On 8/30/18 1:47 PM, Richard (Rick) Karlquist wrote:
Another sign that cluster clickers are calling is
when the station who initially spot is somewhat
off frequency. Then you get 10 callers in a row
who are also off frequency by the same amount.
I've encountered that many times.
If you get 10 callers that are zero beat with the
running station, that may or may not have to do
with spots.
Rick N6RK
I suppose it's HF antenna related enough to continue -
Frequency control is generally much better these days - 1ppm kinds of
tolerances are common. I suspect in the "old days" you'd get things
spread out just from tolerances on everyone's VFO and/or crystals
But, to get more to Brian's analysis and the connection to antenna
gains, I'm not sure the assumption of Rayleigh or Log-Normal
distributions are valid.
One sees Rayleigh distributions in a land mobile signal over time,
because the underlying process (multipath) creates a Rayleigh
distribution. If you combine paths with uniform random phase and random
amplitude, you get a Rayleigh distribution.
However, I don't think that's necessarily a good model for received
signal strength:
a) any *one* signal might show rayleigh distributed fading, if there's
path diversity through the ionosphere - but that would be over a long
time scale, and would be more at some particular path configurations
(where you're close to cutoff, so O and X mode propagate more
differently, and with multiple hops). I will say that having done some
spectrogram kinds of studies, most HF signals are not Rayleigh
distributed, but then, one can argue that in a contesting situation,
you're more likely to be on the ragged edge.
b) what you're really interested in is the distribution of received
power, which is a combination of EIRP and path loss.
EIRP depends on the amateur and their antenna - one might be able to say
that the population of EIRPs has some clumps - lots of people running
100W into a 8-10dBi antenna, some fewer people running 1kW into a 12dBi
or more antenna, and some other hardy souls running 100W (or 10W) into a
dipole (and counting on their unique callsign prefix (P5?) getting the
response desired)
Path loss is primarily influenced by distance, so the distribution
across all the folks in the pileup is some weird combination of:
i) inverse square of the distance distribution (which is quite weird in
itself, since the distribution of amateur transmitters is far from
uniform on the surface of the earth
combined with
ii) the height of the ionosphere for the hops (which affects the path
distance AND the angle of incidence on earth and ionosphere, which in
turn affects the loss)
Phenomena like the skip zone and the bright line just after the skip
zone are something that has significant (many dB) effect.
One might look at ITU or CCIR reports for HF broadcasting - there's
probably some model for this. (and, for all I know, it might turn out
that Rayleigh or Log Normal) happens to fit well. Log Normal does
describe a lot of phenomena.
Sample Matlab/Octave code for Rayleigh distributions
%simulate random paths
N = 10000
p1 = rand(N,1)*2*pi;
p2 = rand(N,1)*2*pi;
s1 = complex(cos(p1),sin(p1)).*rand(N,1);
s2 = complex(cos(p2),sin(p2)).*rand(N,1);
s = s1+s2;
sm = abs(s);
figure(1)
hist(sm,100)
p3 = rand(N,1)*2*pi;
s3 = complex(cos(p3),sin(p3)).*rand(N,1);
s = s+s3;
sm = abs(s);
figure(2)
hist(sm,100)
p4 = rand(N,1)*2*pi;
s4 = complex(cos(p4),sin(p4)).*rand(N,1);
s = s+s4;
sm = abs(s);
figure(3)
hist(sm,100)
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