[Lf] LF antenna array

[Skelly]

I've also been thinking about a similar idea, and outlining some of the
limitations.  Some, but not all, of the efforts applied to single-antenna
reception with DSP would apply.  One possible scheme would be this:
1. Set up two receiving antennas, at least 1/4 wavelength apart, but not
more than about 3 wavelengths apart.
(As in shorter wavelength arrays of antenna elements, the arriving signal
would ideally follow approximately the same propagation path, and arrive at
the two antennas with a phase difference between 0 and about 10 radians.
The analysis of three or more receiving antennas has only slightly more
complicated math, but there's no great advantage that I see.)
2. The front end of the receivers (antennas, couplers, RF amps, etc.) must
be relatively wide-band.  (Because tuned circuits introduce
frequency-dependent phase shifts, narrow-band reception would destroy the
phase information in the signals.)  Similarly, any heterodyne processing
must be phase-locked.
3. Trigger the detection and digitization of a short epoch, synchronized at
both of the antennas; convert the epoch into an array of signal intensities
indexed to time after the trigger, for one to 3 cycles.  The same trigger
and A/D delay indexes must be used at both antennas.  (The trigger could be
TV synch pulses, good for at least +/- 20 microseconds, or the AM BC trigger
that Andre et al. described for spread spectrum, the path-corrected GPS
signal (ideally good for +/- 10 picoseconds, or even local RF or hardwire
links.  WWV would not be useful, because the propagation path and time
varies more a cycle of LF.)
4. Fourier transform (FT) the intensity vs. time arrays into real plus
imaginary term arrays.  (I've been toying with wavelet transforms also, but
the biological types like me didn't get the math background that many of you
EEs have, so it's taking me longer to deal with them.  Suffice it to say
that there may be some advantages to non-Fourier alternatives, but the
digital TV people in the US didn't accept them, partly because they didn't
want to learn any new math.)
5. Correlate (actually deconvolute) the two signals in Fourier space.
(Remember about the product of the FTs of two signals is the FT of their
convolution?  The math is relatively trivial.  The complex conjugate of one
of the arrays is obtained by multiplying the imaginary part of the terms
by -1, or shifting by pi radians.  The rest is polynomial arithmetic.)  The
resulting FT of the Faltung integral, or correlation spectrum, is an array
of real plus imaginary terms indexed to frequency.  The FT of a third (or
more) antenna may also be correlated against this FT.  The inverse FT may be
converted back to analog audio for listening.
6. Variously:
- Display the array as a plot of in-phase and quadrature components, at one
or more frequencies.
- Digitally filter it (spectrum analysis) to select specific frequencies as
several of the AMRAD team have been handling single antenna FFTs.
- Display the array as a plot of phase (arctan of imaginary/real) vs.
frequency
- Digitally filter it to select specific phases.
7. The first two allow discrimination between local and receiver noise and
the signal propagated from a distance.  The last two allow the phase
difference of the signals received at the two antennas to be resolved into
directionality.  The beamwidth depends on the spacing and number of terms in
the original intensity vs. time array/epoch.  A 256-point array, acquiring 3
cycles of RF, could have a beamwidth resolution on the order of 10 degrees.
(The math there is close to my limitations.)  The directionality resolution
is not dependent on the phase difference of signal arrival at the two
antennas.  (The orientation line connecting the two antennas has no bearing
(pun) on which directions can be selected.)
8. Just as in ordinary DSP receivers, the I and Q components of the
deconvoluted FFT product may be used to derive CW, SSB, FM, and other
modulations.

It seems to me that there are still several problems to be solved before
this would be practical.

Mike KA8OPJ