Page 309 - Fundamentals of Radar Signal Processing

FIGURE 4.50 Matched filter output for a 1023-bit pseudorandom biphase code.

While the Barker codes are the only biphase codes with a peak sidelobe
value of 1 that are known to exist, one can seek longer codes with minimum
peak sidelobe (MPS) levels for the length of interest. These MPS codes are
found by exhaustive search techniques, taking advantage of certain properties of
biphase code autocorrelations to prune the search somewhat. As an example, the

MPS code for N = 20 has a maximum sidelobe level of 2, giving a PSL ratio of
1/10 instead of the 1/4 obtained by the nested Barker code above. The state of
the art is summarized and references given in Keel (2010). The peak sidelobe
for MPS codes of lengths 2 through 5, 7, 11, and 13 (Barker codes) is 1; for N =
6, 8 – 10, 12, 14 – 21, 25, and 28 is 2; for N = 22 – 24, 26 – 27, 29 – 48, and 51
is 3; for N = 49 – 50 and 52 – 82 is 4; and for N = 83 – 105 is 5. The MPS has

not been established at this writing for codes longer than 105. Table 4.2 lists
one sample code for the longest code length in each of these sidelobe level
regimes; additional sample codes for other lengths are available in the
references. It is evident that the sidelobe level in dB improves only very slowly
as the code length increases.