For an integer q≥2, new sets of q-phase aperiodic complementary sequences (ACSs) are constructed by using known sets of q-phase ACSs and certain matrices. Employing the Kronecker product to two known sets of q-phase ACSs, some sets of q-phase aperiodic complementary sequences with a new length are obtained. For an even integer q, some sets of q-phase ACSs with new parameters are generated, and their equivalent matrix representations are also presented.

We introduce an extension of Golay complementary sequences in which, for each sequence, there exists another sequence such that the sum of aperiodic autocorrelation functions of these two sequences for a given multiple L-shift (L≥1) is zero except for the zero shift. We call these sequences multiple L-shift complementary sequences. It is well-known that the peak-to-average power ratio (PAPR) value of any Golay complementary sequence is less than or equal to 2. In this paper, we show that the PAPR of each multiple L-shift complementary sequence is less than or equal to 2L. We also discuss other properties of the sequences and consider their construction.

Barker sequences have been used in many existing communications and ranging systems. Unfortunately, the longest known biphase and quadriphase Barker sequences are of lengths 13 and 15, respectively. In this paper, we introduce the so-called quasi-Barker sequences which 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, were obtained by an efficient computer search. These sequences may provide better multipath resistance and tracking accuracy in ranging applications.