Page 279 - Maxwell House

Chapter 5 259

reveal targets behind walls, under forest leaves, etc., that are hidden from the naked eye. Objects
concealed underneath a person’s clothing can be detected by mm-wave SAR radar in airports.

In general, SAR radars are installed on moving platforms like an aircraft, satellite or specialized
scanners and included a comparatively small antenna. The latter illuminates a target on the
Earth’s underlying surface and then receives the scattered signals from the target. Figure
25
5.5.8b demonstrates a side-looking SAR setup schematically. As long as the ground target or
targets are static during the measurements, all returned and stored signals are highly correlated
and can be separated from noise and other interfering signals using well-known signal
processing techniques. The secret of SAR is the so-called Doppler beam sharpening procedure
or Range Doppler Processing Algorithm (RDPA). Since the antenna and target are in motion
around each other, the frequency of EM waves scattered from the target slightly increases or
decreases depending on how the antenna moves with respect to the target, i.e. towards it or
away from it [23]. Including the information about these Doppler frequency variations in signal
processing acts like antenna beam shrinkage. To illustrate this phenomenon, assume that an
antenna of low directivity (for example, elementary electric or magnetic dipole, Huygens’
radiator, etc.) is located on an airborne platform (aircraft, satellite, etc.) flying at constant
velocity along the flight path as shown in Figure 5.5.8b. The wide projection (yellow ovals)
0
of radar transmit antenna beam on the Earth’s surface follows along the ground track. The
sequence of coherent pulses transmitted by radar leaves the set of curved footprints along this
track. In other words, the antenna pattern beamwidth defines the ground swath as the width of
the terrain from which imaging data is collected. Typically, the shape of an antenna pattern
crossing the ground swath is close to the cosecant squared to reduce the deviations of scattered
by target signals due to the beam slant. According to the drawing in Figure 5.5.8b the distance
() between the antenna element and fixed target on the ground as well the phase variation
∆() of received signal becomes time dependent and can be written in the form

2
2
2
∆() = () − = � + ( ) − ≈ ( ) ⁄ (2 ) ≪ 1
0
0
0
0
0
0 � (5.99)
∆() = −2∆() ≈ − 2 ( ) 2
0
0
Here is the range or shortest line-of-sight distance between the element and target at the
0
moment of time = 0. We kept in (5.99) only the first term of Taylor expansion since ≪
0 0
practically for any human-made SAR platform including the fastest (orbital velocity 6.9 – 7.8
km/s) spacecraft on Low Earth Orbit (LEO). Pay attention that we put the factor 2 in the second
expression because the EM wave propagating to and from the target acquires the same phase
shift twice. Subsequently, the instantaneous Doppler frequency () of the return signal is the

time derivative of its phase
2
1 2 0
() = �∆()� = − (5.100)
⁄

2 0
In other words, the linear frequency rate is the inverse function of the range . Therefore, any
0
target can be characterized by its unique frequency rate signature depending on the distance
between target and radar. It makes it possible to discriminate targets installing the bank of
Doppler filters (typically digital) behind the receiver. Each filter in the bank is tuned to respond

25 Public Domain Image, source: http://www.crisp.nus.edu.sg/~research/tutorial/mw.htm