New Classes of Asymptotically Optimal Spectrally-Constrained Sequences Derived from Cyclotomy

Abstract

<p style='text-indent:20px;'>As numerous applications in wireless communications and radar sensing all rely on the finite and precious spectral resource, contiguous spectrum allocation schemes have become very difficult to continue nowadays. Spectrally constrained sequences (SCSs) are specially designed sequences which display low correlation sidelobes to effectively utilize the increasingly congested and fragmented spectrum. Recently, Liu <i>et. al</i> (IEEE Trans. Inf. Theory 64(4):2571-2582, 2018) proposed a lower bound of the maximal correlation for SCSs and constructed two classes of optimal SCSs by using Singer difference sets and perfect ternary sequences. For the application of SCSs, it is desirable that the spectrally constrained position should be as flexible as possible, and the correlation tolerance should be as small as possible. In this paper, we present some systematic constructions based on cyclotomy which generate some asymptotically optimal SCSs with respect to Liu's bound. The proposed constructions result in SCSs with new parameters and are more flexible in terms of the "position of the null constraint". In addition, we propose a framework which control the power of new SCSs while maintaining the correlation magnitudes by using cyclic algorithm-new (CAN) algorithm.</p>