Page 429 - Fundamentals of Radar Signal Processing

(5.140)

The terms ψ and ψ represent the receiver phase shifts, which are different for
a
f
each channel in general.
After the Doppler DFT, the target data model of Eqs. (5.138) and (5.140)
results in the following target range-Doppler domain signal model

(5.141)

where k = (F KT/2π) is the target Doppler shift converted to an equivalent DFT
D
t
bin number. The two impulse functions serve to confine the response to range
bin l and Doppler bin k . If K > M there will be multiple DFT samples on the
t
t
target DTFT mainlobe and the assumption that the target response is essentially
confined to one Doppler bin is less valid.
As before, the SIR can be maximized with a matched filter that computes

the scalar quantity for each range-Doppler bin

(5.142)

Since the target signal AOA is not known a priori the target signal vector is
again averaged over all values of AOA in [–π/2, π/2]. Absorbing out all

common constants into the complex amplitude, the new target vector becomes
simply

(5.143)

The target location in range-Doppler space is not assumed known so the same
target model is used in each range and Doppler bin.
An alternative to assuming an unknown AOA is to assume specific values
for θ . For example, a series of values in an interval equal to the antenna
a
mainlobe width and centered on the nominal steering angle used on transmit
might be generated and used. However, the loss in SIR from using the much

simpler Eq. (5.143) is very small (Shaw and McAulay, 1983).
The exact clutter and noise statistics are also not known a priori.
Consequently, S cannot be known exactly, but it can be estimated from the data.
I
Since the clutter covariance is expected to have essentially the same form in

every range bin, one way to estimate S would be to compute a sample average
I