Sequences exhibiting zero/low ambiguity zone (ZAZ/LAZ) properties play an important role in contemporary communication and radar systems, particularly in Integrated Sensing and Communication (ISAC), which is an emerging wireless technology by sharing the hardware and bandwidth to perform these two tasks simultaneously. By incorporating nonlinear mapping and parity adaptive factor to design novel exponential functions, this letter proposes three methods for constructing ZAZ/LAZ sequence sets with new parameters. The resulting sequences are cyclically distinct and asymptotically optimal with respect to theoretical bounds.

This paper introduces a novel finite Zak transform (FZT)-aided framework for constructing multiple zero-correlation zone (ZCZ) sequence sets with optimal correlation properties. Specifically, each sequence is perfect with zero auto-correlation sidelobes, each ZCZ sequence set meets the Tang-Fan-Matsufuji bound with equality, and the maximum inter-set cross-correlation of multiple sequence sets meets the Sarwate bound with equality. Our study shows that these sequences can be sparsely expressed in the Zak domain through properly selected index and phase matrices. Particularly, it is found that the maximum inter-set cross-correlation beats the Sarwate bound if every index matrix is a circular Florentine array. Several construction methods of multiple ZCZ sequence sets are proposed, demonstrating both the optimality and high flexibility. Additionally, it is shown that excellent synchronization performance can be achieved by the proposed sequences in orthogonal-time-frequency-space (OTFS) systems.

Spectrally-null-constrained (SNC) sequences, characterized by a good zero correlation zone (ZCZ) property, are applied in contemporary communication and radar systems that operate across a non-continuous spectrum. Although a large number of previous studies have been conducted, there has been no work on constructing optimal SNC sequence sets with all-zero inter-set cross-correlation (AZISCC). In this letter, we present a method for constructing SNC-ZCZ sequence sets utilizing the finite Zak transform (FZT). The obtained multiple SNC-ZCZ sequence sets are optimal, and they achieve the theoretical bound. The cross-correlation between sequence sets is 0, and the inter-cell interference can be eliminated. Furthermore, the sparse representation of the sequences is convenient for performing signal processing tasks in many radar, sonar, and communication applications.

This letter is concerned with efficient design of two-dimensional (2-D) Golay complementary array sets (GCASs) with ideal aperiodic sums for two correlation directions. Two new direct constructions of 2-D GCASs with highly flexible array sizes are proposed. The core idea is to truncate certain columns from large arrays generated by 2-D extended generalized Boolean functions (EGBFs). We show that these 2-D GCASs lead to highly flexible uniform rectangular array (URA) configurations for precoding matrices in omni-directional massive multi-input multi-output (MIMO) transmission.

This article aims to propose a novel Analytical Tensor Voting (ATV) mechanism, which enables robust perceptual grouping and salient information extraction for noisy N-dimensional (ND) data. Firstly, the approximation of the decaying function is investigated and adopted based on the idea of penalizing the 1-tensor votes by distance and curvature, respectively, followed by the derivation of analytical solution to the 1-tensor voting in ND space from the geometric view. Secondly, a novel spherical representation mechanism is proposed to facilitate the representation of the elementary tensors in various dimensional spaces, where the high dimensional spherical coordinate system is utilized to construct the controllable unit vectors and corresponding 1-tensors. Accordingly, any elementary K-tensor is represented by the surface integration of the constructed 1-tensors over the unit K-sphere. Thirdly, the ATV mechanism is constructed using the adopted decaying function and proposed spherical representation mechanism, where the analytical solution to tensor voting in ND space is derived, which enables the robust and accurate salient information extraction from noisy ND data. Finally, several interesting properties of the proposed ATV mechanism are investigated. Experimental results on synthetic and real data validate the effectiveness, efficiency and robustness of the proposed method in perceptual grouping tasks in 3D,10D or higher dimensional spaces.

A pair of binary sequences is generalized from the concept of a two-level autocorrelation function of a single binary sequence. In this paper, new families of binary sequence pairs with period N = np, where gcd(n,p) = 1, and optimal correlation values -1 are constructed, as well as new families of binary sequence pairs with three-level correlation and period N≡0(mod 4). For the new binary sequence pairs with optimal correlation values, their corresponding new difference set pairs and almost difference set pairs are also derived.