Binary Almost-Perfect Sequence Sets

Sequence set with lower correlation values is highly desired for engineering applications. However, theoretical results (e.g., Welch bound) show that θ_max ≥ √(N) in general, that is, the maximum out-of-phase autocorrelation and cross-correlation magnitudes of a sequence set is not less than the square root of the sequence period. In this paper, we propose a new concept, namely almost perfect sequence set (APSS), which has the property θ_max ≤ c except for at most m shifts, where c and m are predefined small integers. A uniform method is presented to construct APSS and then the properties of such APSS are discussed. Moreover, a distance inequality on the APSS with m = 1 is obtained and several APSS families such as (2p, 8p + 2, 6, 4) -APSS and (3p, (64p²+8)/3,9,9) -APSS for any prime p ≥ 5 are constructed based on Paley and Paley partial sequences. Finally, it shows that the APSS can be used to construct LCZ sequences and the properties of such LCZ sequences are presented.