Suitability of Correlation Arrays and Superresolution for Minehunting ...

DSTO-TN-0443
To answer this question, note that, in the FBLP method, the decorrelation is not
achieved by arranging for the phase to be shifted repeatedly in real time as the signal is
continuously reflected from the target. Rather, the key to the decorrelation is that ‘the
phase relationships between the targets as seen by the first subarray are different from
those seen by the second subarray’ (S&S 1991, p. 315). Thus there is no need for any
phase shift over time. Consequently it is believed that the problem raised in the
previous paragraph goes away.
Let us now look again at the analogous problem for correlation arrays when data
correlations have to be estimated. Suppose that the FBLP method (a method of
synthetic averaging) can be adapted to achieve this for correlation arrays. Then again
there is no shifting of the phase in real time; and so presumably again there is no
problem of insufficient time.
For correlation arrays, it is difficult to draw rigorous conclusions in this area, but it
seems that the most likely conclusions are as follows: (i) the problem of short averaging
times goes away (as discussed); (ii) the number of point targets that can be
accommodated in the image is quite limited and depends on the number of subarrays
(shifted versions of one subarray) within each of the two ‘arms’ of the total array; and
(iii) the signal-to-noise ratio (of the received signals before processing) must be high
(since the amount of time-averaging performed is small by comparison with radio
astronomy, and so this source of increasing the SNR is not available).
12. Work on General Features of Superresolution
This section briefly reviews literature making general observations on SR methods,
including both comparison of methods and formulae for resolution.
Gabriel [1982] is concerned to resolve sources in cases where the sources are
coherent and have unequal strengths. He discusses and applies a few SR techniques,
as well as the conventional Fourier-transform technique and the ‘SLC’ algorithm
(found to be no better than Fourier).
In the face of coherence between sources, Gabriel says that a ‘Doppler-shift’ method
is sometimes available. In this method, a number of snapshots are taken while the
receiving array is moved sideways. ‘... it is desirable to have enough snapshots to
sample one or more complete Doppler cycles ... .’ (The method may be the same as the
use of aspect-angle diversity.) In a case considered, the improvement is ‘dramatic.’
Gabriel then says: ‘If a Doppler-cycle shift is not available, then we are forced to
address the difficult fixed-phase coherent case.’ And ‘the best technique found to date’
is the ‘forward-backward subaperture-shift’ solution. This appears to be identical to
the FBLP method described by S&S. Gabriel uses simulations to test both this and an
‘eigenvalue/eigenvector algorithm’ derivable from the MLM (maximum likelihood
method) algorithm of Capon and Lacoss (described in Childers [1978], which contains
reprints of some early key papers). In the test, Gabriel compares the two methods with
the Fourier-transform technique. ‘[The] test cases demonstrate the remarkable
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