Page 275 - Fundamentals of Radar Signal Processing

expansion of the square root

(4.101)

Thus, the Rayleigh resolution in time is approximately 1/β seconds,
corresponding to a Rayleigh range resolution ΔR of

(4.102)

The zero-delay response is

(4.103)

which is simply a standard sinc function. The Doppler resolution of the LFM
pulse is the same as that of a simple pulse, namely

(4.104)

Equation (4.103) shows that, like the simple pulse, the Doppler resolution of an
LFM pulse is inversely proportional to the pulse length. Furthermore, the energy
2
in the LFM pulse is still A τ, directly proportional to the pulse length. Equation
(4.102) shows that, unlike the simple pulse, the range resolution is inversely
proportional to the swept bandwidth. The LFM waveform has two parameters,

bandwidth and duration, which can now be used to independently control pulse
energy and range resolution. The pulse length is chosen (along with the pulse
amplitude A) to set the desired energy, while the swept bandwidth is chosen to
obtain the desired range resolution.
The expression c/2β for range resolution is quite general. For instance, the
Rayleigh bandwidth of a simple pulse is β = 1/τ Hz; using this in c/2β gives ΔR
= cτ/2 as before. While bandwidth and pulse length are directly related in the

simple pulse, modulation of the LFM waveform has decoupled them. If βτ > 1
for the LFM pulse the range resolution will be better than that of a simple pulse
of the same duration by the factor βτ. Alternatively, the range resolution of a
simple pulse of length τ can be matched by an LFM pulse that is longer (and thus