Page 187 - Fundamentals of Radar Signal Processing

(3.4)

Many radar antenna beamwidths are small, typically less than 5°. Applying a

small angle approximation to the sin(θ /2) term in Eq. (3.4) gives a simple
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expression for Doppler bandwidth due to platform motion

(3.5)

As can be seen from Fig. 3.5, Eq. (3.4) or (3.5) assumes the radar is

squinted sufficiently that the main beam does not include the velocity vector, that
is, | ψ | > θ /2. If the radar is forward looking or nearly so, then the cos(ψ – θ /2)
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term in Eq. (3.4), which represents the largest Doppler shift in the mainbeam, is
replaced by 1. A more complete expression for the platform motion-induced
Doppler bandwidth is therefore

(3.6)

For example, an L band (1 GHz) side-looking (ψ = 90°) radar with a beamwidth
of 3° traveling at 100 m/s will induce β ≈ 35 Hz, while an X band (10 GHz)
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side-looking radar with a 1° beam flying at 200 m/s will induce β ≈ 233 Hz.
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The same two radars in a forward-looking configuration induce negligible
Doppler bandwidths of only 0.9 Hz and 0.5 Hz, respectively. Thus, while
absolute Doppler shift due to platform motion is highest for a forward-looking

system, the Doppler bandwidth spread is highest for a side-looking system.
In the previous example, the radar was viewing a patch of ground and the
Doppler bandwidth observed by a stationary radar would be 0 Hz. The nonzero
Doppler bandwidth β is entirely due to the motion of the observing radar, not
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to the characteristics of the target scene itself. The total Doppler bandwidth
observed is approximately the sum of the bandwidth induced by platform motion

[Eq. (3.6)] and the intrinsic bandwidth of the scene being measured. The PRF
should be chosen equal to or greater than this value if possible to meet the
Nyquist sampling criterion for the slow-time signal.
Although the Doppler spectrum of the illuminated terrain is both shifted