Time-Frequency-Based Radar Image Formation - Time-Frequency Transforms for Radar Imaging and Signal Analysis - page 117

maximum value of 3.5 Hz as shown in Figure 5.8(b). When the angle f 2
approaches 0 or 180 degrees, the Doppler difference approaches zero; thus,
it is impossible to distinguish these two targets.
In the case of multiple targets at the same range but moving in different
directions as shown in Figure 5.8(c), the Doppler difference between two
targets with angle f 1 and f 2 becomes

2 V
l (cos f 1

D f D 12 - f D 2 - cos f 2 ) =f D 1 = (5.31)

l S 2 sin S D 2

f 2 D sin D 2 D

- 2 V

+

=

If f 2 = 180 degrees, then

l S 2 sin 2 D 2 D

2 V

D f D 12

= (5.32)

where Df is the difference between the direction angles of the two targets.
From (5.31), if V = 60 m/sec, R = 20,000m, and Df = 0.1 degree, as
a function of the angle f 2 ,at f 2 = 90 and 270 degrees, the Doppler
difference reaches a maximum value of 6.35 Hz as shown in Figure 5.8(c).
To distinguish two targets, a coherent processing time of 0.16 sec is enough.
When the angle f 2 approaches 0 or 180 degrees, the Doppler difference
approaches zero, and it is also impossible to distinguish these two targets.
From the first two examples, we can ascertain that when targets are
flying in the same direction, the Doppler difference between targets is rela-
tively small. With a longer coherent processing time, multiple targets may
be resolved. When, however, targets are flying in different directions as shown
in the third example, the Doppler difference is relatively large depending on
the angle difference of their flying directions.
If targets have rotational motion or different velocities, they will have
different Doppler histories. By using conventional motion compensation
algorithms, an image of multiple targets becomes smeared. In these cases,
time-frequency algorithms may help for imaging of multiple targets.

5.5.2 Time-Frequency-Based Phase Compensation for Multiple
Targets
When a number of targets are within the same antenna beam, close to each
other in range, and moving with different velocities or in different directions,