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FIGURE 4.47 Matched filter output for a 13-bit Barker code.
Barker codes have two major disadvantages. The first is that the lack of
Barker codes longer than N = 13 limits the degree of sidelobe suppression
possible. The second is that they are very Doppler intolerant. A Doppler phase
rotation of 360° across the full pulse is more than sufficient to completely break
up the structure of the matched filter output, as seen in the 13-bit Barker
ambiguity function contour plot of Fig. 4.48. As a consequence, it is common to
design Barker coded waveforms to limit the Doppler phase rotation to one-
quarter cycle or less, which requires that the maximum expected Doppler shift
and target velocity satisfy