Page 427 - Fundamentals of Radar Signal Processing

(5.136)

Equation (5.136) points out that the time slip adjustment adds a linear phase

term to the aft channel Doppler data. This effect applies to both target and
interference signal components. For a given range-Doppler bin [l, k], [l, k, n]
is a 2 × 1 column vector.
The signals at each subaperture consist of clutter, noise, and (if present)

target components. Because the weighting will be in the phase center dimension,
a model of the covariance matrix S = E{ * T } of the phase center data for
I
each range-Doppler bin similar to that of Eq. (5.19) is needed. Begin with the
clutter. It is not white in slow time, so its power spectrum is not flat and the

clutter covariance is a function of the range index l and Doppler index k.
The clutter at the same range-Doppler bin is correlated across the spatial phase
center channels to some degree determined by the platform motion and time slip
correction. That correlation is denoted by the normalized phase-center
dimension correlation function ρ[k] and also varies with the Doppler bin. The
thermal noise is assumed uncorrelated between channels and is white.

Therefore, for a fixed range-Doppler bin S will take the 2 × 2 form
I

(5.137)

The coefficient β[k] accounts for any mismatch in the gain and frequency
response or subaperture antenna patterns of the two channels.
Next, a model similar to Eq. (5.23) or (5.25) for the target data in the
Doppler domain is needed. A CPI of fast-time/slow-time data for a moving
point target in range bin l is modeled as
t

(5.138)

complex scalar constants representing the unknown target
where γ and γ = phases and (possibly unequal) amplitudes in the fore and aft
f
a
receive channels
A = target amplitude
t
δ [·] = discrete impulse function

The target phases represented by γ and γ are determined by the absolute range
f
a
and the angle of arrival as well as the electrical lengths of the receive paths.
It is useful to note the relationship between the angle of arrival and the