Page 311 - Fundamentals of Radar Signal Processing

Polyphase codes allow arbitrary values for the chip phases ϕ . Compared
n
to biphase codes, they can exhibit lower sidelobe levels and greater Doppler
tolerance. A number of polyphase codes are in common use. These include
“polyphase Barker codes,” the Frank codes, and the P1, P2, P3, P4, and P(n, k)
codes. All of these except the polyphase Barker codes are related to LFM or
NLFM waveforms. Numerous other polyphase codes have been proposed; many
are described in Levanon and Mozeson (2004). The special case of quadriphase

codes is described in Keel and Baden (2012).
2
Frank codes are codes whose length is a square, N = M for some M. The
phase sequence for a Frank code is given by

(4.137)

As an example, if M = 4 so N = 16, the sequence of phases becomes

(4.138)

Figure 4.51 shows the magnitude of the matched filter output for the case N
9
= 16. Note that while the mainlobe has a local minimum at t = τ , it does not go
c
to zero at that point as the Barker code autocorrelations do. The largest sidelobe
in this example is , larger than the Barker codes. The sidelobe level is
or –21.1 dB. Figure 4.52 shows the ambiguity function in contour plot form. The

main ridge is skewed in the delay-Doppler plane, similar to the range-Doppler
coupling of an LFM ambiguity function.