[Lowfer] DX record?

[Stewart Nelson]

Hi all,

Lyle Koehler wrote:

> It's a known fact that if you integrate a signal long enough,
> eventually it will be detectable in the noise. The trick is to
> find the technique that best meets your own personal interests.

If you don't have a trick, "eventually" will be a long time indeed.  I
thought it might be interesting to estimate the performance of simple
integration over an LF skywave path.

If you have a signal which can barely be copied using QRSS with one
second dots, and you cut the transmitter power in half, you can
compensate by going to two seconds per dot, and making appropriate
adjustments in the Rx software.  However, if you were originally using
one hour dots, halving the power would require you to use _four_ hours
per dot, even if propagation remained relatively constant.  That's
because random phase variations imposed by the path limit the minimum
bandwidth to something like one millihertz, even if your Tx and Rx are
locked to GPS.  With constant bandwidth, although doubling the signal
duration doubles the received signal energy, the integrated noise also
increases by square root of 2, so it takes four times the duration to
compensate for having half the power.  On LF, IMO, this "square law"
requirement starts at about ten minutes per dot.

Now, imagine that you just set the world DX record for a one watt
lowfer signal, receiving a three character ID sent with QRSS-600,
which neatly fit in a five hour window of good propagation.  You ask
the sending operator to choose a new message, cut his Tx power to 100
mW, repeating the message every five hours until you have integrated
enough signal to copy.  You have an automated receive system which
will sound an alarm when the message has been detected.  How long
might it take?

Your first thought is that since the square law applies, one would
need 100 repeats, about three weeks.  That would not be awful, to set
the definitive 100 mW record.  But of course, the good propagation
won't last that long.  Let's assume, optimistically, that average S/N
is only 6 dB worse.  The square law applies here, too, so we now need
about 1600 repeats, roughly a year.

But of course, the season doesn't last that long.  If summer noise is
10 dB above winter levels, the average level might be 7 dB above the
quiet season.  Again applying the square law, it looks like about 25
years are required.

But of course, lowfer beacons don't run that long.  I'll ignore
mundane interruptions like blown-down antennas and lightning-fried
MOSFETs.  If the sending operator loses interest in the hobby after
say, 15 years, and his kid picks it up after another 15, then your
great-grandson might hear the alarm sometime around 2102.

He shouldn't rush to whatever has replaced the Internet to proclaim
his success.  The record will have long been eclipsed by someone who
had a trick.

73,

Stewart KK7KA