Antenna A: rx noise voltage A, signal
voltage a
Antenna B: rx noise voltage B, signal
voltage b
After correlation: (A+a).(B+b)
= A.B + a.b + A.b + B.a
Only a.b may have a non-zero expectation value. This is the desired, correlated signal. The other terms give purely random noise.
In conventional
interferometry, A>>a and B>>b, so A.b and B.a are negligible
compared with A.B . The random noise on the image
is dominated by A.B . The
noise is statistically constant.
With FASR, usually a>>A and b>>B, so A.B becomes negligible, and the noise
on the image is dominated by A.b, B.a & a.b .
Since a and b are also highly variable with time, this can give noise in an image strange properties. Some imaging algorithms may not work as expected.