Thanks Leif for all explications!

As such it is clear that in stable conditions (no polarization change) a signal
emanating from one source must be able to show a fixed polarization state
irrespective of its spectral content, but any offset from the real value is due
to feed line length differences or disparity in pre-amp phase curves or gain
differences (as a function of frequency). And there another source within the
same spectral range would probably result in an error signal, as one
cannot show two different polarization states with a single graphical line,
i.e. at each instant just one phase would be shown, but it is a transformed
(restless) plot of two independent signals?

Actually my plan is to measure the phase difference between two horizontal
antennas (with known radiation patterns) at different heights. With just one
take-off angle (incoming signal) Linrad would be able to show the phase
difference between these two antennas, and the if the amplitude is also
available, then from the math with the radiation pattern, the angle(s) of arrival
would be solved for up to dual-path openings. Of course the ever changing
ionosphere makes it a dynamic challenge, also due to phase reversals of
the skipping wave. However, it would make home-operating a much deeper
experience from the scientific point of view (compared to regular 59-operating).

Recent experiments have involved the phase / out-of-phase combining of any
two given antennas on 50 MHz (still without Linrad). That adds a lot of extras
too in operating. With little more definition and Linrad this will provide lots of fun.

                                              73, "Zaba"  OH1ZAA/2

P.S. Most likely Linrad can do many more miracles in man-made noise removal
than with Gaussian noise. Assumedly it is to the detriment of total sensitivity if one of two pre-amps in e.g. a X-polarized setup would have a markedly higher noise-figure than the other pre-amplifier. Also some operators claim a much higher noise level than on a single horizontal yagi, if a X-yagi setup is configured for plain horizontal polarization (i.e. DX-station signals will be added as linear vectors, but e.g. galactic noise as n^2 from two perpendicular antennas; and Linrad can't help that?) [Thoughts back to 2000 5AM discussions]

From UKSMG 50 MHz Announcements:    >>>   (a week ago)

If your PC-clock is running on time, then old Winrad versions have stopped working... I2PHD's new Winrad 1.25 is available (User Guide 1.2 is not yet up to date with the changes) --- SM5BSZ's latest Linrad is at version 2-34 --- Last week we reactivated OH3MHA at KP20XW in an industrial environment "with sharp pulsing", so probably Linrad/Winrad techniques will be very effective (i.e. mandatory for noise-free reception) ---- 73, "Zaba" OH1ZAA/OHoMZA ---
 - Sunday, June 03 2007 at 08:25 (GMT)

At 19:54 10.6.2007, SM5BSZ wrote:

Hi Joe, Zaba and all,

> Ideally, I suppose, with an xpol antenna one would like to have
> phase-matched preamps for the two polarizations and equal
> electrical lengths for the two Rx feedlines.

> Suppose they are not well matched.  In other words, suppose that
> the complex gains and signal delays in the two polarization
> channels are not equal.  Will Linrad's polarization-matching
> capability be compromised?  As far as I can see, it still works
> well even with poorly matched feedlines.  I suppose this must
> mean that Linrad solves for a differential complex gain, and
> that over a fairly narrow bandwidth a different delay can be
> treated as a phase shift.
From a practical point of view the cables are well matched. I think
it is a safe assumption to guess that the length differences will
be very small and of no concern.

Much more important would be the phase shift through very
narrow filters in case you have such at the output of
the preamplifier. A filter with 1 MHz bandwidth has a
delay of something like 1us and in case the other channel
has a filter with 1.5 MHz bandwidth, it would have much
less delay and that could be a problem.

When the phase is not matched, the polarisation indicator
will not show the correct polarisation. That will not
cause any loss of sensitivity, only make it more difficult
to decide what tx polarisation to use.

When it comes to the amplitude balance and similarity in NF
I no longer remember how important it is for sensitivity.
Not very important in relation to how important it is for
getting correct polarisation readings in any case.

The procedure to follow is like this:

Connect everything. Compare the noise floor levels and insert
an attenuator (or tweak the second RF amp tuning) for the noise
floors of the two channels to become equal.

Listen to a linearly polarised signal that arrives with similar
strength in both polarisations. (This is the strongest reason
why the X configuration is so much better than the + configuration.
It is easy to find a pure H-pol signal. Finding a 45 degree
terrestrial signal is virtually impossible due to ground reflections
so a + configured system has to be calibrated on EME signals.)
Change cable lengths until the signal appears close to linear
on the pol meter. Fine tune by tweaking the second RF amplifiers.
(will affect both amplitude and phase, but there are two second
RF amplifiers so it should be possible to find both amplitude and
phase matching.

It would of course be easy to add parameters for amplitude
and phase balance, but I have not done it since I found
it easy to do in hardware:-)

Once the phase and amplitudes are properly set it will be
a good idea to set the polarisation to + and -45 degrees
with respect to the real orientations of the elements.
The noise floor should ideally be exactly the same
regardless of the phase. (plus, minus, circular or anything
between.) In real life one might see significant differences
in the noise floor and that would be caused by mutual
coupling between the elements (to some extent the noise
would then be correlated.) It is a good idea to verify
that the isolation between polarisations is at least 20 dB
in transmit mode:-)

The procedure Linrad uses is to compute the powers in both channels
as well as the complex correlation. Then like this:

// *****************************************
//Now we have x2,y2 (real values) and xy (complex).
//For explanation purposes, assume im_xy == 0, which corresponds to linear
//polarization. The signal vill then be polarised in a plane.
//a = angle between polarisation plane and the horisontal antenna.
//Assume that the noise level n is the same in the two antennas, and that
//the noise is uncorrelated.
//We then find:
//            x2 = cos(a)**2 + n**2
//            y2 = sin(a)**2 + n**2
//            xy = sin(a)*cos(a)
//From this we find: x2 * y2 - xy*xy = n**2 + n**4
//Neglect n**4:
//cos(a)=sqr( x2 - ( x2 * y2 - xy*xy) )
//sin(a)=sqr( y2 - ( x2 * y2 - xy*xy) )
//The transformation formula to use for rotating the polarization
//plane to produce new signals A and B, where A has all the signal and B
//only noise, will then be:
// A = X * cos(a) + Y * sin(a)
// B = Y * cos(a) - X * sin(a)
//Extending to im_xy != 0 the transformation becomes
//C1 = cos(a)
//C2 = sin(a) * re_xy / sqr( re_xy**2 + im_xy**2)
//C3 = sin(a) * im_xy / sqr( re_xy**2 + im_xy**2)
// **************************************



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