How to analyse your measurements of the signal strengths

Joachim Köppen Strasbourg 2013

The record file looks like this
#Start at: UT 12.04.2010 20:42:24
# time[UT] s-value dBm
20:42:24.820 49 -112.67
20:42:24.920 58 -112.22
20:42:26.021 125 -107.66
20:42:26.122 140 -106.06
20:42:27.223 152 -104.33
20:42:27.323 221 -103.36
20:42:28.425 238 -103.2

As indicated in the header, the first column is the time, and the third is the signal power, measured in dBm, i.e. deciBel with respect to 1 mW. The second column is the number with which the receiver coded the signal strength. It is of no importance for us.

The data can be analyzed with Microsoft Excel or a similar program. Import your file into the program. Under Excel you go to: File -> Import -> TextFile -> Select your TextFile -> Delimited Textfile -> Delimiter is spaces -> Finish

It is a good idea to change the Format of the first column to mm:ss.0 so that we do not lose the fractions of the seconds! The next step is to make a simple plot of the signal power as a function of time. It is best done as a scatter plot, where the first column serves as the x-axis, and the third as the y-axis. We also recommend to switch off the symbols marking each datum, and use a fine trace for the curve only. This will show better all the structure in the signal.

It is also a good idea to create another column which contains the time difference (in seconds) to the first time, which will be close to AOS ...

In this example of XI-IV data we see

From the maximum signal, which would normally occur at minimum range, we can now use the link budget to work out the power of the satellite transmitter.

• our measurements refer to the power at the receiver's antenna socket. We have to correct for the losses in the coaxial cable (-2.5 dB) to the roof, and for the gain of the mast-head pre-amplifier (+20 dB)
• our antenna gain: +19.3 dBi
• there are about 3 dB losses from the long coaxial cable from the antenna to the receiver
• free space loss: needs the range
• neglect other factors, like ionospheric absorption ...
• assume a reasonable value for the transmitting antenna gain: 0 dB

With our software we measure the level of the signal at the antenna socket of the receiver. This is not the signal power picked up by the antenna, because there are the losses in the cable to the roof, the mast-head preamplifier, and the antenna has a cetrain (pattern) gain with respect to an isotropic antenna. We may take all these factors together and define a "station gain". The technical specifications for our ground station give this theoretical value for 430 MHz:

-3 +20 +19.3 = +36.3 dB

In winter 2011, Feng-Lei Wu observed several passes of the cubesats XI-IV and Cute-1, and carefully measured the signal strengths of their telemetry beacons. From his data he established these values of the station gain:

In both values one has to add an estimated uncertainty of +/-1 dB for the calibration of the receiver ... with a signal generator that had not had a recalibration for several years. Also, we assume 0 dBi for the satellite's antenna gain.

As it is unlikely that the transmitter power of a satellite becomes higher with time, and as the value obtained with Cute-1 is closer to the theoretical value, we believe that our ground station has a measured gain of +33.0 dB. We recommend to use this value in your analyses and enter it in the PassFinder applet to get the predicted signal powers. The remaining difference of 3 dB could well be the sum of all additional losses from the connectors and the uncertainties in the calibration of the measuring software.

Now that we have established a good value for the station gain, we can try to measure and monitor the powers of satellites: The above values also show that signal strengths of the two satellites differ significantly, by 3 dB. It appears very likely that the transmitter of XI-IV is really lower. It nominal power is indeed 80 mW (+19 dBm). May be this has come down by another 2 dB since its launch in 2003 ... From a single observation of XI-V, Feng-Lei estimates a transmitter power of +15 dBm (32 mW), whereas its nominal power should be the same as that of XI-IV.

Let us carry our analysis a bit further, by comparing the measured curve of signal power as a function of time with the curve predicted from the link budget and the range-time relation computed from the orbital geometry.

You have three possibilities:

Let us use the first option: compute with the PassFinder applet the passes predicted for the satellite on the day of observation. Also enter the correct value for the station gain. Then click Pass: Textoutput and use the buttons next pass and previous pass to choose the proper pass. Please note that the times are given in local time (CEST)!! Then you will get this table in simple ascii text:

Copy this text into a text editor, store as a file and then import it into Excel. The times are the times (in seconds) after AOS.

It is a good idea not to plot the predicted data straight away, but to allow that the predicted curve can be shifted in time as well as in the power level. In this way you can correct for some delay of the observed data in case the recording was did not start right at AOS. Similarly, you can modify the predicted signal strength in case the real transmitter power might differ from the one assumed in the predictions. Therefore create two cells which contain the values for the time and power shifts, and then create two new columns which contain the predicted times plus the time shift, and the predicted powers plus the shift value. These two columns you then add to the plot of the measured signal strengths, to get a plot like this:

If you want to make any other plot to display any detail of the pass, such as the variation of the Doppler shift with Elevation, you can use either the Applet directly, or plot the data from the table of prediction on your worksheet ...

Now we have to see what can be deduced from this comparison: see the results for our example pass

You might instead use our worksheet: in the yellow cells you input all the various parameters. It would look like this for our example of the XI-IV observation from 24 march 2009:

The measurements were taken every second (as set and indicated by the software), but we are not interested in the ups and downs between the Morse code beeps and the pauses in between. What we really want is an upper envelope of all the curve peaks ... so we may improve the appearance of our measured data:

We proceed in two steps: First, we fill the column D with the maxima of a number, say 5, of the preceeding values in the signal powers in column C. For example, in D100 we put the formula

= MAX(C100:C95)
If we make another plot to check the results:
we see that at each time, we get the maximum value during the past five time points. But this looks rather jumpy, so in a second step we shall smooth this angled curve a bit: We make another column E, where e.g. cell E100 gets the formula
= AVERAGE(D105:D95)
Another plot shows us that the result is now quite close to how we would have drawn an upper envelope curve:
One may play with the numbers over which one takes maximum and over which one smoothes, but numbers around 6 are quite a good compromise between preserving interesting structures and washing out less interesting fluctuations.

In this example of XI-IV data we see

• the maximum signal strength at closest approach was a bit more than -100 dBm
• however, shortly after AOS, the signal was even stronger for about a minute or two
• during the pass, the signal showed almost periodic changes, with a period of more than one minute. It is likely that these fluctuations are caused by the tumbling motion of the satellite, during which the transmitting antenna is directed towards us or is obscured by the satellite's body.

Whatever method you apply, for a direct comparison with the observed data, you make the appropriate links to the worksheets with your measurements and the predictions. We have performed the analysis with the complete 'cosmetics' using a different program and obtain this plot:

which shows that the peaks of the signal roughly follow the predicted smooth curve, but that there are a few discrepancies:
• while the duration of the pass agrees very well with the prediction, the maximum signal does not seem to happen at the predicted time
• the signal just after AOS - when the satellite still is close to the horizon - is larger than at any moment thereafter. Could this be an unusual mode of propagation?
• if one wants to match the peak value of -100 dBm with a satellite's EIRP of 100 mW (from the published satellite specifications) one would need a value of only 28 dBi for our antenna gain. However, the GENSO specifications are 19 dBi antenna gain plus 20 dB preamplifier gain ... thus there seem to be unaccounted losses somewhere in the link budget ...
• ... but if we put in the 36 dBi to account for our antenna, preamplifier, and cable losses, the predicted signal strength shortly after AOS would be about -110 dBm, which is close to the measured signal! We must conclude that this "extraordinarily high" signal at AOS represents the full power received, but that at later times the satellite's antenna was simply not oriented for optimal reception by our station!

last update: Apr. 2013 J.Köppen