The next two graphs show Frequency Change Compensation applied to two adjacent audio subcarriers from a single transmission by VK3LM. This transmission was recorded by: KB4YZ, W8ZCF, and W9NTP. The Frequency Change Compensation applied to the (nominally) 1955 Hz and 1725 Hz subcarriers is shown below
Note in particular the changes applied for the three blocks where the "Framing Sequence Index" at the start of the block is: 0, 3, and 7.
For the 1955 Hz subcarrier, all three receptions showed that the Frequency Change Compensation for the block starting at "Framing Sequence Index" of 3 was higher that it was for the first or last block.
For the 1725 Hz subcarrier, this was still true for the signals recorded by KB4YZ and W9NTP. However, for the signal recorded by W8ZCF, the Frequency Change Compensation for the block starting with "Framing Sequence Index" of 3 covered about the same range as it did for the first and last blocks.
Taken together, I believe these two graphs show that the source of frequency changes during this transmission was not in the transmitting, or receiving, equipment, but was caused by changing motion within the ionosphere.
The next two graphs show an example of dramatically improved performance resulting from applying Frequency Change Compensation.
The first graph shows the Frequency Change Compensation applied to the bottom 4 audio subcarriers for a transmission by VK3LM and a reception by W8ZCF.
Although these Frequency Change Compensations lie within a band about 7 Hz wide, the second graph below shows a dramatic reduction in the nominal capacity of the outer code that had to be used in order to correct the errors left by the inner decoder.
As the red trace in the second graph below shows, without the Frequency Change Compensation (fcc), all but two of the blocks used more than 60% of the nominal capacity of the outer code; two of the blocks used about 106% of the nominal capacity, and block index 6 used in excess of 140% of the nominal capacity of the outer code.
As the blue trace in the second graph below shows, with the "fcc", no more than 30% of the nominal capacity of the outer code was used. Thus, more errors due to noise could have been corrected in this case.
Below is the Frequency Change Compensation applied to the bottom 4 subcarriers of a signal transmitted and received by KB4YZ.
It looks to me like the exponential decay of a 1st order system in response to a step function. The total change in frequency shown here is a little less than 8 Hz.
Below is the outline of the steps used to calculate the Frequency Change Compensation to be applied to the audio subcarriers.
The graph below is based on calculations made by a satellite tracking program, for the conditions listed. The time to pay particular attention to is near 18:00 UTC, when the downlink Doppler shift was predicted to be a little less than 15 KHz.
Below is an estimate of the rate at which the downlink Doppler Shift was changing. The apparent oscillation of the values in this plot results form the limited resolution of the data produced by the satellite tracking program and roundoff error.
Thus, near 18:00 UTC, the estimated rate of change of the downlink Doppler shift of the AO-40 signal was about 50 Hz per minute.
The graph below shows the Frequency Change Compensation applied to the bottom 4 subcarriers of a recording made by W9NTP, from a transmission by W8ZCF through AO-40 at about 18:02 UTC on March 31 of 2003. Applying the compensations for changing frequencies resulted in the successful decoding of this recording.
Also plotted is a line showing a 50 Hz per minute slope.
Although the section from "Framing Sequence Index" equal to 1 through 4, shows some slopes close to 50 Hz per minute, the other sections show radically different slopes. Most of these other slopes are negative, showing frequency DECREASING with time.
Thus, in this case, the frequency changes produced by the rate of change of the downlink Doppler Shift were overwhelmed by other causes, producing an overall result of DECREASING frequency with time for most of this transmission.
The data shown below were obtained from a transmission and reception through AO-40 about 20 minutes later. At this time, the satellite tracking program indicated that the rate of change of the downlink Doppler Shift would be about 55 Hz per minute.
As the Frequency Change Compensations applied to the bottom 4 subcarriers show, in comparison with the 55 Hz per minute line, the overall frequency was actually changing much more slowly.
In the time that the frequencies would be expected to increase by about 25 Hz, due to rate of change of downlink Doppler Shift, the actual change was about 5 Hz.
This example shows conditions that were different than they were 20 minutes previously, and still different than what would be expected from the rate of change of the downlink Doppler Shift alone.
The next three graphs show the: range, downlink Doppler Shift, and rate of change of downlink Doppler shift, for a pass of AO-40 starting on April 15 of 2003 and ending on April 16.
The specific times of interest are: 00:07, 00:10, and 00:13 UTC on April 16, 2003.
The downlink Doppler Shift was predicted to change from about 29 KHz to about 32 KHz over this 6 minute interval. Also, the rate of change of the downlink Doppler Shift was predicted to change from about 170 Hz per minute at the start of this interval to about 180 Hz per minute at the end of this 6 minute interval.
Again, the apparent oscillation of the "Rate of Change of Downlink Doppler Shift" graph is due to limited resolution of data from the satellite tracking program and roundoff error.
The graph below shows the Frequency Change Compensation applied to the (nominally) 1035 Hz audio subcarrier for three successive transmissions by W8ZCF through AO-40 as received by W9NTP. These transmissions took place at about 3 minute intervals.
Also shown are three straight lines, showing the estimated rate of change of frequencies due to the rate of change of the downlink Doppler Shift over this same time interval.
The main point of this plot is that the red trace is significantly different from the blue and green, even though the data for the red trace came from a transmission that was 3 minutes after that for the green trace and 3 minutes before that for the blue trace.
Thus, even relatively high rates of change of downlink Doppler Shift don't dominate the actual changes in frequency of signals received from AO-40.
Additionally, closer examination of the red trace shows that a straight line provides a relatively poor fit to it.
The next two plots show the first and last 8 seconds of what would have been displayed on a suitably adjusted oscilloscope connected to the audio signal recorded by W9NTP at about 00:13 UTC on April 16, 2003, from the signal transmitted through AO-40 by W8ZCF.
In addition to the frequency changes described above, the following plots show drop outs of the signal. I counted 16 drop outs during the first 8 seconds, and 16 drop outs during the last 8 seconds.
Thus, in addition to compensating for a signal that was changing relatively rapidly in frequency, quite a few short drop outs had to be corrected for, in order to recover an exact copy of the file W8ZCF sent. All the errors were corrected, and W9NTP did get an exact copy of the original file sent through AO-40 by W8ZCF.
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