Zero correlation zone (ZCZ) sequences and Golay sequences are two kinds of sequences with different preferable correlation properties. It was shown by Gong textit{et al.} and Chen textit{et al.} that some Golay sequences also possess a large ZCZ and
are good candidates for pilots in OFDM systems. Known Golay sequences with ZCZ reported in the literature have a limitation in the length which is the form of a power of 2. One objective of this paper is to propose a construction of Golay complementary pairs (GCPs) with new lengths whose periodic autocorrelation of each of the Golay sequences and periodic corss-correlation of the pair displays a zero correlation zone (ZCZ) around the in-phase position. Specifically, the proposed GCPs have length $4N$ (where, $N$ is the length of a GCP) and ZCZ width $N+1$. Another objective of this paper is to extend the construction to two-dimensional Golay complementary array pairs (GCAPs). Interestingly the periodic corss-correlation of the proposed GACPs also have large ZCZs around the in-phase position.
Sequences play an important role in many engineering applications and systems. Searching sequences with desired properties has long been an interesting but also challenging research topic. This article proposes a novel method, called HpGAN, to search
desired sequences algorithmically using generative adversarial networks (GAN). HpGAN is based on the idea of zero-sum game to train a generative model, which can generate sequences with characteristics similar to the training sequences. In HpGAN, we design the Hopfield network as an encoder to avoid the limitations of GAN in generating discrete data. Compared with traditional sequence construction by algebraic tools, HpGAN is particularly suitable for intractable problems with complex objectives which prevent mathematical analysis. We demonstrate the search capabilities of HpGAN in two applications: 1) HpGAN successfully found many different mutually orthogonal complementary code sets (MOCCS) and optimal odd-length Z-complementary pairs (OB-ZCPs) which are not part of the training set. In the literature, both MOCSSs and OB-ZCPs have found wide applications in wireless communications. 2) HpGAN found new sequences which achieve four-times increase of signal-to-interference ratio--benchmarked against the well-known Legendre sequence--of a mismatched filter (MMF) estimator in pulse compression radar systems. These sequences outperform those found by AlphaSeq.
Quasi-complementary sequence sets (QCSSs) can be seen as a generalized version of complete complementary codes (CCCs), which enables multicarrier communication systems to support more users. The contribution of this work is two-fold. First, we propos
e a systematic construction of Florentine rectangles. Secondly, we propose several sets of CCCs and QCSS, using Florentine rectangles. The CCCs and QCSS are constructed over $mathbb{Z}_N$, where $Ngeq2$ is any integer. The cross-correlation magnitude of any two of the constructed CCCs is upper bounded by $N$. By combining the proposed CCCs, we propose asymptotically optimal and near-optimal QCSSs with new parameters. This solves a long-standing problem, of designing asymptotically optimal aperiodic QCSS over $mathbb{Z}_N$, where $N$ is any integer.
