The Radar Ambiguity Function - MATLAB Simulations for Radar Systems Design - page 202

4.3. Ambiguity Diagram Contours
Plots of the ambiguity function are called ambiguity diagrams. For a given
waveform, the corresponding ambiguity diagram is normally used to determine
the waveform properties such as the target resolution capability, measurement
(time and frequency) accuracy, and its response to clutter. Three-dimensional
ambiguity diagrams are difficult to plot and interpret. This is the reason why
contour plots of the 3-D ambiguity diagram are often used to study the charac-
teristics of a waveform. An ambiguity contour is a 2-D plot (frequency/time) of
a plane intersecting the 3-D ambiguity diagram that corresponds to some
threshold value. The resultant plots are ellipses. It is customary to display the
ambiguity contour plots that correspond to one half of the peak autocorrelation
value.

Fig. 4.9 s hows a sketch of typical ambiguity contour plots associated with a
gated CW pulse. It indicates that narrow pulses provide better range accuracy
than long pulses. Alternatively, the Doppler accuracy is better for a wider pulse
than it is for a short one. This trade-off between range and Doppler measure-
ments comes from the uncertainty associated with the time-bandwidth product
of a single sinusoidal pulse, where the product of uncertainty in time (range)
and uncertainty in frequency (Doppler) cannot be much smaller than unity.
Note that an exact plot for Fig. 4.9 can be obtained using the function
Ðsingle_pulse_ambg.mÑ and the MATLAB command contour .

frequency frequency

time time

1 τ′ ⁄ 1 τ′ ⁄

τ′

τ′

long pulse

short pulse

Figure 4.9. Ambiguity contour plot associated with a sinusoid
modulated gated CW pulse. See Fig. 4.2.

Multiple ellipses in an ambiguity contour plot indicate the presence of multi-
ple targets. Thus, it seems that one may improve the radar resolution by
increasing the ambiguity diagram threshold value. This is illustrated in Fig.