Copyright 2001 by Barry Sanderson
Permission is hereby granted for the verbatim reproduction, or storage, of this document, including this copyright notice, and its accompanying images. All other rights are reserved.
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Analysis of the 12:14 UTC 10 April 2001 transmission by VK3LM (near Talangada Valley, Australia) to W8ZCF (near Cincinnati Ohio USA) and W9NTP (near Waldron Indiana USA) shows that propagation delay time varies with: frequency, time, and space.
In the plot below, the demodulated waveforms for 10 consecutive symbols are shown for two of the subcarriers, for a portion of the 2nd codeblock in the transmission. The green and magenta traces are the "ideal" case, resulting from demodulating the signal VK3LM used as input to his sound card. The red and blue traces result from demodulating the signal recorded by W8ZCF, from this transmission.
Look at the red and green traces in the plot below. Note that the red trace (as received by W8ZCF) seems to be slid to the right and also to be slid down, with respect to the green trace (the ideal case). The red and green traces are for the, nominally, 1035 Hz subcarrier.
Also note, in the plot above, that the apparent delay from the green to the red trace is about the same as it is from the magenta to the blue trace. These two traces are for the, nominally, 1265 Hz subcarrier (magenta is the ideal case, blue is from what W8ZCF actually received).
The next two plots provide an example of the propagation delay of the 1035 Hz energy noticeably INCREASING, for symbols about 122 milliseconds apart, with the propagation delay of the 1265 Hz energy being about the same for the same pair of symbols.
The plot below shows the demodulated waveforms for 10 consecutive samples for the 1495 Hz and the 1725 Hz subcarriers. The green and magenta traces show the ideal case; the red and blue show demodulation results from the signal recorded by W8ZCF. Look in the area around demodulated sample numbers 36540 to 36720. Note the apparent delay of the red trace with respect to the green trace, and the apparent delay of the blue trace with respect to the magenta trace.
The start of the plot below is 10 symbol times from the end of the plot just above. In the plot below, look in the area around demodulated symbol numbers 37890 to 38670. Note the apparent delay of the red trace with respect to the green trace, and the apparent delay of the blue trace with respect to the magenta trace.
The two regions whose demodulated symbol numbers are listed above are 15 symbol periods apart; this is about 122.449 milliseconds apart. Observe that the apparent delay of the red trace from the green trace is noticeably greater in the plot just above, than it was in the prior plot. Also, the apparent delay of the blue trace from the magenta trace is about the same in the regions listed above in the two preceding plots.
This shows that the propagation delay of the 1495 Hz energy was about 1.7 milliseconds greater near demodulated symbol numbers 37890 to 38670 than it was near demodulated symbol numbers 36540 to 36720, and that the propagation delay of the 1725 Hz energy was about the same near both of these ranges of demodulated symbol numbers. These ranges of demodulated symbol numbers are about 122.449 milliseconds apart.
By calculating the cross-correlation between the ideal demodulated waveform and the demodulated waveform from the actual received signal, for various shifts in time between the two, an image showing how much time shift is needed for the best alignment between the two can be created. This has been done for the 1035 Hz, and 2185 Hz subcarriers, for receptions by W8ZCF and W9NTP of the same transmission by VK3LM, in order to produce the next four images below.
In the following images, the tic marks along the horizontal axis are close to the actual codeblock boundaries. The tic marks along the vertical axis are spaced at 1/3 of a symbol period (2.721 milliseconds between tic marks). The left side of the image corresponds to the start of the message, the right side of the image corresponds to the end of the message. Each pixel horizontally represents 3 successive symbol periods (24.49 milliseconds). The top of the image corresponds to a shift of +1 1/3 symbol periods, the bottom of the image corresponds to a shift of -1 1/3 symbol periods. Each pixel vertically represents one sample period (907.03 microseconds).
What is plotted is the correlation between the ideal demodulated waveform (for the corresponding group of 3 symbols) and the demodulated waveform from the signal actually received, for the range of time shifts listed in the previous paragraph. The color code used is outlined below.
Correlation Range | Color
---------------------------
(0.99 - 1.00) | red
(0.98 - 0.99) | yellow
(0.97 - 0.98) | green
. | .
. | .
. | .
[-1.0 - 0.86) | black
Each color spans a range of 0.01 correlation values. Correlation values less than 0.86 are plotted in black. Thus, red indicates shifts in time that yield a correlation between 0.99 and 1.0 for the 3 symbol period waveforms. Black indicates cases where the correlation is less than 0.86.
Below is an image showing the 3rd codeblock from the above 4 images. In the image below, the top half is from data received by W8ZCF, and the bottom half is from data received by W9NTP. Also in the image below, the left half is from the 1035 Hz subcarrier, and the right half is from the 2185 Hz subcarrier.
Compare the above 1035 Hz images (left half) near the point two thirds of the way through the third codeblock. For the signal recorded by W8ZCF (upper left), there is an upward slanting red region, showing that the propagation delay was INCREASING for this subcarrier, during this time. For the signal recorded by W9NTP (lower left), there is a downward slanting red region, showing that the propagation delay was DECREASING for this subcarrier, during this same time.
Even though W8ZCF and W9NTP were located only about 80 miles apart, the 1035 Hz energy transmitted by Vk3LM, from Australia, was taking different paths to W8ZCF and W9NTP.
Compare the 1035 Hz case (upper left) to the 2185 Hz case (upper right) for the signal recorded by W8ZCF, near the point two thirds of the way through the third codeblock. For the 2185 Hz subcarrier, the propagation delay (shown by the red region) was slightly decreasing, before taking an apparent step up, while the propagation delay for the 1035 Hz subcarrier was increasing.
Thus, the 1035 Hz energy and the 2185 Hz energy were taking different paths from VK3LM to W8ZCF.
Compare the 1035 Hz case (lower left) to the 2185 Hz case (lower right) for the signal recorded by W9NTP, near the point two thirds of the way through the third codeblock. For the 2185 Hz subcarrier, the propagation delay (shown by the red region) was INCREASING, while the propagation delay for the 1035 Hz subcarrier was DECREASING.
Thus, the 1035 Hz energy and the 2185 Hz energy were taking different paths from VK3LM to W9NTP.
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