[TowerTalk] Busting a Pileup

jimlux jimlux at earthlink.net
Thu Aug 30 17:45:55 EDT 2018

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);
p3 = rand(N,1)*2*pi;
s3 = complex(cos(p3),sin(p3)).*rand(N,1);
s = s+s3;
sm = abs(s);
p4 = rand(N,1)*2*pi;
s4 = complex(cos(p4),sin(p4)).*rand(N,1);
s = s+s4;
sm = abs(s);

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