Beacon satellite receiver software for ionospheric

tomography

Juha Vierinen

July 27, 2010

Abstract

We first give a short introduction to dual-frequency satellite tomog-raphy. We then introduce a beacon satellite receiver software that wehave developed using the Universal Software Radio Peripheral (USRP).We also discuss the cost of a receiver station when implemented using thisconcept.

1 Introduction

There are various methods for performing tomographic measurements of iono-spheric electron density. The most commonly used method uses delays of elec-tromagnetic waves transmitted from satellites and received at ground stations.These are linearly related to line integrals of the refractive index of medium.There are two different families of satellites that can be used for this purpose,low earth orbit VHF dual frequency beacon satellites [1, 2] and GPS satellites[find citation].

In the most optimal case, a receiver should be capable of observing both ofthese types of satellites and there should be a fairly dense network of stationsto allow good tomographic reconstructions at lower altitudes1. This type ofa receiver is only realistically feasible using a software defined radio, whichbasically means that most of the signals processing is performed with softwareon a general purpose computer instead of custom-designed signal processinghardware.

A software defined beacon satellite receiver consists of the following parts:

1. RF frontend (antennae, amplifiers and filters).

2. Personal computer with a sampler and a suitable RF front-end

3. Satellite ephemeris program that provides the geometry, timetables andfrequencies for passes.

4. Recording software, which records the dual-band signals from satellites atgiven times and stores them to disk.

5. Phase curve calculation software, which calculates the relative phase oftwo beacon frequencies.

1More specific details of geometry are currently being studied in the master’s thesis workof Johannes Norberg

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This approach has several advantages compared to custom made black-box typesolutions as the software is more easily customizable and in most cases resultsin cheaper hardware. We will thus focus on this approach.

The main part of this work has been to program VHF beacon satellite phasecurve measurement software that can be used automatically to record multipledifferent satellites simultaneously and produce phase curves, which can then beused in further analysis. We have also studied various other practical issues,such as antennas, amplifiers, filters, existing satellites, ephemeris calculationsetc.

The software that has been produced in the course of this work is in mostparts usable for routine ionospheric measurements already, but a good antennaand analogue front-end is missing.

Provided the necessary software, the hardware used in this study should alsobe capable of GPS TEC measurements, although this work does not explore thispossibility further.

It should be noted that Prof. Mamoru Yamamoto has been working on arelative TEC estimation software [3] that has many similarities with the systemthat we are building. It is likely that our projects will also collaborate on somelevel, as there are many possible synergies.

However, our purpose is to build a fully automated receiver that can beused for a large semi-autonomous chain of receivers. For this reason we haveopted to implement our own software from scratch. While our programs areindependently developed, we also will publish our software under the GNU opensource license.

2 Theory

The phase velocity of high frequency radio waves in plasma is

vp = cn−1, (1)

where n is the refractive index of plasma defined as

n =(1 − ω2

p/ω2) 1

2 . (2)

Here

ωp =

√Nee2

ε0me(3)

is the plasma frequency (rad/s) and ω (rad/s) is the frequency of the electro-magnetic wave propagating in the plasma. Ne is the electron density, e is thecharge of an electron, ε0 is the permittivity of vacuum, and me is the mass ofan electron.

The electric field amplitude of an electromagnetic wave propagating along zfrom a satellite at z = 0 with phase velocity vp is described as

E(z, t) = E0 cos(ω(t− z/vp)). (4)

From this we can determine the phase E(z, t) = cos(φ(t)) of a signal at a groundstation at z = L that has been transmitted from the satellite

φ(t) = ωt− ω

c

∫ L

0

n(z)dz. (5)

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In order to convert this into an integral of Ne(z) we remember that n(z) is afunction of Ne(z)

Ne(z) = −ε0meω2

e2(n(z)2 − 1), (6)

and we can with reasonable accuracy approximate this as a first order Taylorpolynomial expanded around n(z) = 1

Ne(z) ≈ −2ε0meω2

e2(n(z) − 1), (7)

and now inserting this into Eq. 5 we get

φ(t) = ωt− ωL

c+ aω−1

∫Ne(z)dz, (8)

where

a =e2

2ε0mec, (9)

which relates phase difference to the line integral of electron density between atransmitter and a receiver.

Now assuming that our geometry is known, we could directly use Eq. 8 toinfer about electron density along the ray path. However, in typical satellitemeasurements there are time dependent errors in satellite range r(t), whichcauses an additional term to the measured phase and assuming that this erroris small enough, the measured phase is:

φ(t) = ωt− ωL

c+ aω−1

∫Ne(z)dz +

ωr(t)

c, (10)

Now if there are two measurements at different frequencies ω1 and ω2{φ1(t) = aω−1

1

∫Ne(z)dz +R(t)ω1

φ2(t) = aω−12

∫Ne(z)dz +R(t)ω2

, (11)

there are two measurements and two unknowns, here R(t) = t+ (r(t) − L)c−1.which can be solved:∫

Ne(z)dz = TEC = a−1

(ω2

ω−21

− 1

ω2

)−1 (ω2ω

−11 φ1(t) − φ2(t)

), (12)

and

r(t) =

(ω1φ1(t) − ω2φ2(t)

ω21 − ω2

2

− t

)c+ L. (13)

The first equation is the basic principle behind dual frequency total electroncontent measurements (measurements of the electron density line integral). Thesecond equation is also useful, e.g., for accurate orbital elements determination,and this equation might also be useful if the chain of tomography receivers,as it provides a way of measuring orbital elements of “secret” beacon satelliteswith no published orbital elements, such as DMSP F15. More precise orbitalelements can also be used to further improve phase curve measurements.

In practice, a single receiver station cannot measure the full phase differenceω2ω

−11 φ1(t)−φ2(t). Instead, the receiver measures a relative phase curve, which

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measures the phase difference which the satellite transits over the receivingstation, and there will be an unknown phase difference factor that cannot bemeasured using one station only because the initial phase difference (when thesatellite is first observed) can only be measured up to modulus of 2π:

m(0) = [ω2ω−11 φ1(0) − φ2(0)] mod 2π (14)

This is why single station measurements are called relative total electron con-tent measurements, as the initial unknown phase difference contributes to anunknown additional total electron content, that must be added in order to ob-tain the true line integral of the electron density. This can be done e.g., byusing prior information on electron density or using multiple receiver stationsobserving the same volume.

3 Prototype hardware

Our prototype hardware consists of two λ4 ground-plane antennas, pre-amplifiers,

150 and 400 MHz band-pass filters and a USRP1 equipped with two WBX (50-2200 MHz) daughterboards. In addition to the 150 and 400 MHz frequenciesused by LEO beacon satellites, the daughterboards are capable of receiving L1(1575.42 MHz) and L2C (1227.6 MHz) GPS channels, which might be useful infuture applications.

The antenna was chosen simply because no better working antenna wasavailable at the time of this study. A better solution would be to design andmanufacture a quadrifiliar helical antenna similar to the one used by Yamamoto(2007).

To test the antennas, we recorded a spectrogram of the beacon satellite bandto see what is out there. This is shown in Fig. 2. It is evident that there aremany usable satellites on all of the existing satellite bands.

3.1 Receiver testing

In order to test that the receiver functions as expected, we fed several differenttest signals into a USRP sampler running the beacon receiver software. Thesignal generator and the usrp were both locked to the same reference so thatthe signals could be analytically checked. In this setup, we had a 60 MHz clockthat was fed into the beacon receiver as the sample clock. This 60 MHz wasderived from a 10 MHz Rb source, which was also used as a reference clockfor the signal generator that consisted of a USRP2 with a BasicTX and WBXdaughterboards installed. In practice, the dual frequency receiver does notrequire a very accurate reference, but our testing procedure does.

• Initially, we directly sampled the 10 MHz reference clock with the beaconreceiver and the BasicRX daughterboard tuned to 10 MHz. The signalappeared on baseband as expected.

• We then fed a frequency of 149.970 MHz, generated using a BasicTX tothe beacon receiver. It was correctly received both with the BasicRX andthe WBX daughterboards with a frequency accuracy better than 10−12.

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Figure 1: USRP1 with two WBX daughterboards (top left), Russian tomog-raphy antenna (top right), temporary antenna consisting of two λ/4 lengthelements (bottom left), prototype front-end including amplifiers, filters and abias-tee (bottom right).

• We then repeated the same setup and generated a 149.970 MHz signalusing a WBX in the USRP2. This was again correctly received withsimilar accuracy.

• Finally, we generated a 399.920 MHz test signal generated with the WBXonly, as the BasicTX cannot transmit over 170 MHz signals. This againwas successfully recorded using the WBX on the beacon receiver.

The tests indicate that the system is indeed phase coherent and can be used asa beacon satellite receiver.

We also tested that the beacon receiver worked with the internal 64 MHz os-cillator. The quartz oscillator had an Allan standard deviation of approximately10−10 in the order of 100 s.

Provided that the receiver frequency is calibrated (this can be done e.g.,from beacon satellites), it would be feasible to use the internal oscillator fortwo-frequency measurements. The only reason for the need of calibration is tomake it easier to find beacon signals. In theory, it would be possible to still findthe signals even without calibration, but wider channels would be needed insteadof the currently used 40 kHz and 15 kHz as the frequency error combined withthe beacon Doppler shifts could otherwise push the signal outside the receivedband.

4 Ephemeris programs

We have written several programs in python for the purpose of calculating thenecessary satellite ephemerides that are needed as geometry information for to-

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Figure 2: A spectrogram of beacon satellite passes over a ≈ 6 hour period (they-axis is time). The S-shaped lines are the Doppler shifted signals of beaconsatellites passing over the receiver station.

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Listing 1: beacon.tleOSCAR 231 19070U 88033A 10077.60011991 .00000056 00000−0 10000−3 0 73982 19070 90.2627 191.7413 0188614 318.0163 40.6635 13.27115826 60232−80

Listing 2: passes.txt# sta r t t ime end time f r eq1 (MHz) f r eq2 (MHz) bw1 (kHz) bw2 (kHz) peak e l eva t i on name1271099231.206 1271099391.208 150.012 400.032 40 .0 40 .0 31.705 OSCAR 231271105491.278 1271106001.284 150.012 400.032 40 .0 40 .0 67.754 OSCAR 23

mography and determining satellite the timetable and Doppler shifts for satellitepasses. These programs are implemented as command-line scripts, which canbe called on an automatic basis in an semi-autonomous network of tomographyreceivers.

4.1 predictpasses.py

The python program predictpasses.py is used to create a list of satellites thatpass over during the next day. The program can be configured to only acceptsatellites flying over some threshold elevation and which have a large enoughpeak elevation. The program also stores a file containing accurate geometryinformation for each satellite pass, which can be used for phase curve calculationand tomography. The program expects to have satellite orbital elements andcenter frequency information in the file beacon.tle. The format for this fileis very simple: The first three lines are standard TLE-format orbital elementsas obtained from celestrak or NORAD. The fourth line contains the parts permillion frequency deviation from 150 MHz and 400 MHz.

The program is called as follows: ./predictpasses.py "2010/04/12 14:10:00".The only argument is the starting time of the prediction. An example of theresulting passes.txt that contains a timetable of passes during the next 25hours is shown in listing 2.

4.2 get beacontle.py

There is a script called get_beacontle.py, which reads the newest ephemerisfiles from celestrak2 and generates a beacon.tle file. This should be updated ona daily basis, as satellite orbits are not stable on a longer timescale. The satel-lites of interest are listed in satellites.txt where the two comma-separatedcolumns indicate the name of the satellite and its part per million frequencydeviation, an example is shown in listing 3.

2an up-to-date database of satellite ephemerides

Listing 3: satellites.txtOSCAR 23,−80OSCAR 25,−80OSCAR 31,−145

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Listing 4: passes.txtj@l iang :˜/ Pro j e c t s /beacon\$ ./ beacon −−help

Program opt ions : u s r p t ex t r x [ opt ions ] f i l ename :−h [ −−help ] produce help message−W [ −−which ] arg s e l e c t which USRP board−r [ −−rx−subdev−spec1 ] arg s e l e c t USRP Rx s id e A or B ( de f au l t=A)−R [ −−rx−subdev−spec2 ] arg s e l e c t USRP Rx s id e A or B ( de f au l t=B)−d [ −−decim ] arg s e t fgpa decimation ra te to DECIM−f [ −−f r eq1 ] arg s e t f requency to FREQ1−F [ −−f r eq2 ] arg s e t f requency to FREQ2−g [ −−gain1 ] arg s e t gain 1 in dB ( de f au l t i s midpoint )−G [ −−gain2 ] arg s e t gain 2 in dB ( de f au l t i s midpoint )−8 [ −−width−8 ] Enable 8−b i t samples ac ro s s USB−−no−hb don ’ t use hal fband f i l t e r in usrp−e [ −−samplec lock ] arg sample c lock ra te ( d e f a i l t =64e6 )

5 Beacon Recorder

A program called beacon is used to record dual-band signals from satellitespassing over a receiving station. The program reads in passes.txt and usesa USRP device to record coherent two-channel band-limited data. The data isstored in binary format with single precision floating point complex interleavedIQ samples. There are two binary files for each pass, one for each channel.

The program tunes the two USRP daughterboards to two requested centerfrequencies (e.g., 150 and 400 MHz). These channels are then sampled at therequested bandwidth (e.g., 1 MHz) that is assumed to contain all the beacontransmissions. After the raw voltage data is transfered to the PC, the soft-ware further shifts each of the recorded channels to baseband and decimatesaccordingly. The band-limited and phase shifted data of each satellite pass isthen saved to disk in two channels for further off-line processing by the phasedifference curve calculation software.

Most of the program options are fairly trivial and can be accessed using the--help command-line option:

6 Beacon Phasecurve

The phasecurve calculation software is an R routine that is used for calculatingphase curves, given data files recorded using the beacon recorder software. TheR subroutine estimatePhaseCurve() can be used to estimate the phase curveof a given satellite pass. There are also various other routines that can be usedfor diagnostic purposes.

The phase curve calculation is implemented as an R script, which operatesfaster than real-time on a fairly new PC computer. The program first removesthe Doppler shift from both signals using the ephemeris. After this step, thebeacon signal appears very close to baseband on both channels. An examplespectrogram of a Doppler-removed beacon signal is shown in Fig. 3. After theDoppler removal, both satellite signals are very narrow band (¡ 50 Hz) makingit possible to store the “raw” voltage data using only several megabytes for eachsatellite pass.

The next step is then to calculate the phase difference between the twochannels. An example phase curve measured in 150 MHz scale is shown in Fig.4 The spectrogram of the signal, and the azimuth and elevation paths for thissame pass are shown in Fig. 6.

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Figure 3: Doppler corrected beacon signal. The satellite ephemeris is used tomove the signal Doppler shift to zero.

9

0 200 400 600 800

05

15

Phase curve 2010−07−11 14:13:24

Time (s)

TE

CU

0 200 400 600 800

015

30

150 MHz power

Time (s)

Pow

er

0 200 400 600 800

020

50

400 MHz power

Time (s)

Pow

er

Figure 4: A phase difference curve of satellite COSMOS 2429. The phase dif-ference is reported in relative TEC units (1016 Ne/m

2).

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Figure 5: COSMOS 2429 pass. There is still some interference in the band, dueto the noisy test environment and poor test antenna, but the satellite signalscan be clearly seen.

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Listing 5: Example usage for the satellite survey program%sudo ./ s g o f f t . py −R B −2 A −F 150 e6 −f 400 e6 −W −d 128 −e 1 −m 0 −p 65536 −t 10

−50 0 50 100

4050

6070

8090

All transits 2010.05.01

Longitude (degrees)

Latit

ude

(deg

rees

N)

●

Figure 6: Transits of all known 150/400 MHz beacon satellites above Sodankylaon 21/05/2010. The plot shows the foot point trajectory of each satellite.

7 Usable satellites

The number of usable satellites is still a bit uncertain, because our antenna isnot very optimal. The Russian satellites seem to be giving the strongest signals.The other satellites seem fairly weak although most of them give a detectablesignal. However, because the signals were too weak, we have only been able toverify that the Russian satellites give usable signals.

We have implemented a special measurement mode, which can be used tosurvey all of the satellites that produce signals within the bands. The programis basically a dual channel spectrogram analysis program with a relatively widebandwidth and high frequency resolution. The program can be left to run forseveral days, and the data can then be used to produce images such as the oneshown in Fig. 2. An example of how the program can be run is shown in listing5.

There is a fairly comprehensive list of current and historical beacon satel-lites on the internet. A plot of all possible measurable satellite passes aboveSodankyla on a single day is shown in Fig. 2: http://www.zarya.info/

Frequencies/FrequenciesAll.php. In addition to this, it might also be pos-

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sible for the same system to use the Chinese 180/480 MHz beacon satellitesand also the third 1 GHz channel transmitted by FORMOSAT. The receivercards are capable of using them already, but a different antenna and an antennaswitch would be needed.

8 Cost

An estimated minimum price for a beacon satellite receiver station hardware is3500 e, depending on how many receivers are built and what type of analoguefront-end is needed. However, a better antenna might increase costs significantly.The minimum price estimate is based on the cost of the cheapest componentsthat have been found for the purpose. However, the final cost depends on the

Device Price (e)

USRP 500PC 500

WBX 360BasicRX 50

Preamplifiers 100-200Filters 50

Antennas 200GPS clock 900

Cabling 200UPS 500

Total ≈ 3500 e.

Table 1: Cost breakdown of the digital beacon satellite receiver components.

specific choice of components, cost of labor and design of the receiver antenna.

9 Grand unified geophysical observatory

As the USRP is a general purpose radio acquisition device capable of operatingon a very large swath of radio spectrum, it is possible to also perform other geo-physical measurements with the device. In the introduction, we mentioned thepossibility of using the system also for GPS TEC measurements. But with littleadditional hardware and software, one can also use the system for ionosphericHF soundings. For example, with an additional USRP2 and a magnetic loopantenna, it is possible to perform oblique ionosonde soundings. Fig. 7 showsan ionosonde sounding performed with a USRP2 using the Sodankyla FM-CWchirp transmission. Due to the software defined nature of USRP2, very littleeffort was required to produce an ionospheric sounding with the hardware.

The Sodankyla ionosonde signal should be usable in all of the planned iono-spheric tomography sites. And in addition to the Sodankyl ionosonde, there arealso several other ionosondes that can be used.

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Figure 7: An ionosonde sounding performed with a single magnetic loop antennaand a USRP2 listening to the Sodankyla transmitter.

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10 Conclusions

We have implemented a working prototype of a beacon satellite receiver system.And while it is yet a prototype, most of the software would be usable alreadyfor a production system with some minor modifications that allow autonomousreceiver operation. The software already is fast and stable enough for real-timeoperation, so no difficult modifications are needed.

References

[1] M. Markkanen, M. Lehtinen, T. Nygren, J. Pirttila, P. Henelius, E. Vile-nius, E.D. Tereshchenko, and B.Z. Khudukon. Bayesian approach to satel-lite radiotomography with applications in the scandinavian sector. AnnalesGeophysicae, 13:1277–1287, 1995.

[2] T. Nygren, M. Markkanen, M. Lehtinen, E. D. Tereshchenko, B. Z.Khudukon, O. V. Evstafiev, and P. Pollari. Comparison of f-region electrondensity observations by satellite radio tomography and incoherent scattermethods. Annales Geophysicae, 14:1422 – 1428, 1997.

[3] M. Yamamoto. Digital beacon receiver for ionospheric TEC measurementdeveloped with GNU radio. Earth Planets Space, 60:21–24, 2008.

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