Page 428 - Fundamentals of Radar Signal Processing

phase difference between the signals observed at the same moment on the fore

and aft antenna subapertures. Figure 5.47 shows a wavefront impinging on two
receivers representing the two antenna phase centers separated by a distance d .
pc
The angle of arrival of the wavefront, measured from the normal to the line
connecting the two receivers, is θ . As shown in the figure, the additional
a
distance the wavefront must travel after arriving at the first receiver before it
reaches the second receiver is d sinθ . Consequently, the phase difference in
a
pc
the signals received at the two sites becomes

FIGURE 5.47 Geometry for relating angle of arrival to phase difference at two
subaperture receive phase centers. The angle of arrival shown is considered
negative; positive angles of arrival are clockwise from the normal to the line

connecting the phase centers.

(5.139)

The subscript k on the wavelength has been added to emphasize that the

appropriate wavelength should be used for each Doppler bin to which Eq.
(5.139) will be applied.
Using Eq. (5.139), assuming |γ | = |γ | = 1, and letting R be the range from
a
f
the scatterer to the fore aperture (rightmost in Fig. 5.47), γ and γ of Eq. (5.138)
a
f
can be expanded as follows