Suitability of Correlation Arrays and Superresolution for Minehunting ...

DSTO-TN-0443
4.3.1 Conclusions for Sonar; Decorrelation
The corresponding situation in active sonar would be for the effective source strengths of
the point targets to be uncorrelated. To see what this means, consider a typical cross term
in (4.5) when r , r
j
and r
j ′ are no longer equal. To evaluate phases, let us drop the two
angular factors ( G
1
and G ∗ 2
) and, in each factor ξ , consider just the factor
exp ( j2π
f
ct)
that represents the carrier wave in ξ () t . The typical cross term is then
essentially
∗
a
ja
j′ exp [ j( 4π λc
)( rj
′ − rj
)]
(4.8)
the two terms in r having cancelled out. The phase of this term is what counts in
respect of correlation. An alternative argument for (4.8) is to consider the phase change
along the go-and-return path from the transmitter to j and back to the array (where
presumably the array may be taken at the transmitter for this purpose). The phase
difference yields the exponential factor. If the target strengths are complex, thus
∗
producing a phase change, the factors a
j
and a
j′ obviously must be included too. We
may define the source strength of target j to be
s = a exp − j 4π λ r ; (4.9)
j
j
[ ( c
) j ]
∗
then (4.8) may be written as s s j j′ . Thus for the cross term to vanish, i.e. for the targets
to be uncorrelated, we require
s = 0
(4.10)
∗
j s j′
where represents some average, to be discussed.
Normally r
j
, r
j ′ , a
j
and a
j ′ are simply constants; there is no averaging and the
cross term does not vanish: thus normally the targets are correlated. For the targets to be
uncorrelated, either a target would have to undergo a random motion with a radial
component (change of r
j
in Eqn 4.9), or else its elastic properties would have to change
(change of a
j
), during the period of the correlation measurement. Normally neither of
these things happens. A second condition is required for lack of correlation, namely,
the correlation run must last for a sufficient time for the randomness to be sensed. This
requirement is discussed in Section 4.4 and again in Section 11.4.
To make the correlation array work in spite of the correlation problem, it appears
that some method for the decorrelation of targets must be found. To this end, we may
adopt either of two approaches. The first is to persist with the time-based approach,
searching for some other feature of the environment that can induce random phase
shifts over time. One such method has in fact been used: it makes use of reflections
from the disturbed surface of the water. This method is discussed in Section 11.1. It
also seems worthwhile to investigate whether fluctuations in the medium give rise to
suitable phase shifts.
There is a second approach to achieving decorrelation, which is analogous to
synthetic aperture sonar. We shall sometimes call this second approach ‘synthetic
decorrelation’; however in practice the term ‘decorrelation’ is commonly used to refer
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