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Z-complementary code set (ZCCS), an extension of perfect complementary codes (CCs), refers to a set of two-dimensional matrices having zero correlation zone properties. ZCCS can be used in various multi-channel systems to support, for example, quasi-synchronous interference-free multicarrier code-division multiple access communication and optimal channel estimation in multiple-input multiple-output systems. Traditional constructions of ZCCS heavily rely on a series of sequence operations which may not be feasible for rapid hardware generation particularly for long ZCCSs. In this paper, we propose a direct construction of ZCCS using second-order Reed-Muller codes with efficient graphical representation. Our proposed construction, valid for any number of isolated vertices present in the graph, is capable of generating optimal ZCCS meeting the set size upper bound.

Continuous phase modulation (CPM) plays an important role in wireless communications due to its constant envelope signal property and tight spectrum confinement capability. Although CPM has been studied for many years, CPM training waveforms having autocorrelations with zero sidelobes have not been reported before, to the best of our knowledge. Existing works on CPM system design mostly assume that the channel fading coefficients are either perfectly known at the receiver or estimated using random CPM training waveforms. In this work, we propose a novel class of CPM training waveforms displaying autocorrelation sidelobes close to zero. The key idea of our construction is to apply differential encoding to Golay complementary pair having perfect aperiodic autocorrelation sum properties.

Vehicular networks, an enabling technology for Intelligent Transportation System (ITS), smart cities, and autonomous driving, can deliver numerous on-board data services, e.g., road-safety, easy navigation, traffic efficiency, comfort driving, infotainment, etc. Providing satisfactory Quality of Service (QoS) in vehicular networks, however, is a challenging task due to a number of limiting factors such as erroneous and congested wireless channels (due to high mobility or uncoordinated channel-access), increasingly fragmented and congested spectrum, hardware imperfections, and anticipated growth of vehicular communication devices. Therefore, it will be critical to allocate and utilize the available wireless network resources in an ultra-efficient manner. In this paper, we present a comprehensive survey on resource allocation schemes for the two dominant vehicular network technologies, e.g. Dedicated Short Range Communications (DSRC) and cellular based vehicular networks. We discuss the challenges and opportunities for resource allocations in modern vehicular networks and outline a number of promising future research directions.

As a special case of sparse code multiple access (SCMA), low-density signatures based code-division multiple access (LDS-CDMA) was widely believed to have worse error rate performance compared to SCMA. With the aid of Eisenstein numbers, we present a novel class of LDS which can achieve error rate performances comparable to that of SCMA in Rayleigh fading channels and better performances in Gaussian channels. This is achieved by designing power-imbalanced LDS such that variation of user powers can be seen both in every chip window and the entire sequence window. As LDS-CDMA is more flexible in terms of its backwards compatibility, our proposed LDS are a promising sequence candidate for dynamic machine-type networks serving a wide range of communication devices.

A pair of sequences is called a Z-complementary pair (ZCP) if it has zero aperiodic autocorrelation sums (AACSs) for time-shifts within a certain region, called zero correlation zone (ZCZ). Optimal odd-length binary ZCPs (OB-ZCPs) display closest correlation properties to Golay complementary pairs (GCPs) in that each OB-ZCP achieves maximum ZCZ of width (N+1)/2 (where N is the sequence length) and every out-of-zone AACSs reaches the minimum magnitude value, i.e. 2. Till date, systematic constructions of optimal OB-ZCPs exist only for lengths $2^{\alpha} \pm 1$, where $\alpha$ is a positive integer. In this paper, we construct optimal OB-ZCPs of generic lengths $2^\alpha 10^\beta 26^\gamma +1$ (where $\alpha,~ \beta, ~ \gamma$ are non-negative integers and $\alpha \geq 1$) from inserted versions of binary GCPs. The key leading to the proposed constructions is several newly identified structure properties of binary GCPs obtained from Turyn's method. This key also allows us to construct OB-ZCPs with possible ZCZ widths of $4 \times 10^{\beta-1} +1$, $12 \times 26^{\gamma -1}+1$ and $12 \times 10^\beta 26^{\gamma -1}+1$ through proper insertions of GCPs of lengths $10^\beta,~ 26^\gamma, \text{and } 10^\beta 26^\gamma$, respectively. Our proposed OB-ZCPs have applications in communications and radar (as an alternative to GCPs).

This paper presents a family of training preambles for offset QAM (OQAM) based filter-bank multi-carrier (FBMC) modulations with low peak-to-average power ratio (PAPR) property. We propose to use binary Golay sequences as FBMC preambles and analyze the maximum PAPR for different numbers of zero guard symbols. For both the PHYDYAS and Hermite prototype filters with overlapping factor of 4, as an illustration of the proposed preambles, we show that a preamble PAPR less than 3 dB can be achieved with probability of one, when three or more zero guard symbols are inserted in the vicinity of each preamble.

The contributions of this paper are twofold: Firstly, we introduce a novel class of sequence pairs, called "cross Z-complementary pairs (CZCPs)", each displaying zero-correlation zone (ZCZ) properties for both their aperiodic autocorrelation sums and crosscorrelation sums. Systematic constructions of perfect CZCPs based on selected Golay complementary pairs (GCPs) are presented. Secondly, we point out that CZCPs can be utilized as a key component in designing training sequences for broadband spatial modulation (SM) systems. We show that our proposed SM training sequences derived from CZCPs lead to optimal channel estimation performance over frequency-selective channels.

The concept of paraunitary (PU) matrices arose in the early 1990s in the study of multi-rate filter banks. So far, these matrices have found wide applications in cryptography, digital signal processing, and wireless communications. Existing PU matrices are subject to certain constraints on their existence and hence their availability is not guaranteed in practice. Motivated by this, for the first time, we introduce a novel concept, called $Z$-paraunitary (ZPU) matrix, whose orthogonality is defined over a matrix of polynomials with identical degree not necessarily taking the maximum value. We show that there exists an equivalence between a ZPU matrix and a $Z$-complementary code set when the latter is expressed as a matrix with polynomial entries. Furthermore, we investigate some important properties of ZPU matrices, which are useful for the extension of matrix sizes and sequence lengths. Finally, we propose a unifying construction framework for optimal ZPU matrices which includes existing PU matrices as a special case.

A major drawback of orthogonal frequency division multiplexing (OFDM) systems is their high peak-to-mean envelope power ratio (PMEPR). The PMEPR problem can be solved by adopting large codebooks consisting of complementary sequences with low PMEPR. In this paper, we present a new construction of polyphase complementary sets (CSs) using generalized Boolean functions (GBFs), which generalizes Schmidt's construction in 2007, Paterson's construction in 2000 and Golay complementary pairs (GCPs) given by Davis and Jedwab in 1999. Compared with Schmidt's approach, our proposed CSs lead to lower PMEPR with higher code-rate for sequences constructed from higher-order ($\geq 3$) GBFs. We obtain polyphase complementary sequences with maximum PMEPR of $2^{k+1}$ and $2^{k+2}-2M$ where $k,M$ are non-negative integers that can be easily derived from the GBF associated with the CS.

A quasi-complementary sequence set (QCSS) refers to a set of two-dimensional matrices with low non-trivial aperiodic auto- and cross- correlation sums. For multicarrier code-division multiple-access applications, the availability of large QCSSs with low correlation sums is desirable. The generalized Levenshtein bound (GLB) is a lower bound on the maximum aperiodic correlation sum of QCSSs. The bounding expression of GLB is a fractional quadratic function of a weight vector $\mathbf{w}$ and is expressed in terms of three additional parameters associated with QCSS: the set size $K$, the number of channels $M$, and the sequence length $N$. It is known that a tighter GLB (compared to the Welch bound) is possible only if the condition $M\geq2$ and $K\geq \overline{K}+1$, where $\overline{K}$ is a certain function of $M$ and $N$, is satisfied. A challenging research problem is to determine if there exists a weight vector which gives rise to a tighter GLB for \textit{all} (not just \textit{some}) $K\geq \overline{K}+1$ and $M\geq2$, especially for large $N$, i.e., the condition is {asymptotically} both necessary and sufficient. To achieve this, we \textit{analytically} optimize the GLB which is (in general) non-convex as the numerator term is an indefinite quadratic function of the weight vector. Our key idea is to apply the frequency domain decomposition of the circulant matrix (in the numerator term) to convert the non-convex problem into a convex one. Following this optimization approach, we derive a new weight vector meeting the aforementioned objective and prove that it is a local minimizer of the GLB under certain conditions.