This report deals with the design of a satellite link between Mars and Earth. The mission on Mars consists on landers, which have to make measurements of Mars’s atmospheric conditions as well as to send pictures to earth. I propose a link with 1 satellite and 10 landers. This report discusses the different parts of the link like the antennas, the power needed or the orbital problems. Finally, it is shown that a satellite using equipment already existing on earth will fulfil the conditions.
During the last two years the interest for Mars hasincreased and the research area about the red planet are multiple. Is therewater on mars and under which form, was there a life on this planet somebillions years ago. Did the atmosphere has been comparable to the one onEarth. For these reasons and some others the necessity of a mission on theplanet to measure different parameters as well as to take pictures of thesurface increased. The last artificial satellite sent to mars was viking2.Our mission is going to land at the same place. But that was 25 years ago.The need of new datas leads the American and Russian governements to organizenew missions. Last year a small vehicule called "rocky" landedon the planet and has transmitted pictures to earth as well as it performedsome analysis of the martian ground. This year the mission mars polar landerwill land several small modules to analyze mars atmosphere, weather conditionand will send new pictures. In order to recover these data, a link betweenthe Earth and Mars is needed. Of course it will involve one or more satellites.The topic of this report is a model for this link with the condition thatit would be possible to communicate with the lander in less than three hours.First of all we will see the overall review of the project with a few detailsabout orbits. The technicals details and results will be explain in a secondpart.
I - OVERALL REVIEW OF THE PROJECT, GENERAL CHOICES
1 - PROJECT PRESENTATION
As explained in the introduction, the goal of thisproject is to establish a satellite link to transmit data from Mars to Earthwith one or several satellites. The number of satellites is not limitedbecause we don’t have any financial limits. The only requirement ofthis link is to be able to communicate with Mars within a 3 hours period.Of course the communication takes place at the speed of light so the signalwill only take 20 minutes to travel from one end to the other in the worstcase. This case occurs when Earth and Mars are on the two opposite sidesof the sun. The signal has to travel 2,5 Astronomical units (AU). We guessthat a lot of power will be necessary to carry the signal through space.
The design I propose is the following. The landerson mars will send their datas to a satellite above them. The satellite willbe on a equatorial geostationnary orbit and will be always in touch withthe landers. On the earth side, we will use three ground stations. Thesestations will be located at the followings places : Madrid (spain), Camberra(Australia) and in the states of Nevada (USA). These places have not beenchosen at random but to match the three tops of an equilateral triangle.By this mean we will always have one station able to communicate with thesatellite. These places have an other advantage, they are located in verydry area. Raining conditions are almost avoid and it appears that the disturbancedue to rain conditions can be neglected (<0,01dBs). The ground stationexists and are used for the mission Deep Space. Nevertheless we will seethat we use three times the same antenna. The existing antennas have differentsize.
Some orbital problems will occur. Due to the movementof the planets around the sun at different speeds, the satellite and Earthwill not be everytime at the right place to communicate. Details about thesepossible problems are provided in the part I-2.
2 – GENERAL CONSIDERATIONS ABOUT ORBITS
The major problem is to know how long Mars is outof sight from Earth. It means that when Mars is behind the sun and bothalign with Earth. This problem can be solved with the following assumption:The orbits of the planets are circular what is not true but avoid problemswith ellipsoid calculations. For this calculation and the following we usedthe data from table 1.
| Distance | Earth - Sun (R1) | 149,6 E9 m - 1 AU |
| Mars - Sun (R2) | 149,6 E9 * 1,524 m | |
| Radius | Sun (Rs) | 6,96 E8 m |
| Mars | 3,397 E6 m | |
| Year duration | Mars | 687 days |
| Earth | 365 days |
I only calculated the case from Earth. Earth is closerof the sun than Mars. So the sun aperture angle is the biggest and the nocommunication time too. The sun aperture angle from Earth is given by
The relative angular speed of Mars is Wrel=0,4623°/day.So the time taken by Mars to travel through the no communication zone is
This mission is designed to last 2,5 years. It meansthis phenomenon will occur one time during the mission so I assume thatit is not a problem to lose two days data.
Another problem is when the satellite is behind Marsrelatively to Earth. First we need to calculate the geostationnary orbitof Mars. This can be done using the Kepplers third law.
Where T is the orbital period in seconds, a the radiusof the orbit, m=GM/(10E9) and M the mass of Mars. This gives the resulta=20337 kms from the centre of Mars. The radius of the planet is 3397 kmsso the distance between the satellite and the landers is approximately 18200kms. The landers are near the place where Viking 2 landed. This is 46°north.
It’s easy to calculate (There’s no interestin giving more details about calculations)
Now we know b, we also know the satellite orbital period (the same as Mars)we can calculate the time the satellite cannot be seen from Earth.
This is within the 3 hours limit. Therefore, it wouldnot be a problem.
After this quick study of the possible interferencedue to the movement of planet around the sun and movements of satellitearound Mars, it’s time to see the technical details of this project.
II - TECHNICAL CHOICES
1-THE ANTENNAS
First, the antennas we use are parabolic reflectors. The choice of theantenna is correlated to the carrier frequency choice. Because as we knowthe gain of an antenna is given by the formula below.
where l is the wavelength and Ae the effectivearea equal to the physical area times the efficiency of the antenna.
Roughly, this formula shows that if the size of the antenna is very smallcompared to the wavelength then it yields to a negative gain. On the otherhand it’s not possible to put some very big antennas on the landers.We chose to have geostationnary satellite so it’s possible to use directiveantenna on the landers. A reasonnable size for them is radius = 1 m. Onthe satellite it’s possible to have bigger antennas, 3 meters. Finallyfor the earth station we chose 30 meters antenna mainly because it providesa gain very usefull when you receive weak signals. The properties, sizeand gain of the antenna are summarised in the table 2. For the noise temperatureof the earth station antenna, the value is a typical value for clear sky.The frequency used from satellite to Earth is 5 Ghz and 1 Ghz from satelliteto Mars.
| Diameter (meters) | |||
| 30 (earth stations) | |||
| 3 (satellite-> earth) | |||
| 3 (satellite->mars) | |||
| 1 (landers) |
Between the satellite and the landers, one antenna is used on the satellitefor both transmission and reception but with different frequencies. Onlyone antenna is used for the communication with the earth. The uplink frequencyis different from the downlink one.
| Antennas diameter (metre) | 3dB Beamwidth (deg) |
| 30 | 0,28 |
| 3 (Earth->Satellite) | 1,44 |
| 3 (Satellite->landers) | 7,2 |
| 1 | 4,32 |
2 - Power transmitted and received by the different antennas
On Earth, there’s nearly no problem with the power amplifier becausethere’s no weight limit and no battery or solar cells problems to provideenergy. We can assume that we will be able to amplify the signal as longas it is not under the noise level.
The power received by each antenna is given by the following formula.
Where Pt is the power transmitted, Gt/Gr the gains of the transmitting/receivingantennas and R the distance between the transmitter and the receiver. Dueto the rotation speed around the sun the calculation of the received powerfrom a satellite on earth has been done when the distance between the twoplanets is 2,5 AUs which is the worst case. The power requirements are basedon this value.
The satellite has 200 Watts transmitting capability provided by a 2 stages100 Watts amplifier. This amplifier is used for both transmitting to Earthand to Mars. If we apply the formula above we obtain the received powerat the different places. I list the different attenuation values and theantenna gains. The next results don't take into account the possible poweramplifier on the receiver side.
| Link | |||||
| Satellite -> Earth | |||||
| Earth ->Satellite | |||||
| Satellite -> Landers | |||||
| Landers ->Satellite |
I didn't take the atmospheric attenuation into account but if we referto figure 8.6 in (1) we can estimate it equal to - 0,5 dB because the stationsare more or less at the see level. It's possible to neglect this effect.The Earth transmitting amplifier is a 8,5 kW (39 dB).
For high tech electronics it's no problem to work with a signal as weakas -50 dB so we need to amplify the signal from the landers to this level.Approximately 80 dB what can be achieve with 4 stages 100 Watts low noiseamplifier. After this amplifier, the signal is regenerated and then transmittedto Earth.
Each part of the amplification system has its own gain and noise temperature.These parameters are summarised in table 5. The system uses a cooled LNAand cooled downconverter. The cooling is done with liquid helium (4°K)
| LNA | ||
| Downconverter | ||
| IF amplifier | ||
| Wave guide | ||
| Antenna |
The system noise temperature is
For the landers and the satellite, the system noise temperature is verylow due to Mars’s thin atmosphere and temperature in space (3°K).We will see in the part II-4 that the only critical part of the link isfrom the satellite to the Earth. The natural conditions give us a low noisetemperature so it will lead with other factors to good signal to noise ratiofor all the other links. The noise temperature of the receiving and transmittingsystems with Earth on the satellite is less than 10°K. For the communicationwith Mars it’s 170°K due to the antenna looking Mars.
These values will be used in the part II-4 to calculate the signal tonoise ratio.
3 - THE COMMUNICATION SYSTEM AND PROTOCOL
Further than the physical problems we need to set up a communicationprotocol between the landers and the earth station. The aim of this protocolis to give the possibility to the landers to send their data in relativelyshort amount of time and to the earth to send commands to the landers. Todesign this protocol the following assumptions have been done:
- There are ten landers. Each one is transmitting one picture per hourand data every ten minutes.
- The picture is a typical SVGA picture with 1024*768 resolution and256 colours (or 256 grey levels). So each pixel is coded with 8 bits.
- The data are measurements like temperature, moisture and wind. Eachone is coded with 8bits.
With these assumptions, it’s possible to calculate the minimum bitrate required in order being able to transmit the picture and the data.
The size of the picture is 1024*768*8=6291456 bits or 786,432 Kbytes.
The size of one hour of data is 3*6*8=144 bits or 18 Bytes.
Our goal is to transmit 786432+18=786450 Bytes in less than one hour.That yields to a minimum bit rate of 219 Bytes per seconds. That is, wechose 300 Bytes as a bit rate to have a reasonable margin and a carrierfrequency of 1 Ghz (This choice is correlated with the antenna design).To avoid a too complex communication protocol we use a FDMA protocol. Eachlander transmit with its own carrier which is far enough from the othercarrier (1 MHz) to suppress intermodulation noise but not so far becausethe bandwidth needed is not important.
The modulation technique use is a differential PSK for several reasons.First, it provides an auto synchronisation for the receiver. Second, itachieves a good signal to noise ratio for a reasonable power. Finally there’sno need for a QPSK or MPSK because we don’t need a bit rate higherthan the bandwidth. The receivers are coherent receivers, that leads tothe same bit error rate as a non-coherent one but with less power. Therefore,with the same power we would be able to achieve a bit error rate of 10E-6.
The worst case for the satellite is when all the landers are transmittingat the same time. Its link to the earth has to be able to transmit 10 timesthe bit rate of the landers. To avoid synchronisation problem and bit lossa bit rate of 3 Kbytes per second has been chosen. The carrier frequencyof this link will be 5 Ghz.
The figure below shows the structure of the frames use by the communicationprotocol. The structure is very simple. In order to simplify the circuitin the satellite, each lander does their own frame, which they fill withdata and address. Address is used by the TDMA system to know the originof a frame or to whom a frame is sent.
The system inside the satellite is as shown on the figure below. Thearriving signal is Bandpass filtered, demodulated and then buffered. Thereare 10 primary buffers and 10 secondary buffers. The size of the bufferis the same as the frame (The frame structure is given figure 5). When aprimary buffer is full, it is copied to the secondary. This one is emptiedat the bit rate of 3 Kbytes per second. All the frames are multiplexed intime (TDMA) and then modulated with the carrier 5 Ghz. Of course, a HF amplifieris present after the modulator. It provides the necessary power to signalto travel to earth. The details of this amplifier are discussed in the partII-2.
From earth to satellite, a 4 Ghz carrier will be used. To send commandto the landers, a 1 Ghz carrier will be used. One frequency will carry theorder from the satellite to landers. As we can see, the system is much simplerthan in the other direction. The reason is that all the landers receivethe order but only the one who reads its address in the frame applies thecommand.
On earth a computer is in charge of the reconstruction of the picture.This is fairly simple because each frame carries the kind of data and thelander from which it comes.
4 – Signal to noise ratio
It’s important to maintain a good signal to noise ratio. A goodprobability of error (or bit error rate) would be 10E-6. This rate leadsto a couple of error each hour. This can be achieve with
The probability of error is given by
Where erfc is the complementary error function, N0 is thenoise power and Eb the energy of the signal.
If we apply this formula we obtain Eb/N0=11,06 or 10,4dB.
The SNR at the output of the Earth station is given by
This result fits the required 11,06 to achieve a 10E-6 bit error rate.I assume that Eb/N0=C/N which means that the bandwidth of the signal andthe bandwidth of the receiving filter are the same in addition to the factthat we transmit one bit per symbol. The following table summarises thebit error rate for the other parts of the link. But, these results are lessimportant because they are not critical as the link between satellite andEarth.
| Link | ||||
| Earth->Satellite | ||||
| Satellite->Earth | ||||
| Satellite->Mars | ||||
| Mars->Satellite |
The good results obtained are due to the low bit rate and the power received.Even the critical path will suffer only a couple of error per picture.
In this report many things have been neglected but the main aspects arepresent and study. Each time there was a choice to do, I tried to determinatewhat was the worst case. This method led me to the report you just red.Nevertheless, I think this design is reasonnable but my knowledge in thearea of satellite communication is not so wide. However, I increased thisknowledge during the making of this report. Soon we will see the resultof the Mars polar lander mission actually in progress. The goal of thismission is more or less the same than ours. The architecture of this missionis very close to ours and then it will be a good test to see how the missionworks. Of course, it will work.
[ 1] Timothy Pratt,Charles W. Bostian : Satellite communications John Wiley & son,1986
[ 2] Simon HaykinDigital Communications John Wiley & son, 1988
[ 3] G. Maral andM. Bousquet: Satellite Communications Systems, Techniques and Technology,John Wiley & son, 1998