Within the zero-correlation-zone (ZCZ), ZCZ sequence sets exhibit ideal correlation properties, which is highly advantageous for both wireless communications and radar sensing applications. Recently, to achieve optimal training for spatial modulation (SM), Paiet al. introduced the concept of sparse ZCZ (SZCZ) sequence sets, where each column contains only one non-zero element. In this paper, we first extend the SZCZ sequence set concept by permitting multiple non-zero elements per column, thereby accommodating training design requirements for generalized SM (GSM) systems. Then, we propose a direct construction of SZCZ sequence sets with parameter (qn+k,qm+n+k, (q−1)qπ(2)−1+(q−2)qπ(3)−1, (qn,qm+n)) based on restricted extended Boolean functions. Compared to existing works, the proposed SZCZ sequence sets exhibit a greater ZCZ width and can be applied to both SM and GSM training designs simultaneously. Simulation results show that compared with other training sequences, the channel estimation performance is significantly improved when the proposed SZCZ sequence set is used as the training sequences.

Sequences with low ambiguity zone (LAZ) properties are employed in integrated sensing and communication (ISAC) systems. In this letter, we introduce a new class of LAZ sequence sets based on cubic sequences. The proposed LAZ sequence set is asymptotically optimal with respect to the Ye-Zhou-Fan-Liu-Lei-Tang (YZFLLT) bound when the sequence length is odd. Otherwise, it achieves$\sqrt{2}$times of the YZFLLT bound. Furthermore, the sequence sets provide flexible choices for the sequence lengths, set size, and the LAZ region.

This paper studies Doppler resilient complementary sequences (DRCSs) whereby the ambiguity functions (AFs) of multiple element sequences are summed to attain low/zero AF values. We first derive a set of AF lower bounds for unimodular DRCS sets, which include the existing bounds on AFs as special cases. These bounds may be used as theoretical design guidelines to measure the optimality of DRCS sets against Doppler effect. In addition, we introduce some constructions of DRCS sets based on mathematical tools such as orthogonal matrices, circular Florentine rectangles and difference sets, which can generate the optimal DRCS set. Finally, we evaluate the feasibility of DRCSs for pulse train waveform design.

Complete complementary codes (CCCs) have important applications in communication, radar, and information security. In modern communication and radar systems, certain spectrum is reserved or prohibited from transmission, which leads to the so-called spectrally null constrained (SNC) problem. Compared with vast works on conventional CCCs, relatively little is known about SNC-CCCs. One objective of this paper is to derive several constructions of CCCs with more flexible settings from the graph of extended Boolean functions. This generalizes earlier achievements on CCCs from recent literature. Another objective of this paper is to employ the graphs of extended Boolean functions and polynomial representation of sequences to construct SNC-CCCs.

Due to their beautiful aperiodic correlation properties and low peak-to-average power ratio (PAPR), Golay complementary pairs (GCPs) and complementary sequence sets (CSSs) have been well studied. However, conventional GCPs and CSSs can only adapt to contiguous spectral resource allocation in wireless communication systems, and it is difficult for them to be compatible with non-contiguous resource allocation. Inspired by recent constructions of non-contiguous GCPs given by Şahin and Yang, we propose a new construction of non-contiguous GCPs, which can be regarded as an extension of Turyn’s construction. Besides, we then propose some constructions of non-contiguous CSSs, which can adapt to flexible resource allocation, having more flexible lengths, and lower time domain cross correlation than non-contiguous GCPs. Finally, we propose a CSS-based physical uplink control channels (PUCCH) scheme for up to 2 uplink control information (UCI) bits. Simulations show that its performance is similar to the GCP-based PUCCH scheme.

Recently, mutually orthogonal complementary sequence sets (MOCSSs) have been found many important applications in communication systems, radar, etc. Most of the known constructions of MOCSSs are based on generalized Boolean functions (GBFs) and hence mostly have lengths of power-of-two. A few constructions of MOCSSs are also based on paraunitary (PU) matrices and hence mostly have power-of-an-integer lengths. The objective of this paper is to develop a general framework to construct more MOCSSs consisting of sequences with non-power-of-two lengths. The proposed framework is based on complete complementary codes and even-shift complementary sequence sets.

A pair of sequences is called odd-length binary Z-complementary pair (OB-ZCP) if it is of odd-length and has zero aperiodic autocorrelation sums (AACSs) for all time-shifts within a certain region around the in-phase position, commonly known as zero correlation zone (ZCZ). There are two types of OB-ZCPs, namely Type-I OB-ZCPs and Type-II OB-ZCPs. Type-I OB-ZCPs have ZCZ around the in-phase position. Type-II OB-ZCPs have the ZCZ around the end-shift position. An OB-ZCP (Type-I or Type-II) of odd-length N is called Z-optimal if it achieves a maximum ZCZ width of (N + 1)/2. To date, a systematic construction of Type-II Z-optimal OB-ZCPs exist only for very limited lengths of the form 2m± 1, where m is a positive integer. It employs insertion method and delete method on binary Golay complementary pairs (GCPs) of length 2mderived from second order Reed-Muller codes. In this article, based on iterative insertion method, we construct Type-II Z-optimal OB-ZCPs of lengths 2m+ 3.