Jim Lux wrote:

1 - Do you intend to actually make and record measurements of
the radiated field, or do you want to determine the minimum distance
at which the measurements can be made?



yes



An interesting problem. What you're presumably trying to do is
determine how far do I need to be to bound the uncertainty on a
measurement in an arbitrary direction. Or, another way, at what distance
is the collective effects of the phase error for each of the signals
(due to path length differences) smaller than your measurement
uncertainty (so you don't care anymore).

This can be quite challenging if you want to worry about -40dB nulls,
for instance, because a very small phase error can result in a -40dB
null becoming a -30 dB null.

I'm not really that bothered about the depth of nulls to any great
extent. Since this is radiating an unwanted signal, the concern is
finding where the gain is highest and how high it is.

Complicating it a bit is that what you're probably really concerned with
is a statistical problem.. you've got multiple sources, a random
direction of observation, (and practically speaking, some propagation
uncertainties between antenna and observation point).

You might want to look for a paper by Dybdal and Ott: "Coherent RF
Error Statistics", IEEE Trans MTT, v34,n12, Dec 86, pp1413-1420 which
discusses this in some detail, and, as well, provides some nice
approximations that are useful in practical systems.

In this case, it is certainly a statistical thing. As I said before, the
amplitudes and phases of the radiators are random(ish) and will be
changing all the time.

2 - What prevents the use of a computer modeling program to
predict the pattern?



nothing. I think that will be done. But a theoetical analysis would be
nice if possible.


One can come up with a "bound" for the performance from analytical
means, and a Monte Carlo analysis can give you some statistics.

Jim

I will look at doing some MC analysis.
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