Searching for the best biphase and quadriphase quasi-Barker sequences

Sequences achieving the minimum peak aperiodic autocorrelation sidelobe level one are called the Barker sequences. Such sequences have been used in numerous real-world channel estimation, radar and spread spectrum communication applications. Unfortunately, the longest known biphase and quadriphase Barker sequences are of lengths 13 and 15 respectively. In this paper, motivated by quasi-synchronous applications, we investigate the quasi-Barker sequences that achieve the minimum peak sidelobe-level one within a certain window centered at the mainlobe. As our key results, all the best biphase and quadriphase quasi-Barker sequences of lengths up to 36 and 21, respectively, have been obtained by an efficient computer search.