New spectrally null constrained mutually orthogonal complementary sets and Z-complementary code sets

Abstract

Spectrally null constrained (SNC) sequences play a significant role in orthogonal frequency division multiplexing (OFDM) systems operating over a non-continuous spectrum. However, most current research has focused on the design of single-channel SNC sequences and few studies have concentrated on the constructions of mutually orthogonal complementary sets (MOCSs)/Zcomplementary code sets (ZCCSs) under spectral null constraints, where Z denotes the zero correlation zone (ZCZ) width. Our objective of this paper is to present some constructions of SNC-MOCSs with low peak-to-average power ratio (PAPR) property and SNC-ZCCSs. Firstly, extended Boolean function (EBF) and polynomial representation are employed to design SNC-MOCSs and SNC-CSSs. The proposed parameters of SNC-CSSs include a recent iterative result as a special case. Then SNC-ZCCSs, which have potential applications for cognitive radio (CR) multiple-input multiple-output (MIMO) channel estimation and CR quasi-synchronization communications to achieve interferencefree performance, are constructed by using the same method.