate all around the world and into space without wires and at the speed of light.
It was just a telegraph, but enough to change telecommunications forever.
Radio waves are a type of electromagnetic radiation within the electromagnetic spectrum and they range between 3kHz and 300GHz with respective wavelengths between 100Km to 1mm. In the previous chapter I said the radio waves travel at the speed of light, but to be exact, the speed of light is possible only in a vacuum, such as space, while on Earth will be only slightly below the speed of light due to the atmosphere.
Note: I am going to add some formulas from now on, but they are not necessary for the general understanding.
Of the electromagnetic spectrum, we are interested only in the radio waves, and as we can see from the image above, the wavelength is inversely proportional to frequency, hence, the higher the frequency, the smaller the wavelength, and the lower the frequency, the bigger the wavelength. We then can state the following formulas:
We have understood that radio waves are the carrier we use to transmit and receive information to then be used by media such as smartphones, televisions, computers, satellites, space probes (you don't say!), and many many others. What is obvious is that for this system to work we need at least two (or more) actors, and all parts will transmit and receive through the so-called antennas.
When transmitting, an electric signal coming from the radio transmitter is applied to the antenna that radiates it under the form of radio waves. When receiving, the behavior is exactly the opposite. The energy of the radio wave is intercepted by the antenna that turns it into an electric signal that will be processed from the radio receiver.
The dimension of the antenna changes with the frequency we want to transmit and/or receive, but also there are a variety of antennas depending on the application and frequency band.
Of course, the schema above can be also applied vice-versa, meaning the probe/satellite transmitting all the way back to the base station on Earth.
Yet another piece into this puzzle, and we will be ready to understand all we need to comprehend what an incredible piece of science and engineering is the interplanetary telecommunications.
The radio wave spectrum is divided into different bands, which go from the lowest frequency ranges to the highest. This division is arbitrarily made by the international body called ITU, International Telecommunications Union. This union is an agency part of the UN and it is specialized for everything that is information and communications technologies. It has been established in 1865 (formerly called International Telegraph Union).
At this stage, we know what radio waves are, how they are classified, and that we can use this physical phenomenon to carry information in a wireless manner, and that we need antennas to transmit or receive any of them.
The exercise we are going to do now is to make the information above a little more specific with a real application that is interplanetary telecommunications. The question we will answer (always in a nutshell) is, for instance, how do we communicate with the Mars missions?
ESA Mars Express
The Mars Express is a space exploration mission started in 2003 (and still active) operated by the European Space Agency (ESA) and it has the objective of studying Mars. It was also the very first interplanetary mission for ESA. The mission was made of two parts, the Mars Express Orbiter and the Beagle 2, which was a lander for performing exobiology and geochemistry experiments on Mars surface. Unfortunately, the lander failed its deployment after landing on Mars, but the orbiter has been successful and still active today.
The problem here is quite clear. How do we communicate with our orbiter and all the assets we have on the surface of Mars from the Earth? How can we get data and all the fancy images we see on the internet?
Mars is very far away, although, for the cosmic orders of size, is here in the backyard, and what we know for sure is that we are going to leverage radio waves, and looking at the distances we can immediately point out challenges.
The great cold distance
- Minimum: 54.6 million Km;
- Maximum: 401 million Km;
- Average: 225 million Km.
Transmission and reception times
We won't have any real-time communication and this is easily calculated:
From the formula above we can state the following:
- Minimum distance: 54.6 millions km = 186 seconds (3 min 6 sec);
- Maximum distance: 401 millions km = 1336 seconds (22 min 16 sec);
- Average distance: 225 millions km = 750 seconds (12 min 30 sec).
Line of sight
We have to take into account the relative motion of planets because both Earth and Mars are revolving around the Sun at different speeds (which is the reason why we have the minimum and the maximum distances) and rotating on themselves as well. The line of sight problem is quite a big one because say we have an antenna on Earth and we want to receive a signal from our orbiter on Mars, what happens is that we have to wait for that precise moment when both we and the orbiter around Mars can look at each other and for enough time for the signal to travel from Mars to Earth. Tricky, ah?
The solution is to have a network of antennas at different locations on Earth so that whatever is our position in relation to Mars the orbiter will always have a line of sight towards Earth. It already exists and it is called DSN, Deep Space Network.
In the specific case of ESA Mars Express, the orbiter is also making the use of other three ESA stations, for a total of six:
- New Norcia, Perth (Australia);
- ESOC OCC, Darmstadt (Germany, EU);
- Kourou (French Guyana).
Distance also affects the so-called bitrate. The more we are far away the less bitrate we can use. In the case of Mars, this is still not a "big deal" (and we will see why), but if we take into account missions like the Voyager or New Horizons then, this gap becomes wider. This problem is addressed by the Shannon–Hartley theorem that calculates the maximum rate (bits per second) at which information can be sent error-free through a channel of a given bandwidth and in presence of noise. This is also known as Shannon's channel capacity.
The attenuation of the radio energy over the distance between two antennas is identified by the FSPL, Free Space Path Loss and it increases with the square of the distance as the radio waves spread following the inverse square law.
Therefore, we can state that the total signal power received can be calculated by summing the power and the gain of the transmission antenna, the power of the receiving antenna, and subtracting the FSPL.
We also have to consider another variable that is the noise, and it is calculated by summing the receiver noise figure and the noise given by the components inside the signal chain, also known as the signal processing electronic components.
Hold tight because we did it! We have all we need to calculate the transmission capacity — better called the channel capacity — applying Shannon’s limit.
As I said in a note inside this article, the mathematics I am showing here is not really necessary to have the general understanding of how telecommunications work between one probe on Mars and an antenna on Earth, but I think it is fun to see a little snapshot of the world that enables these communications to happen, so, let’s put the ESA Mars Express numbers into the equations.
I will leave also a little code snippet in R to run all the calculations, moreover, I am planning to make a special article in order to go deep into the Shannon-Hartley theorem and also the link budget (which I didn't mention in the article, but still part of a bigger picture).
Note: the signal-to-noise (SNR) ratio will change over time during the communication and it can be for a number of reasons, such as the antennas on Earth adjusting their elevation (and some also the azimuthal position) to compensate for the relative motion and so will do their system-noise factor, but also the weather can have an impact because snow and rain are slightly changing the surface of the reflector of the antenna.
After calculating the Channel capacity we know that we can’t transmit over 5.17 Mbit/s without risking a big number of errors in the communication. After all, if you think about it, this bitrate is amazing given the gigantic distance in between us and Mars.
The ESA Mars Express orbiter is equipped with antennas for S-Band and X-Band. If you look again at the calculations you will understand that we were working on the X-Band transmissions. These antennas are of two types:
- HGA (High Gain Antennas, 1.60m diameter dish reflector mounted on a gimble for adjusting the orientation) — Both for S-Band and X-Band. The transmission via the HGA antenna can be either S-Band or X-Band one at a time, but both bands can be received at the same time.
- LGA (Low Gain Antennas) — There are two LGA antennas and they are only used to transmit and receive S-Band.
HGA antennas are also known as directional antennas. As for the ESA Mars Express orbiter, they are mainly used for receiving and transmitting at greater power and greater precision (they produce a very narrow beam) at very specific directions (they are extremely directional), characteristics that make them perfect for long-range communications.
LGA antennas radiate signals in an omnidirectional manner (the opposite of HGA that are directional). All spacecraft are equipped with LGA antennas and are usually used as backups.
One of the most important ground stations is the DSN (Deep Space Network) and it is a network of arrays of reflector antennas located in three different locations:
- Goldstone (USA);
- Madrid (Spain, EU);
- Canberra (Australia).
These stations are located more or less at 120 degrees one from another. 120 + 120 + 120 = 360 degrees. This will make sure that the orbiter around Mars (and whatever other deep space mission) is able to always communicate with at least one location.
The typical bands of frequencies used for communicating with spacecraft are microwaves (or slightly lower):
- S-Band: frequency 2–4 GHz, wavelength = 15–7.5 cm;
- X-Band: frequency 8–12 GHz, wavelength = 3.75–2.5 cm;
- Ka-Band: frequency 26.5–40 GHz, wavelength = 11.1–7.5 mm.
There are also other types of antennas that the ground stations are using (such as HEF), but the Beam Waveguide (BWG) antennas are now taking place to replace the others. Normally, the antennas used for performing these types of communications are reflectors, and with their very large dishes (usually between 34 to 70 meters), they are intended to literally collect radio waves and reflect them into a central focal point.
Reflector antennas are extremely directional, which means that the probe on Mars (or whatever deep space probe) must be precisely aligned towards Earth in order to get its signal received. This extreme directionality, though, is also working as a filter for all the rest of the radio waves that reach Earth.
Once the radio waves are reflected into the subreflector, they are channeled into the so-called beam waveguide (BWG). The BWG has a series of mirrors that are guiding the radio waves beam into a series of filters which will decouple the right frequency bands (S-Band, X-Bans, Ka-Band) to be then amplified and computer-processed into electric signals and sent to the central control room.
The very reason why BWG antennas are being used is that if the signal is translated into an electric signal directly in the subreflector, then the signal would be too weak to be sent via wires to the control room, and then there would be the necessity of filters and amplifiers in the subreflector, and this will make the subreflector extremely big and heavyweight.
Note: the live view of the DSN traffic is available at DSS Now.
Deep-space telecommunications doesn't work as our Internet, like the TCP/IP protocol where the client and the server are continuously checking that their communication is happening the right way. As for the challenges that we have mentioned before, despite radio waves runs at the speed of light, the great distance between us and the spacecraft is simply too big to be covered in a real-time manner and that won't allow us a continuous data acknowledgment. So, how do we cope with errors in communications? The answer is channel coding.
Channel coding is a wide error correction technique based on redundancy. There are many solutions within the coding theory, but to just make the simplest example, one of them is the repetition code where the information is encoded by an algorithm (before being sent) and literally repeated many many times. The probability of getting all the repeated information corrupted is very low and then the receiver will be able to find at least one good piece of information to continue reading correctly.
In conclusion, error correction techniques are used when the communications channels we are using to communicate are unreliable, noisy, and distances bigger than the speed of light are involved, and this is exactly the case when, for instance, we have to exchange data with a deep-space spacecraft.
I didn’t want to make this article that long, but when I started writing it I have realized that some more context was needed even if the article is meant to be for those who are not experts in this field. I skipped a few topics such as polarization, beamwidth calculation, and modulation (and I will be probably doing specific articles for these topics), but again, this article is meant to be for an entry-level understanding of a very complex topic. I hope this article has satisfied your curiosity. Thanks for having read!
As I said in the preface, I have started a series of articles about the Apollo AGC, more specifically about the Lunar Lander AGC. I hope you will follow that. I will try to publish a chapter every two weeks starting from May 2021.
Also a little off-topic, discover how many Martian years you have. I would be 19!
Thank you again!