[TowerTalk] measuring arrival angles

[David Robbins]

this topic has been brought up a couple times recently.  i have done some more
thought and a bunch of trig and convinced myself that it may not be all that
hard to do with some restrictions on the signal source you are trying to
measure.  

first, the basic relationship between the received phase for 2 antennas
separated by a horizontal distance d is:
phi=2*pi*d*cos(azimuth)*cos(elevation)/lambda
where:
	d is the distance between 2 rx antennas
	lambda is the wavelength
	azimuth is the angle from the line between the antennas
	elevation is the elevation angle above horizontal
assuming the source is far enough away that the arriving wavefront is a plane. 
the problem with this is that if the source of the signal is not directly on the
line between the antennas the phase shift is proportional to the azimuth error. 
this makes it necessary to measure both the azimuth and the phase shift of the
signal to use this formula to get the elevation.

a better system would use 3 antennas in a triangle or 4 antennas in a square and
measure the relative phase of the arriving signal at each of them.  by doing
some basic trig the azimuth can be computed from any combination of 3 antennas. 
you can then use that angle to solve for the elevation by using the above
relationship for any pair of antennas (preferably the pair pointed most directly
at the source for best sensitivity).

after doing much trig that i probably didn't need to if i had thought about it a
bit, my idea is to use one of those 4 antenna doppler direction finder systems
to make the measurements.  now, you may say that this only gives you azimuth,
which is true for the commercial systems i have used.  but that is only because
in the normal system all that is measured is the phase of the synthesized fm
modulation.  it is the amplitude that is required to determine the elevation.
what is interesting is that those two readings are essentially independent the
way the math works out for this kind of system.  using a system like this you
can determine the azimuth using any of the normal methods, phase discrimination,
zero crossing, or peak detection.  and then by measuring the amplitude you get
the elevation by the relationship:
elevation=arccos(amplitude/amplitude_0)
where amplitude_0 is the amplitude of a zero elevation signal.  while this can
be calculated in theory, it will have to be measured in a real system because of
the variations in the demodulation circuit and physical parameters of the
antennas.  this should be easy enough to do by using a nearby(but not too close)
transmitter to generate a ground wave signal.  i will also have to look at this
in some more detail, there may also be a function of azimuth necessary to
correct for amplitude variations from the synthesized fm.  i.e. signals
broadside to the square may produce lower amplitude signals than those on the
diagnonals due to the way the discriminator circuit detects them.

the limitations of this system would be:
1. requires unmodulated carrier signal source.  i would think that for
experimenting the ncdxf/iaru beacon network would be adequate.  other sources
such as AM shortwave broadcast should also suffice.
2. requires fm receiver.  a direct phase detector would be better, but the
discriminator circuit in a normal 2m fm receiver is adequate for the systems
i've used on fox hunts.  i would expect that any hf receiver with fm capability
should be adequate, though it may be necessary to get direct access to the
discriminator output to get the amplitude measurement before it gets processed
by the audio circuits.
3. would proabably require reasonably long and relatively strong signal input. 
depending on the phase and amplitude measurement circuits it may require a
couple seconds of measurement to lock in on the signal adequately.  this could
probably be improved by doing some waveform capture and post processing, but i
wouldn't count on getting a reading from fast cw... again, the ncdxf beacons
should be adequate when they give their long dah's at the various power levels.
4. requires 4 antennas in a square, relatively clear of obstructions and
reflecting objects.  if i remember right the best sensitivity is with a square
about 1/4 wave on a side, though it is not critical.  i do seem to remember that
going longer than 1/4 wave on a side is bad though as it may produce ambiguity
in a simple fm detector.  1/8-1/4 wave is probably a practical range to use
which would require multiple antenna arrays to cover the mf/hf spectrum.  it may
also be possible to do with 3 antennas but i would expect more errors in the
readings due to coarser signals.  8 antennas would probably be better, though 4
is adequate for the vhf systems i have used.
5. would require known signal source to calibrate both the azimuth and
elevation.  though this should be easy enough with a transmitter close enough to
generate a ground wave signal, but far enough away that the arriving signal is
close to a plane wave over the area of the receiving array.


well, who's going to build the first one?

-- 
David Robbins K1TTT
e-mail: mailto://k1ttt@berkshire.net
web: http://www.berkshire.net/~robbins/k1ttt.html or http://www.k1ttt.net
AR-Cluster node: 145.69MHz or telnet://k1ttt.net

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