Page 302 - Fundamentals of Radar Signal Processing

FIGURE 4.43 Barker coded waveform, N = 13.

FIGURE 4.44 Binary sequence describing the Barker code of Fig. 4.43.

Recall that pulse compression waveforms have a bandwidth β 1/τ.
Because phase coded waveforms are constant frequency, it may not be obvious
that their spectrum is spread. However, the discontinuities caused by the phase

transitions do spread the signal spectrum. As an example, Fig. 4.45 shows the
effect of a single phase switch of 180° on the spectrum of a constant-frequency
waveform. While the effect depends on the point in the pulse at which the switch
occurs, clearly it significantly spreads the signal energy in frequency. Multiple
phase transitions increase this effect: Fig. 4.46 compares the spectra of the 13-
bit Barker coded waveform with that of a simple pulse of the same duration.
The Rayleigh bandwidth of the Barker spectrum is β = 1/τ Hz (about 13 times
c
as wide as that of the simple pulse in this specific case). In addition, the

sidelobes of the Barker waveform spectrum decay much more slowly than those
of the simple pulse.