We study irregular repetition slotted ALOHA (IRSA) with multi-antenna reception over Rayleigh block fading channels. An exact closed-form expression for the average decoding error probability ¯ϵm,L is derived for collision sizes m = 1 and m = 2 by applying the inclusion–exclusion principle, which generalizes known single-antenna results and remains valid for any finite number of antennas. Using this result, we develop a density-evolution-based analysis of multi-antenna IR-SA systems and characterize belief-propagation (BP) thresholds. Numerical results for the corresponding maximum a posteriori (MAP) decoding thresholds and converse bounds are also presented, demonstrating threshold saturation with spatial coupling.

The low-altitude economy (LAE), an emerging economic paradigm encompassing various flight activities in low-altitude airspace, has attracted widespread attention from academia and industry due to its appealing economic and social benefits. In this paper, we investigate the design of integrated sensing and communication (ISAC) waveforms for LAE applications. Specifically, we propose an adaptive ISAC waveform, which integrates the maximum distance separable (MDS) code and index modulation (IM) into the orthogonal frequency division multiplexing (OFDM) waveform, namely A-MDS-OFDM-IM. This design combines the hybrid benefits of MDS code, IM, and OFDM techniques, i.e., the error detection capability of MDS code, the high spectral efficiency (SE) of IM, and the high sensing resolution of OFDM, thereby enabling robust communication and sensing. A comprehensive performance analysis of A-MDS-OFDM-IM is provided, including its bit error rate (BER), peak-to-sidelobe level (PSL), and peak-to-average power ratio (PAPR). Moreover, to address the high PAPR issue of A-MDS-OFDM-IM, we develop an adaptive design criterion based on the alternating direction method of multipliers (ADMM), which is capable of jointly optimizing the communication, sensing, and PAPR performance of the proposed system. Simulation results demonstrate that the proposed waveform achieves better BER performance than conventional OFDM-based waveforms under a non-ideal high power amplifier (HPA), owing to its low-PAPR characteristic. Additionally, the proposed waveform ensures robust sensing with satisfactory PSL performance, making it a promising ISAC waveform for LAE applications.

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.

This paper proposes, for the first time, a hybrid multiple access framework that integrates the principles of rate-splitting (RS) and sparse code multiple access (SCMA) in an SISO downlink scenario. The proposed scheme, termed RS-SCMA, unifies the powerful interference management capability of rate-splitting multiple access (RSMA) with the near-optimal multiuser detection of SCMA. A key feature of RS-SCMA is a tunable splitting factor α, which governs the allocation between the genericM-ary modulated common messages and SCMA-encoded private messages. This enables dynamic control over the fundamental trade-off between system sum-rate, bit error rate (BER), and the overloading factor. We develop novel transmitter and receiver architectures based on soft successive interference cancellation (SIC), incorporating message passing algorithm (MPA) detection and soft-symbol reconstruction. Furthermore, a unified analytical expression for the achievable sum-rate is derived as a function of the splitting factor α. The performance of the proposed RS-SCMA system is evaluated in terms of both BER and sum-rate. Simulation results confirm the superiority of RS-SCMA over conventional SCMA and multi-carrier RSMA, demonstrating its scalability and robustness even in the presence of channel estimation errors.

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.

The impact of both multiplicative and additive hardware impairments (HWIs) on multiple-input multiple-output affine frequency division multiplexing (MIMO-AFDM) systems is investigated. For small-scale MIMO-AFDM systems, a tight bit error rate (BER) upper bound associated with the maximum likelihood (ML) detector is derived. By contrast, for large-scale systems, a closed-form BER approximation associated with the linear minimum mean squared error (LMMSE) detector is presented, including realistic imperfect channel estimation scenarios. Our first key observation is that the full diversity order of a hardware-impaired AFDM system remains unaffected, which is a unique advantage. Furthermore, our analysis shows that 1) the BER results derived accurately predict the simulated ML performance in moderate-to-high signal-to-noise ratios (SNRs), while the theoretical BER curve of the LMMSE detector closely matches that of the Monte-Carlo based one. 2) MIMO-AFDM is more resilient to multiplicative distortions, such as phase noise and carrier frequency offset, compared to its orthogonal frequency division multiplexing (OFDM) counterparts. This is attributed to its inherent chirp signal characteristics; 3) MIMO-AFDM consistently achieves superior BER performance compared to conventional MIMO-OFDM systems under the same additive HWI conditions, as well as different velocity values. The latter is because MIMO-AFDM is also resilient to the additional inter-carrier interference (ICI) imposed by the nonlinear distortions of additive HWIs. In a nutshell, compared to OFDM, AFDM demonstrates stronger ICI resilience and achieves the maximum full diversity attainable gain even under HWIs, thanks to its intrinsic chirp signalling structure as well as to the beneficial spreading effect of the discrete affine Fourier transform.

This paper proposes a novel multi-carrier modulation framework for high-mobility communication scenarios. Our key idea lies in spreading data symbols across the delay-Doppler (DD) domain through orthogonal chirp-Zak transform (CZT). To enable efficient signal multiplexing, the proposed modulation scheme employs a transmitter signal that maintains orthogonality with the inherent resolution characteristics of the DD plane. Termed as Orthogonal Chirp Delay-Doppler Division Multiplexing (CDDM), we demonstrate a synergistic integration of chirp waveform properties with the channel structure of the DD domain, thereby achieving advantages with both lower computational efficiency and improved detection performance. We introduce a novel CZT-based superimposed sparse pilot structure to enable simultaneous estimation of delay-Doppler shifts and channel coefficients. For enhanced performance, we further develop an embedded pilot scheme that demonstrates channel estimation performance comparable to that of Orthogonal Delay-Doppler Division Multiplexing (ODDM) systems. Simulation results demonstrate that CDDM achieves significant bit error rate (BER) improvements over existing modulation schemes , under perfect channel state information (CSI), as well as superior out-of-band emissions (OOBE). Further, for the imperfect CSI case, the proposed CZT-based superimposed pilot scheme leads to significantly reduced normalized mean square error (NMSE), whilst attaining equivalent estimation accuracy to that of ODDM with lower computational complexity.

The emergence of sixth generation communication (6G) wireless networks is set to revolutionize vehicular communication by enabling ultra-reliable, low-latency, and high-capacity connectivity in cellular vehicle-to-everything (C-V2X) environments. This paper presents a theoretical framework on novel cooperative vehicular communication and information perception algorithms for large-scale 6G C-V2X networks while leveraging integrated space-air-ground communication system. Specifically, we address key challenges in real-time information exchange and fusion among multiple vehicles. Utilizing inequality theory and functional mapping theory, we derive an upper bound on channel capacity for a fixed number of relays and propose a low-complexity, multi-class relay selection algorithm. Furthermore, we introduce an optimal mobile edge computing (MEC) based correspondence strategy to improve vehicle-to-vehicle communication, alongside an efficient information estimation algorithm to facilitate real-time data sharing. Our simulation results confirm that the proposed algorithms significantly outperform existing cooperative vehicular schemes in terms of channel capacity, while the developed evaluation theory ensures accurate cooperative perception with reduced computational complexity. The proposed framework and theoretical contributions offer a foundational basis for 6G C-V2X networks.

Affine frequency division multiplexing (AFDM) has recently emerged as an excellent backward-compatible 6G waveform. In this paper, we study matched filtering (MF) assisted channel estimation (CE) for AFDM systems in complex doubly selective channels. By deriving the complete input-output relationship of the continuous-time signal, the inter-chirp-carrier interference, signal-to-interference-plus-noise ratio (SINR), and the effective SINR loss of AFDM, are investigated in discrete affine Fourier transform (DAFT) domain. Further, we propose two low-complexity methods for constructing the channel matrix by taking advantage of its inherent discrete Fourier transform structure and the staircase structure of the piecewise functions in the channel matrix, respectively. It is shown that complexity reduction by at least two orders of magnitude can be achieved for a large number of chirp subcarriers. For the CE problem in doubly selective channels, we introduce an MF assisted CE scheme. This allows us to sequentially estimate the parameters of each path by exploiting the separability and approximate orthogonality of different paths in the DAFT domain, thus leading to significantly reduced complexity. Furthermore, based on generalized Fibonacci search (GFS), an MF-GFS scheme is proposed to avoid significantly redundant computation, which can be extended to typical wide-band systems. Extensive simulation results indicate that the proposed schemes offer superior advantages in terms of their improved communication performance and lower complexity.

Affine frequency division multiplexing (AFDM) is a promising chirp-assisted multicarrier waveform for future high-mobility communications. This paper is devoted to enhanced receiver design for multiple-input–multiple-output AFDM (MIMO-AFDM) systems. Firstly, we introduce a unified variational inference (VI) approach to approximate the target posterior distribution, under which the belief propagation (BP) and expectation propagation (EP)-based algorithms are derived. As both VI-based detection and low-density parity-check (LDPC) decoding can be expressed by bipartite graphs in MIMO-AFDM systems, we construct a joint sparse graph (JSG) by merging the graphs of these two for low-complexity receiver design. Then, based on this graph model, we present the detailed message propagation of the proposed JSG. Additionally, we propose an enhanced JSG (E-JSG) receiver based on the linear constellation encoding model. The proposed E-JSG eliminates the need for interleavers, de-interleavers, and log-likelihood ratio transformations, thus leading to concurrent detection and decoding over the integrated sparse graph. To further reduce detection complexity, we introduce a sparse channel method by approaximating multiple graph edges with insignificant channel coefficients into a single edge on the VI graph. Simulation results show the superiority of the proposed receivers in terms of computational complexity, detection and decoding latency, and error rate performance compared to the conventional ones.

Generalized spatial modulation-aided affine frequency division multiplexing (GSM-AFDM) is conceived for reliable multiple-input multiple-output (MIMO) communications over doubly selective channels. We commence by proposing several low-complexity detectors for large-scale GSM-AFDM systems to meet the diverse requirements of heterogeneous receiver designs in terms of detection complexity and reliability. Specifically, we introduce the linear minimum mean square error (LMMSE) equalizer-based maximum likelihood detector (LMMSE-MLD). By exploiting the GSM properties, we then derive the LMMSE-based transmit-antenna activation pattern (TAP) check-based log-likelihood ratio detector (LMMSE-TC-LLRD). In addition, we propose a pair of new detectors, namely the greedy residual check detector (GRCD) and the reduced space check detector (RSCD). We also derive a bit error rate (BER) upper-bound by considering the MLD. Our analytical results are also available for multiple-input multiple-output (MIMO)-AFDM, since MIMO-AFDM can be regarded as a special case of the proposed GSM-AFDM. Our simulation results demonstrate that 1) the BER upper bound derived is tight for moderate to high signal-to-noise ratios (SNRs), 2) the proposed GSM-AFDM achieves lower BER than its conventional orthogonal frequency division multiplexing (OFDM), orthogonal time frequency space (OTFS) and AFDM counterparts. Specifically, at a BER of 10−4and a velocity of 540 km/h, the proposed GSM-AFDM is capable of attaining about 6 dB SNR gain compared to GSM-OFDM, and 3) the conceived detectors strike a compelling trade-off between the BER and complexity.

This paper proposes a novel non-orthogonal affine frequency division multiplexing (nAFDM) waveform for reliable high-mobility communications with enhanced spectral efficiency (SE). The key idea is to introduce a bandwidth compression factor into the AFDM modulator to enable controllable subcarrier overlapping. We first detail the proposed nAFDM transceiver and derive the corresponding input-output signal relationship. Then, an efficient nAFDM signal generation method based on the inverse discrete Fourier transform (IDFT) is proposed, enabling practical implementation using existing inverse fast Fourier transform (IFFT) modules without additional hardware complexity. Next, to characterize the impact of non-orthogonal modulation, we derive a closed-form expression of inter-carrier interference (ICI), showing its dependence on the bandwidth compression factor. To mitigate the resulting interference, we propose a soft iterative detection algorithm and a low-complexity implementation approach that leverages the distribution characteristics of ICI. Simulation results demonstrate that 1) in terms of bit error rate (BER), the proposed nAFDM can achieve nearly identical BER compared to conventional AFDM, while outperforms other waveform counterparts; 2) nAFDM is capable of striking higher SE compared to other existing waveforms; and 3) the proposed nAFDM achieves an attractive BER vs. SE trade-off, and the proposed soft iterative detection (ID) scheme can attain a trade-off between BER and complexity.

This paper proposes a spectrum-efficient non-orthogonal affine frequency division multiplexing (AFDM) waveform for reliable high-mobility communications in the upcoming sixth-generation (6G) mobile systems. Our core idea is to introduce a compression factor to enable controllable subcarrier overlapping in chirp-based AFDM modulation. To mitigate inter-carrier interference (ICI), we introduce linear precoding at the transmitter and an iterative detection scheme at the receiver. Simulation results demonstrate that these techniques can effectively reduce interference and maintain robust bit error rate (BER) performance even under aggressive compression factors and high-mobility channel conditions. The proposed non-orthogonal AFDM waveform offers a promising solution for next-generation wireless networks, balancing spectrum efficiency and Doppler resilience in highly dynamic environments.

This paper proposes a novel multi-carrier modulation scheme, orthogonal chirp delay-Doppler division Multiplexing (CDDM), tailored for future high mobility communications. The core innovation lies in spreading data symbols over chirps in the Delay-Doppler (DD) domain using a novel chirp-Zak transform (CZT), and enabling orthogonal pulse transmission within the DD plane. This approach fully leverages the advantages of both chirp signals and DD channels. Key contributions of CDDM include: efficient implementation through pre-computation techniques, synergistic exploitation of chirp signal characteristics and DD channel properties, and novel data detection via DD chirp correlation. Simulation results demonstrate that CDDM achieves significant bit error rate (BER) improvements compared to benchmarking schemes, validating its potential for high mobility communication systems.

This paper introduces a novel cooperative vehicular communication algorithm tailored for future 6G ultra-massive vehicle-to-everything (V2X) networks leveraging integrated space-air-ground communication systems. Specifically, we address the challenge of real-time information exchange among rapidly moving vehicles. We demonstrate the existence of an upper bound on channel capacity given a fixed number of relays, and propose a low-complexity relay selection heuristic algorithm. Simulation results verify that our proposed algorithm achieves superior channel capacities compared to existing cooperative vehicular communication approaches.

To fulfil the demand for high energy and spectral efficiency (SE) while serving multiple users concurrently for next-generation 6G systems, both non-orthogonal multiple access (NOMA) and orthogonal frequency division multiplexing (OFDM) aided index modulation (IM) endorse the requirements. NOMA serves several users concurrently while sharing the frequency and time resources. In addition, the single-mode OFDM-IM system improves the SE by broadcasting the additional bits of active subcarrier selection. Meanwhile, dual-mode OFDM-IM relatively enhances the SE via transmitting different constellation sets over a subblock OFDM vector. Furthermore, broadcasting the baseband NOMA symbols over a dual-mode OFDM-IM scheme improves the SE compared to the conventional IM schemes. This paper describes a dual-mode aided cooperative relaying OFDM-IM-based downlink hybrid NOMA system serving multiple users simultaneously. The Monte Carlo simulation results demonstrate that the bit error rate (BER) performance of the proposed system accessed using the maximum likelihood (ML) detector for different modulation schemes is significantly better as compared to the existing cooperative relaying OFDM-IM-aided NOMA systems, including single-mode and hybrid systems.

This paper studies one-time pad (OTP) secure communication by leveraging the unpredictable physical layer channel characteristics. Existing OTP schemes based on physical-layer key generation (PKG) require additional transmission overhead of information reconciliation and may face security threats of information leakage under slow-varying channels. To tackle these challenges, we investigate a fault-tolerant privacy amplification method through variable bloom filters to address the underlying security problems. Specifically, the quantized bit sequence of the channel state information goes through a bloom filter to improve the randomness within the sequence while the parameters of bloom filter vary to avoid the correlations between adjacent sequences. We then optimize the parameters of the error-correcting code used during communication based on the position of the eavesdropper and the length of the quantized bits, thereby further enhancing the system security. Through comprehensive simulations, it is shown that our proposed approach can achieve a near-perfect pass rate in NIST randomness tests, and with a bit replacement rate around 0.45, whilst capable of resisting attacks under slow-varying channels. These results indicate that the proposed scheme significantly outperforms previous OTP secure transmission schemes.

Pilot sequence design over doubly selective channels (DSC) is challenging due to the variations in both the time- and frequency-domains. Against this background, the contribution of this paper is twofold: Firstly, we investigate the optimal sequence design criteria for efficient channel estimation in orthogonal frequency division multiplexing systems under DSC. Secondly, to design pilot sequences that can satisfy the derived criteria, we propose a new metric called oversampled ambiguity function (O-AF), which considers both fractional and integer Doppler frequency shifts. Optimizing the sidelobes of O-AF through a modified iterative twisted approximation (ITROX) algorithm, we develop a new class of pilot sequences called “oversampled low ambiguity zone (O-LAZ) sequences”. Through numerical experiments, we evaluate the efficiency of the proposed O-LAZ sequences over the traditional low ambiguity zone (LAZ) sequences, Zadoff-Chu (ZC) sequences and m-sequences, by comparing their channel estimation performances over DSC.

Cross Z-complementary sets (CZCSs) are useful for optimal training design in spatial modulation (SM) system over frequency-selective channels. Recently, several generic constructions of CZCSs have been proposed based on special sequences. Based on the algebraic tool of generalized Boolean functions, we make the first attempt for two constructions of CZCSs having flexible non-power-of-two lengths and large zero correlation zone properties. It is shown that the proposed CZCSs lead to optimal SM training sequences which can achieve the minimum mean square error of channel estimation performance in frequency-selective channels.

In this paper, we consider the physical layer security (PLS) problem for integrated sensing and communication (ISAC) systems in the presence of hybrid-colluding eavesdroppers, where an active eavesdropper (AE) and a passive eavesdropper (PE) collude to intercept the confidential information. To ensure the accuracy of sensing while preventing the eavesdropping, a base station transmits a signal consisting of information symbols and sensing waveform, in which the sensing waveform can be also used as artificial noise to interfere with eavesdroppers. Under this setup, we propose an alternating optimization-based two stage scheme (AO-TSS) for improving the sensing and communication performance. In the first stage, based on the assumptions that the perfect channel state information (CSI) of the AE and statistical CSI of the PE are known, the communication and sensing beamforming problem is formulated with the objective of minimizing the weighted sum of the beampattern matching mean squared error (MSE) and cross-correlation, subject to the secure transmission constraint. To tackle the non-convexity, we propose a semi-definite relaxation (SDR) algorithm and a reduced-complexity zero-forcing (ZF) algorithm. Then, the scenarios are further extended to more general cases with imperfect AE CSI and unknown PE CSI. To further improve the communication performance, the second-stage problem is developed to optimize the secrecy rate threshold under the radar performance constraint. Finally, numerical results demonstrate the superiority of the proposed scheme in terms of sensing and secure communication.

This paper presents a novel training matrix design for spatial modulation (SM) systems, by introducing a new class of two-dimensional (2D) arrays called sparse zero correlation zone (SZCZ) arrays. An SZCZ array is characterized by a majority of zero entries and exhibits the zero periodic auto-and cross-correlation zone properties across any two rows. With these unique properties, we show that SZCZ arrays can be effectively used as training matrices for SM systems. Additionally, direct constructions of SZCZ arrays with large ZCZ widths and controllable sparsity levels based on 2D restricted extended generalized Boolean functions (REGBFs) are proposed. Compared with existing training schemes, the proposed SZCZ-based training matrices have larger ZCZ widths, thereby offering greater tolerance for delay spread in multipath channels. Simulation results demonstrate that the proposed SZCZ-based training design exhibits superior channel estimation performance over frequency-selective fading channels compared to existing alternatives.

This paper studies enhanced physical-layer key generation (PKG) for multiuser orthogonal frequency division multiple access (OFDMA) networks. In practical OFDMA systems, our key observation is that there are frequency correlations between different subcarriers which potentially lead to compromised randomness of the generated keys as well as reduced sum secret key rate. Motivated by this, we show that subcarrier allocation plays a key role in enhancing the PKG performance in OFMDA networks. We prove that when a single user terminal selects a finite number of subcarriers for key generation, adopting uniformly spaced subcarriers is the optimal solution as it leads to higher secret key rates and better randomness. Moreover, we derive a closed-form expression for the sum secret key rate and introduce a low-complexity near-optimal algorithm that can achieve an appropriate subcarrier allocation policy in a timely manner. Simulation results show that our proposed near-optimal algorithm exhibits significant advantages in maximizing the sum secret key rate and improving key randomness compared with existing subcarrier allocation algorithms.

This paper presents generalized Arlery-Tan-Rabaste-Levenshtein lower bounds on the maximum aperiodic ambiguity function (AF) magnitude of unimodular sequences under certain delay-Doppler low ambiguity zones (LAZ). Our core idea is to explore the upper and lower bounds on the Frobenius norm of the weighted auto- and cross-AF matrices by introducing two weight vectors associated with the delay and Doppler shifts, respectively. As a second major contribution, we demonstrate that our derived lower bounds are asymptotically achievable with selected Chu sequence sets by analyzing their maximum auto- and cross-AF magnitudes within certain LAZ.

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.

Sequences with low/zero ambiguity zone (LAZ/ZAZ) properties are useful in modern communication and radar systems operating over mobile environments. This paper first presents a new family of ZAZ sequence sets motivated by the “modulating” zero correlation zone (ZCZ) sequences which were first proposed by Popovic and Mauritz. We then introduce a second family of ZAZ sequence sets with comb-like spectrum, whereby the local Doppler resilience is guaranteed by their inherent spectral nulls in the frequency domain. Finally, LAZ sequence sets are obtained by exploiting their connection with a novel class of mapping functions. These proposed unimodular ZAZ and LAZ sequence sets are cyclically distinct and asymptotically optimal with respect to the existing theoretical bounds on ambiguity functions.

Recently, the concept of enhanced cross Z-complementary sets (E-CZCS) has been proposed for training sequence design in generalized spatial modulation (GSM). Based on generalized Boolean functions, we present a new construction of E-CZCSs having maximum zero correlation zone (ZCZ) width. Based on the proposed E-CZCSs, numerical simulation results indicate that the resultant training sequences lead to superior channel estimation performance in broadband GSM systems.

In wireless Internet-of-Thing (IoT) networks, massive nodes/users congest in limited resource blocks (RB, i.e., time-frequency block). Sparse code division multiple access (SCMA) technology is a most potential solution for massive IoT access due to its superior resource utilization; however, the prototypical SCMA likely suffers from severe interference/jamming because of lacking reliable transmission strategies. To address this issue, a reliable SCMA based on factor-graph (FG) hopping scheme (FG based FH-SCMA) is proposed for massive connectivity and band-limited IoT in this paper. To meet the sparsity of transmitted FH-SCMA codewords, a FG hopping pattern with long-period is designed via Bernoulli chaotic map. Through the proposed system design, physical RBs utilized by SCMA codewords are randomly hopped within one RB-group so as to obtain efficient RB utilization and robust transmission; meanwhile, iteration error in message-passing-algorithm (MPA) resulted from the hopping RB-collision in the SCMA receiver can be alleviated. The numerical and simulation results show that, under the jamming attack, the proposed FH-SCMA system can attain the reliable transmission performance, compared to the traditional SCMA and previous FH-SCMA systems.

This paper investigates the model-driven federated learning (FL) for channel estimation in multi-user millimeter-wave (mmWave) massive multiple-input multiple-output (MIMO) systems. Firstly, we formulate it as a sparse signal recovery problem by exploiting the beamspace domain sparsity of the mmWave channels. Then, we propose an FL-based learned approximate message passing (LAMP) channel estimation scheme, namely FL-LAMP, where the LAMP network is trained by an FL framework. Specifically, the base station (BS) and users jointly train the LAMP network, where the users update the local LAMP network parameters by local datasets consisting of measurement signals and beamspace channels, and the BS calculates the global LAMP network parameters by aggregating the local network parameters from all the users. The beamspace channel can thus be obtained in real time from the measurement signal based on the parameters of the trained LAMP network. Simulation results demonstrate that the proposed FL-LAMP scheme can achieve better channel estimation accuracy than the existing orthogonal matching pursuit (OMP) and approximate message passing (AMP) schemes, and provides satisfactory prediction capability for multipath channels.

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 paper presents a coding approach for achieving omnidirectional transmission of certain common signals in massive multi-input multi-output (MIMO) networks such that the received power at any direction in a cell remains constant for any given distance. Specifically, two-dimensional (2D) Golay complementary array set (GCAS) can be used to design the massive MIMO precoding matrix so as to achieve omnidirectional transmission due to its complementary autocorrelation property. In this paper, novel constructions of new 2D GCASs with arbitrary array lengths are proposed. Our key idea is to carefully truncate the columns of certain larger arrays generated by 2D generalized Boolean functions. Finally, the power radiation patterns and numerical results are provided to verify the omnidirectional property of the GCAS-based precoding. The error performances of the proposed precoding scheme are presented to validate its superiority over the existing alternatives.

Quasi-complementary sequence sets (QCSSs) have attracted sustained research interests for simultaneously supporting more active users in multi-carrier code-division multiple-access (MC-CDMA) systems compared to complete complementary codes (CCCs). In this paper, we investigate a novel class of QCSSs composed of multiple CCCs. We derive a new aperiodic correlation lower bound for this type of QCSSs, which is tighter than the existing bounds for QCSSs. We then present a systematic construction of such QCSSs with a flexible alphabet size and a low maximum correlation magnitude, and also show that the constructed aperiodic QCSSs can meet the newly derived bound asymptotically.

This work presents a novel K-Repetition based Hybrid Automatic Repeat reQuest (HARQ) scheme for uplink sparse code multiple access (SCMA) systems. Our core idea is to apply network coding (NC) principle to re-encode different packets (after channel coding and interleaving) or their fragments, where K-Repetition is an emerging HARQ technique (recommended in 3GPP Release 15) for enhanced reception in future massive machine-type communications. Such a proposed scheme is referred to as the NC aided K-repetition SCMA (NCK-SCMA) in this paper. We aim to understand the optimal NCK-SCMA design criteria for maximizing the channel diversity as well as the efficient receiver processing for superior error rate performances. It is found that NC can enable a larger diversity order for NCK-SCMA with fewer resources (i.e., higher spectrum efficiency). Toward this objective, some novel design criteria are developed for the efficient configuration of NCK-SCMA. Moreover, we propose an iterative network decoding and SCMA detection (INDSD) algorithm for robust and low-complexity recovery of the transmit data from a low-density parity-check (LDPC) coded uplink NCK-SCMA system. Simulation results demonstrate that the proposed NCK-SCMA lead to higher throughput and improved reliability over the conventional K-SCMA.

Sparse code multiple access (SCMA) is a promising technique for the enabling of massive connectivity in future machine-type communication networks, but it suffers from a limited diversity order which is a bottleneck for significant improvement of error performance. This paper aims for enhancing the signal space diversity of sparse code multiple access (SCMA) by introducing quadrature component delay to the transmitted codeword of a downlink SCMA system in Rayleigh fading channels. Such a system is called SSD-SCMA throughout this work. By looking into the average mutual information (AMI) and the pairwise error probability (PEP) of the proposed SSD-SCMA, we develop novel codebooks by maximizing the derived AMI lower bound and a modified minimum product distance (MMPD), respectively. The intrinsic asymptotic relationship between the AMI lower bound and proposed MMPD based codebook designs is revealed. Numerical results show significant error performance improvement in the both uncoded and coded SSD-SCMA systems.

This paper studies the affine frequency division multiplexing (AFDM)-empowered sparse code multiple access (SCMA) system, referred to as AFDM-SCMA, for supporting massive connectivity in high-mobility environments. First, by placing the sparse codewords on the AFDM chirp subcarriers, the input-output (I/O) relation of AFDM-SCMA systems is presented. Next, we delve into the generalized receiver design, chirp rate selection, and error rate performance of the proposed AFDM-SCMA. The proposed AFDM-SCMA is shown to provide a general framework and subsume the existing OFDM-SCMA as a special case. Third, for efficient transceiver design, we further propose a class of sparse codebooks for simplifying the I/O relation, referred to as I/O relation-inspired codebook design in this paper. Building upon these codebooks, we propose a novel iterative detection and decoding scheme with linear minimum mean square error (LMMSE) estimator for both downlink and uplink channels based on orthogonal approximate message passing principles. Our numerical results demonstrate the superiority of the proposed AFDM-SCMA systems over OFDM-SCMA systems in terms of the error rate performance. We show that the proposed receiver can significantly enhance the error rate performance while reducing the detection complexity.

This paper is focused on multiuser load modulation arrays (MU-LMAs) which are attractive due to their low system complexity and reduced cost for millimeter wave (mmWave) multi-input multi-output (MIMO) systems. The existing precoding algorithm for downlink MU-LMA relies on a sub-array structured (SAS) transmitter which may suffer from decreased degrees of freedom and complex system configuration. Furthermore, a conventional LMA codebook with codewords uniformly distributed on a hypersphere may not be channel-adaptive and may lead to increased signal detection complexity. In this paper, we conceive an MU-LMA system employing a full-array structured (FAS) transmitter and propose two algorithms accordingly. The proposed FAS-based system addresses the SAS structural problems and can support larger numbers of users. For LMA-imposed constant-power downlink precoding, we propose an FAS-based normalized block diagonalization (FAS-NBD) algorithm. However, the forced normalization may result in performance degradation. This degradation, together with the aforementioned codebook design problems, is difficult to solve analytically. This motivates us to propose a Deep Learning-enhanced (FAS-DL-NBD) algorithm for adaptive codebook design and codebook-independent decoding. It is shown that the proposed algorithms are robust to imperfect knowledge of channel state information and yield excellent error performance. Moreover, the FAS-DL-NBD algorithm enables signal detection with low complexity as the number of bits per codeword increases.

This paper presents a novel class of complex-valued sparse complementary pairs (SCPs), each consisting of a number of zero values and with additional zero-correlation zone (ZCZ) property for the aperiodic autocorrelations and crosscorrelations of the two constituent sequences. Direct constructions of SCPs and their mutually-orthogonal mates based on restricted generalized Boolean functions are proposed. It is shown that such SCPs exist with arbitrary lengths and controllable sparsity levels, making them a disruptive sequence candidate for modern low-complexity, low-latency, and low-storage signal processing applications.

This paper studies an unmanned aerial vehicle (UAV)-aided downlink sparse code multiple access (SCMA) sys-tem to serve multiple users under finite resources. The objective of this work is to maximize the average sum-rate of UAV-SCMA system by optimizing the three-dimensional (3D) UAV trajectory within the UAV energy and mobility constraints, and the inter-user interference in SCMA. The formulated problem is non-convex in nature, we reformulate it using logarithmic approximation and solve it iteratively. The simulation results validates that the proposed UAV 3D trajectory outperforms the benchmark schemes with around a 20% increase in the overall sum-rate under the available energy budget.

Non-orthogonal multiple access (NOMA) is a promising candidate radio access technology for future wireless communication systems, which can achieve improved connectivity and spectral efficiency. Without sacrificing error rate performance, link adaptation combining with adaptive modulation and coding (AMC) and hybrid automatic repeat request (HARQ) can provide better spectral efficiency and reliable data transmission by allowing both power and rate to adapt to channel fading and enabling re-transmissions. However, current AMC or HARQ schemes may not be preferable for NOMA systems due to the imperfect channel estimation and error propagation during successive interference cancellation (SIC). To address this problem, a reinforcement learning based link adaptation scheme for downlink NOMA systems is introduced in this paper. Specifically, we first analyze the throughput and spectrum efficiency of NOMA system with AMC combined with HARQ. Then, taking into account the imperfections of channel estimation and error propagation in SIC, we propose SINR and SNR based corrections to correct the modulation and coding scheme selection. Finally, reinforcement learning (RL) is developed to optimize the SNR and SINR correction process. Comparing with a conventional fixed look-up table based scheme, the proposed solutions achieve superior performance in terms of spectral efficiency and packet error performance.

Spectrally constrained sequences (SCSs) play an important role in modern communication and radar systems operating over non-contiguous spectrum. Despite numerous research attempts over the past years, very few works are known on the constructions of optimal SCSs with low cross-correlations. In this paper, we address such a major problem by introducing a unifying framework to construct unimodular SCS families using circular Florentine rectangles (CFRs) and interleaving techniques. By leveraging the uniform power allocation in the frequency domain for all the admissible carriers (a necessary condition for beating the existing periodic correlation lower bound of SCSs), we present a tighter correlation lower bound and show that it is achievable by our proposed SCS families including multiple SCS sets with zero correlation zone properties.

Sequences play an important role in many engineering applications. Searching sequences with desired properties has long been an intriguing but also challenging research topic. This article proposes a novel method, called HpGAN, to search desired sequences algorithmically using generative adversarial networks (GANs). 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 complex problems which are intractable by mathematical analysis. We demonstrate the search capabilities of HpGAN in two applications: 1) HpGAN successfully found many different mutually orthogonal complementary sequence sets (MOCSSs) and optimal odd-length binary 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 and 2) HpGAN found new sequences which achieve a four-times increase of signal-to-interference ratio-benchmarked against the well-known Legendre sequences-of a mismatched filter (MMF) estimator in pulse compression radar systems. These sequences outperform those found by AlphaSeq.

Cognitive radio-based Internet of Things (CR-IoT) network provides a solution for IoT devices to efficiently utilize spectrum resources. Spectrum sensing is a critical problem in CR-IoT network, which has been investigated extensively based on deep learning (DL). Despite the unique advantages of DL in spectrum sensing, the black-box and unexplained properties of deep neural networks may lead to many security risks. This article considers the fusion of traditional interference methods and data poisoning which is an attack method on the training data of a machine learning tool. We propose a new adversarial attack for reducing the sensing accuracy in DL-based spectrum sensing systems. We introduce a novel design of jamming waveform whose interference capability is reinforced by data poisoning. Simulation results show that significant performance enhancement and higher mobility can be achieved compared with traditional white-box attack methods.

This paper conceives a novel sparse code multiple access (SCMA) codebook design which is motivated by the strong need for providing ultra-low decoding complexity and good error performance in downlink Internet-of-things (IoT) networks, in which a massive number of low-end and low-cost IoT communication devices are served. By focusing on the typical Rician fading channels, we analyze the pair-wise error probability of superimposed SCMA codewords and then deduce the design metrics for multi-dimensional constellation construction and sparse codebook optimization. For significant reduction of the decoding complexity, we advocate the key idea of projecting the multi-dimensional constellation elements to a few overlapped complex numbers in each dimension, called low projection (LP). An emerging modulation scheme, called golden angle modulation (GAM), is considered for multi-stage LP optimization, where the resultant multi-dimensional constellation is called LP-GAM. Our analysis and simulation results show the superiority of the proposed LP codebooks (LPCBs) including one-shot decoding convergence and excellent error rate performance. In particular, the proposed LPCBs lead to decoding complexity reduction by at least 97% compared to that of the conventional codebooks, whilst owning large minimum Euclidean distance. Some examples of the proposed LPCBs are available athttps://github.com/ethanlq/SCMA-codebook.

Providing quality communications under adversarial electronic attacks, e.g., broadband jamming attacks, is a challenging task. Unlike state-of-the-art approaches which treat jamming signals as destructive interference, this paper presents a novel active anti-jamming (AAJ) scheme for a jammed channel to enhance the communication quality between a transmitter node (TN) and receiver node (RN), where the TN actively exploits the jamming signal as a carrier to send messages. Specifically, the TN is equipped with a programmable-gain amplifier, which is capable of re-modulating the jamming signals for jamming modulation. Considering four typical jamming types, we derive both the bit error rates (BER) and the corresponding optimal detection thresholds of the AAJ scheme. The asymptotic performances of the AAJ scheme are discussed under the high jamming-to-noise ratio (JNR) and sampling rate cases. Our analysis shows that there exists a BER floor for sufficiently large JNR. Simulation results indicate that the proposed AAJ scheme allows the TN to communicate with the RN reliably even under extremely strong and/or broadband jamming. Additionally, we investigate the channel capacity of the proposed AAJ scheme and show that the channel capacity of the AAJ scheme outperforms that of the direct transmission when the JNR is relatively high.

This paper studies a downlink system that combines orthogonal-time-frequency-space (OTFS) modulation and sparse code multiple access (SCMA) to support massive connectivity in high-mobility environments. We propose a cross-domain receiver for the considered OTFS-SCMA system which efficiently carries out OTFS symbol estimation and SCMA decoding in a joint manner. This is done by iteratively passing the extrinsic information between the time domain and the delay-Doppler (DD) domain via the corresponding unitary transformation to ensure the principal orthogonality of errors from each domain. We show that the proposed OTFS-SCMA detection algorithm exists at a fixed point in the state evolution when it converges. To further enhance the error performance of the proposed OTFS-SCMA system, we investigate the cooperation between downlink users to exploit the diversity gains and develop a distributed cooperative detection (DCD) algorithm with the aid of belief consensus. Our numerical results demonstrate the effectiveness and convergence of the proposed algorithm and show an increased spectral efficiency compared to the conventional OTFS transmission.

Making a timely and precise scheduling in Industrial Internet of Things (IIoT) is fundamental and critical. Recently, Age of Incorrect Information (AoII) is proposed and utilized to measure the timeliness and accuracy of monitoring. In this work, we investigate a multi-sensor update system and leverage AoII to quantify the information freshness. Our goal is to obtain an optimal scheduling policy to minimize the system-wide cost. We first model the source statuses monitored by sensors as Markov chains and the scheduling problem as a Markov decision process (MDP). Due to the heterogeneity of source statuses in IIoT, it is prohibitive to solve the formulated MDP problem by conventional methods. To this end, we make use of a deep reinforcement learning (DRL) algorithm to solve this scheduling problem. Extensive numerical results verify the effectiveness of the adopted DRL algorithm. In addition, comparing to the conventional Age of Information (AoI) oriented method, we find that the AoII oriented method is much more effective, from the perspective of system-wide cost.

In this paper, we present a new family of cross Z-complementary pairs (CZCPs) based on generalized Boolean functions and two roots of unity. Our key idea is to consider an arbitrary partition of the set {1,2,⋯,n} with two subsets corresponding to two given roots of unity for which two truncated sequences of new alphabet size determined by the two roots of unity are obtained. We show that these two truncated sequences form a new q-ary CZCP with flexible sequence length and large zero-correlation zone width. Furthermore, we derive an enumeration formula by considering the Stirling number of the second kind for the partitions and show that the number of constructed CZCPs increases significantly compared to the existing works.

This paper presents an efficient construction of two-dimensional (2D) complete complementary codes (CCCs) for their modern application as omnidirectional precoding matrices in massive MIMO systems to attain enhanced cell coverage. Unlike the traditional 1D CCCs, little progress has been made on efficient and systematic constructions of the 2D counterpart. In contrast to the existing recursive constructions with the aid of various sequence operations, certain 1D seed sequences or 2D arrays, we propose to use 2D generalized Boolean functions for direct synthesis of 2D CCCs. Simulation results show that the proposed 2D CCCs appear to be good candidates for precoding matrices to achieve omnidirectional transmission in massive MIMO systems.

This article studies the freshness of information with the aid of Age of Information (AoI) in the Industrial Internet of Things (IIoT), which plays a vital role to ensure quality and timely delivery of data services. To reduce the AoI, we leverage mobile-edge computing (MEC) to partially offload information to the mobile edge server. Aiming to cope with the packet error in the setting of short packet communication (SPC) in IIoT, we consider the standard automatic repeat request (ARQ) protocol with two policies, i.e., either retransmitting an out-of-date packet (RO) or transmitting a freshest packet (TF), when a packet error occurs. We derive the closed form of average AoI under these two policies, respectively, and then formulate the average AoI minimization problem by jointly optimizing the short packet blocklength and MEC offloading ratio. Due to the nonconvexity nature of the problem, we tackle it by employing block coordinate descent (BCD) and successive convex approximation (SCA) methods and then prove their convergence. Our extensive numerical results show that the optimal average AoI yielded by our proposed approach is almost identical to that from the high-complexity exhaustive search method, and has significant improvement over the benchmark methods. From the AoI perspective, it is revealed that the optimal strategy tends to offload all information to mobile edge server when the computing capacity of local device is less than a threshold. Furthermore, it is found that the RO policy is suitable for the relatively small bandwidth and large local computing capability scenario, whilst the TF policy is better for the large bandwidth and small local computing capability case.

The explosive growth of Internet of Things (IoT) has mandated the security of data access. Although authentication methods can enhance network security, their vulnerability to malicious attacks may be a barrier for the wide deployments in IoT scenarios. To address the security issue, we advocate the use of physical-layer security through radio-frequency (RF) fingerprint recognition. Observing that most RF fingerprint recognition methods show a degradation of performance under low signal-to-noise ratio (SNR) environments, we present a dynamic shrinkage learning network (DSLN) to enhance security for IoT applications, particularly in the setting of low SNR. We design a novel dynamic shrinkage threshold for improving the accuracy of recognition under low-SNR environments. Additionally, we design an identity shortcut for reducing the running time of RF fingerprint recognition. In comparison with convolutional neural network (CNN), recurrent neural network (RNN), and a hybrid CNN+RNN network (CRNN), our proposed DSLN yields accuracy improvements of up to 20%. Moreover, DSLN can reduce the running time by up to 60%, indicating its great potential to a real-time IoT system, e.g., an intelligent automotive system.

In radar sensing and communications, designing Doppler resilient sequences (DRSs) with low ambiguity function for delay over the entire signal duration and Doppler shift over the entire signal bandwidth is an extremely difficult task. However, in practice, the Doppler frequency range is normally much smaller than the bandwidth of the transmitted signal, and it is relatively easy to attain quasi-synchronization for delays far less than the entire signal duration. Motivated by this observation, we propose a new concept called low ambiguity zone (LAZ) which is a small area of the corresponding ambiguity function of interest defined by the certain Doppler frequency and delay. Such an LAZ will reduce to a zero ambiguity zone (ZAZ) if the maximum ambiguity values of interest are zero. In this paper, we derive a set of theoretical bounds on periodic LAZ/ZAZ of unimodular DRSs with and without spectral constraints, which include the existing bounds on periodic global ambiguity function as special cases. These bounds may be used as theoretical design guidelines to measure the optimality of sequences against Doppler effect. We then introduce four optimal constructions of DRSs with respect to the derived ambiguity lower bounds based on some algebraic tools such as characters over finite field and cyclic difference sets.

We are on the cusp of a new era of connected autonomous vehicles with unprecedented user experiences, tremendously improved road safety and air quality, highly diverse transportation environments and use cases, and a plethora of advanced applications. Realizing this grand vision requires a significantly enhanced vehicle-to-everything (V2X) communication network that should be extremely intelligent and capable of concurrently supporting hyperfast, ultrareliable, and low-latency massive information exchange. It is anticipated that the sixth-generation (6G) communication systems will fulfill these requirements of the next-generation V2X. In this article, we outline a series of key enabling technologies from a range of domains, such as new materials, algorithms, and system architectures. Aiming for truly intelligent transportation systems, we envision that machine learning (ML) will play an instrumental role in advanced vehicular communication and networking. To this end, we provide an overview of the recent advances of ML in 6G vehicular networks. To stimulate future research in this area, we discuss the strength, open challenges, maturity, and enhancing areas of these technologies.

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.

Visible light communication (VLC) has recently emerged as an affordable and scalable technology supporting very high data rates for short range vehicle-to-vehicle (V2V) communication. In this work, we advocate the use of vehicular-VLC (V-VLC) for basic safety messages (BSMs) dissemination in lieu of conventional vehicular radio frequency (V-RF) communication in road intersection applications, where the reception performance is affected by interference from the concurrent transmissions of other vehicles. We make use of stochastic geometry to characterize the interference from the same lane as well as the perpendicular lane for various network configurations, i.e., standalone V-VLC, stand-alone V-RF and hybrid V-VLC/V-RF network. Specifically, by modelling the interfering vehicles’ locations as a spatial Poisson point process (PPP), we are able to capture a static two-dimensional road geometry as well as the impact of interference due to vehicles clustering in the vicinity of road intersection in terms of outage probability and throughput. In addition to above, the performance of spatial ALOHA and carrier sense multiple access with collision avoidance medium access control (CSMA/CA MAC) protocol for standalone V-VLC, standalone V-RF and hybrid V-VLC/V-RF network configuration for relaying BSMs at road intersection is also compared. The performance metrics such as delay outage rate (DOR) and information outage rate (IOR) are utilized to investigate the impact of latency associated with various network configurations. Our numerical results reveal that our proposed hybrid V-VLC/V-RF leads to significant improvement in terms of outage performance, throughput and latency as compared to stand-alone V-VLC or stand-alone V-RF network.

This paper is focused on the fusion of radar and wireless communication, called RadCom, which has been extensively studied in recent years for future intelligent transportation systems. We propose a new waveform design algorithm for reducing peak-to-average power ratio (PAPR) in OFDM-based RadCom systems. We consider a flexible and generic RadCom structure in which a number of non-contiguous sub-bands for data transmission are located within a large contiguous spectrum band for radar detection/sensing. New RadCom waveforms with low PAPR are obtained by carrying out optimization over those subcarriers which are complementary to the communication bands. As an application of the majorization-minimization (MM) optimization method, our major contribution is an$l$-norm cyclic algorithm which is capable of efficiently reducing the maximum PAPR of RadCom waveforms. We show by numerical simulation results that significant performance enhancements can be achieved compared to OFDM RadCom waveforms from legacy approaches.

This paper is concerned with the enabling of massive connectivity in a multi-cluster network. In order to tackle significant amount of interference imposed by inter- and intra-cluster users, we consider a frequency-hopping (FH) system where an improved quasi-orthogonal hopping pattern, called optimal strong no-hit-zone FH sequence (SNHZ-FHS) set, is adopted in each cluster. We propose a flexible construction of SNHZ-FHS sets and derive their Hamming correlation values at different access delays. Since the maximum number of supportable users under traditional FH networks is strictly limited by the number of frequency slots, we investigate the design of a novel class of adaptive array beam-forming (BF) receiver in which SNHZ-FHS patterns (i.e., SNHZ-FH/BF) are reused over asynchronous multi-cluster uplink channels. Extensive numerical comparisons show that our proposed SNHZ-FH/BF system provides an effective means for attaining higher user capacity as well as remarkable capability of interference suppression.

Non-orthogonal multiple access (NOMA) and millimeter wave (mmWave) are two key enabling technologies for the fifth-generation (5G) mobile networks and beyond. In this paper, we consider uplink communications with a hybrid beamforming structure and focus on improving the spectral efficiency (SE) and energy efficiency (EE) of mmWave multiple-input multiple-output (MIMO)-NOMA systems with enhanced user grouping and power allocation. It is noted that the optimization of the SE/EE is a challenging task due to the non-linear programming nature of the corresponding problem involving user grouping, beam selection, and power allocation. Our idea is to decompose the overall optimization problem into a mixed integer problem comprised of user grouping and beam selection only, followed by a continuous problem involving power allocation and digital beamforming design. Exploiting the directionality property of mmWave channels, we first propose a novel initial agglomerative nesting (AGNES) based user grouping algorithm by taking advantage of the channel correlations. To avoid the prohibitively high complexity of the brute-force search approach and to address the overlapping beam problem, we propose two suboptimal low-complexity user grouping and beam selection schemes, the two-stage direct AGNES (D-AGNES) scheme and the joint successive AGNES (S-AGNES) scheme. We also introduce the quadratic transform (QT) to recast the non-convex power allocation optimization problem into a convex one subject to a minimum required data rate of each user. The continuous problem is solved by iteratively optimizing the power and the digital beamforming. Extensive simulation results have shown that our proposed mmWave-NOMA design outperforms the conventional orthogonal multiple access (OMA) scenario and the state-of-art NOMA schemes.

Sparse code multiple-access (SCMA) is an emerging technique to support massive connectivity in 5G networks and beyond. In SCMA transmissions, some resource-blocks may undergo certain contamination due to deep fading and/or jamming attacks, thus leading to severe performance degradation over such contaminated ones. Besides, the current SCMA infrastructure is normally deployed in single-cell. To deploy the SCMA into multicell networks under contaminated/jamming channels, we propose a novel frequency-hopping based SCMA (FH-SCMA) for quasi-synchronous multi-cell networks, in which the entire subcarrier-channels of every codeword keep hopping over the multiple resource-blocks according certain hopping pattern. We propose and design a pseudo-randomly orthogonal hopping pattern to adapt to the specific requirements of quasi-synchronous FH-SCMA multi-cell networks. Our analysis and simulation results indicate that the proposed FH-SCMA leads to both improved user capacity and error-rate performance, whilst remaining resilient to the inter-cell interference.

This paper aims to construct optimal Z-complementary code set (ZCCS) with non-power-of-two (NPT) lengths to enable interference-free multicarrier code-division multiple access (MC-CDMA) systems. The existing ZCCSs with NPT lengths, which are constructed from generalized Boolean functions (GBFs), are sub-optimal only with respect to the set size upper bound. For the first time in the literature, we advocate the use of pseudo-Boolean functions (PBFs) (each of which transforms a number of binary variables to a real number as a natural generalization of GBF) for direct constructions of optimal ZCCSs with NPT lengths.

Algebraic codes such as BCH code are receiving renewed interest as their short block lengths and low/no error floors make them attractive for ultra-reliable low-latency communications (URLLC) in 5G wireless networks. This article aims at enhancing the traditional adaptive belief propagation (ABP) decoding, which is a soft-in-soft-out (SISO) decoding for high-density parity-check (HDPC) algebraic codes, such as Reed-Solomon (RS) codes, Bose-Chaudhuri-Hocquenghem (BCH) codes, and product codes. The key idea of traditional ABP is to sparsify certain columns of the parity-check matrix corresponding to the least reliable bits with small log-likelihood-ratio (LLR) values. This sparsification strategy may not be optimal when some bits have large LLR magnitudes but wrong signs. Motivated by this observation, we propose a Perturbed ABP (P-ABP) to incorporate a small number of unstable bits with large LLRs into the sparsification operation of the parity-check matrix. In addition, we propose to apply partial layered scheduling or hybrid dynamic scheduling to further enhance the performance of P-ABP. Simulation results show that our proposed decoding algorithms lead to improved error correction performances and faster convergence rates than the prior-art ABP variants.

This paper investigates the impact of intelligent reflecting surface (IRS) enabled wireless secure transmission. Specifically, an IRS is deployed to assist multiple-input multiple-output (MIMO) secure system to enhance the secrecy performance, and artificial noise (AN) is employed to introduce interference to degrade the reception of the eavesdropper. To improve the secrecy performance, we aim to maximize the achievable secrecy rate, subject to the transmit power constraint, by jointly designing the precoding of the secure transmission, the AN jamming, and the reflecting phase shift of the IRS. We first propose an alternative optimization algorithm (i.e., block coordinate descent (BCD) algorithm) to tackle the non-convexity of the formulated problem. This is made by deriving the transmit precoding and AN matrices via the Lagrange dual method and the phase shifts by the Majorization-Minimization (MM) algorithm. Our analysis reveals that the proposed BCD algorithm converges in a monotonically non-decreasing manner which leads to guaranteed optimal solution. Finally, we provide numerical results to validate the secrecy performance enhancement of the proposed scheme in comparison to the benchmark schemes.

Mutually orthogonal complementary sets (MOCSs) have received significant research attention in recent years due to their wide applications in communications and radar. Existing MOCSs which are constructed based on generalized Boolean functions (GBFs) mostly have lengths of power-of-two. How to construct MOCSs with non-power-of-two lengths whilst having large set sizes is a largely open problem. With the aid of GBFs, in this paper, we present new constructions of such MOCSs and show that the maximal achievable set size is 1/2 of the flock size of an MOCS.

This paper is focused on code-domain non-orthogonal multiple access (CD-NOMA), which is an emerging paradigm to support massive connectivity for future machine-type wireless networks. We take a comparative approach to study two types of overloaded CD-NOMA, i.e., sparse code multiple access (SCMA) and dense code multiple access (DCMA), which are distinctive from each other in terms of their codebooks having sparsity or not. By analysing their individual diversity orders (DO) in Rayleigh fading channels, it is found that DCMA can be designed with the aid of generalized sphere decoder (i.e., a nonlinear multiuser detector) to enjoy full DO which is equal to the maximum number of resource nodes in the system. This is in contrast to SCMA whose error rate suffers from limited DO equal to the codebook sparsity (i.e., the effective number of resource nodes occupied by each user). We conduct theoretical analysis for the codebook design criteria and propose to use generalized sphere decoder for DCMA detection. We numerically evaluate two types of multiple access schemes under “ 4×6” (i.e., six users communicate over four subcarriers) and “ 5×10” NOMA settings and reveal that DCMA gives rise to significantly improved error rate performance in Rayleigh fading channels, whilst having decoding complexity comparable to that of SCMA.

Spatial modulation (SM) is a new multiple-input multiple-output (MIMO) paradigm in which only one transmit antenna is activated over every symbol duration. So far, efficient SM training sequences (different from the existing design for conventional MIMO systems) remain largely open. Motivated by this research problem, 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 cross-correlation sums. A CZCP may be transmitted in two non-orthogonal SM channels and hence proper design should be conducted to minimize the cross-interference of the two constituent sequences. We construct perfect CZCPs based on selected Golay complementary pairs. We show that the training sequences derived from our proposed CZCPs lead to optimal channel estimation performance over frequency-selective SM channels.

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 (≥ 3) GBFs. We obtain polyphase complementary sequences with maximum PMEPR of 2k+1and 2k+2- 2M where k,M are non-negative integers that can be easily derived from the GBF associated with the CS.

Orthogonal Frequency Division Multiple Access (OFDMA) with Dynamic spectrum allocation (DSA) is able to provide a wide range of data rate requirements. This paper is focused on the design of preamble sequences in OFDMA systems with low peak-to-mean envelope power ratio (PMEPR) property in the context of DSA. We propose a systematic preamble sequence design which gives rise to low PMEPR for possibly non-contiguous spectrum allocations. With the aid of Golay-Davis-Jedwab (GDJ) sequences, two classes of preamble sequences are presented. We prove that their PMEPRs are upper bounded by 4 for any DSA over a chunk of four contiguous resource blocks.

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 2α± 1, where α is a positive integer. In this paper, we construct optimal OB-ZCPs of generic lengths 2α10β26γ+ 1 (where α, β, γ are non-negative integers and α ≥ 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 × 10β-1+ 1, 12 × 26γ-1+ 1 and 12 × 10β26γ-1+ 1 through proper insertions of GCPs of lengths 10β, 26γ, and 10β26γ, respectively. Our proposed OB-ZCPs have applications in communications and radar (as an alternative to GCPs).

The concept of massive spatial modulation (SM) assisted vertical bell labs space-time (V-BLAST) (SM-VBLAST) system [1] is proposed, where SM symbols (instead of conventional constellation symbols) are mapped onto the VBLAST structure. We show that the proposed SM-VBLAST is a promising massive multiple input multiple output (MIMO) candidate owing to its high throughput and low number of radio frequency (RF) chains used at the transmitter. For the generalized massive SM-VBLAST systems, we first derive both the upper bounds of the average bit error probability (ABEP) and the lower bounds of the ergodic capacity. Then, we develop an efficient error correction mechanism (ECM) assisted compressive sensing (CS) detector whose performance tends to achieve that of the maximum likelihood (ML) detector. Our simulations indicate that the proposed ECM-CS detector is suitable both for massive SM-MIMO based point-to-point and for uplink communications at the cost of a slightly higher complexity than that of the compressive sampling matching pursuit (CoSaMP) based detector in the high SNR region.

A salient disadvantage of orthogonal frequency division multiplexing (OFDM) systems is the high peak-to-mean envelope power ratio (PMEPR). The PMEPR problem can be solved by using complementary sequences with low PMEPR. In this paper, we present a new construction of complementary set (CS) by using generalized Boolean functions (GBFs), which generalizes the constructions given by Davis et al., Paterson and Schmidt. The proposed CS provides lower PMEPR upper bound as compared to Schmidt's method for the sequences corresponding to higher order (≥ 3) GBFs. We obtain complementary sequences with maximum PMEPR of 2k+1and 2k+2- 2M where k, M are non-negative integers that can be easily derived from the GBF associated with the CS.

Zero correlation zone (ZCZ) sequence sets play an important role in interference-free quasi-synchronous code-division multiple access communications. In this paper, for the first time, we investigate the periodic correlation properties of polyphase sequences obtained from paraunitary (PU) matrices, which shows the inherent relationship between PU matrix and ZCZ sequence sets. Our investigation suggests that any arbitrary PU matrix can produce ZCZ sequence sets by controlling its expanded form. The key idea is to impose certain restrictions on the expanded forms of the PU matrices to enable precise computation of the periodic correlation functions of the constructed sequences. We show that our proposed construction leads to near-optimal ZCZ sequence sets with regard to the ZCZ set size upper bound.

Z-complementary code set (ZCCS), an extension of perfect CCs, refers to a set of 2-D 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 the 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.

This paper is focused on the optimal design and performance analysis of a novel class of no-hit-zone frequencyhopping sequences (NHZ-FHSs) in quasi-synchronous FH multiple-access (QS-FHMA) systems. Although traditional NHZ-FHSs can offer interference-free FHMA performance when the signal arrival delay (τ) does not exceed the width of NHZ (Znh), i.e., |τ| ≤ Znh, the same performance cannot be guaranteed for |τ| > Znhin which traditional NHZ-FHZs may have large Hamming correlation (which denotes the total number of frequency hits of sequences) and consequently poor error probability performance. Since the strict quasi-synchronization (i.e., |τ| ≤ Znh) may be hard to maintain at all times in practical FHMA networks (e.g., infrastructureless ad hoc networks), it is also important to minimize the Hamming correlation for time-shifts outside of the NHZ. Such FHSs are called strong NHZ-FHSs (SNHZ-FHSs) in this paper. We derive a lower bound on the maximum Hamming correlation outside of the NHZ and then present a design algorithm for the optimal SNHZ-FHS set meeting our proposed lower bound with equality. We analyze the bit-error-rate (BER) performance of the FHMA system employing the proposed SNHZ-FHS sets using the average Hamming correlation function. The theoretical analysis and simulation results show that the proposed optimal SNHZ-FHS sets are feasible for practical FHMA networks with relaxed timing requirement and enhanced BER performance.

Unmanned aerial vehicles (UAVs) have attracted a lot of attention due to their enormous potentiality in civil and military applications over the past years. In order to allow accurate control action of UAV, a robust and real-time state estimation technique is required. In this paper, we propose a Kalman filter based UAV state estimation technique when the communication takes place over wireless links in an Internet of Things (IoT) network. We consider that a set of sensors observes the state of the UAV and transmits the observation to a control center (central server) over a distributed wireless IoT network. To deal with the communication impairments due to wireless communication links between the UAV's sensors and the IoT system components, e.g., IoT gateways, a Bose-Chaudhuri-Hocquenghem coded communication system is presented. Based on the received signals at the IoT gateways, a global state estimation technique is proposed. Performance of the proposed communication and estimation scheme is demonstrated through numerical results for different conditions. From the comparison with a conventional estimation scheme, it is observed that the proposed scheme significantly outperforms the conventional scheme in terms of state estimation and error performance.

This letter is focused on increasing the zero correlation zone (ZCZ) of even-length binary Z-complementary pairs (EB-ZCPs). Till date, the maximum ZCZ ratio (i.e., ZCZ width over the sequence length) for systematically constructed EB-ZCPs is 2/3. In this letter, we give a construction of EB-ZCPs with lengths 2α+210β26γ+ 2 (where α, β, and γ are nonnegative integers) and ZCZ widths 3 × 2α10β26γ+ 1, thus achieving asymptotic ZCZ ratio of 3/4. The proposed EB-ZCPs are constructed via proper insertion of concatenated odd-length binary ZCPs. The ZCZ width is proved by exploiting several newly identified intrinsic structure properties of binary Golay complementary pairs, obtained from Turyn's method. The proposed EB-ZCPs have aperiodic autocorrelation sums (AACS) magnitude of 4 outside the ZCZ region (except for the last time-shift taking AACS value of zero).

Owing to their ideal correlation properties, complete complementary codes (CCCs) have attracted great research attentions, particularly in wireless communications. In this letter, we propose a construction of CCCs having size M and length P N (M, P ≥ 2, P |M; N ∈ N) based on Kronecker product of paraunitary (PU) matrices, which generalizes our previous PU generator for CCCs. We show that our proposed construction leads to new antipodal PU (APU) matrices, which can be used as precoding matrices for orthogonal frequency division multiplexing (OFDM), multiple-input multiple-output OFDM, and spread-signature code division multiple access systems in order to obtain better error probability performances. The proposed construction has an advantage over our previous PU method and some previous constructions for APU matrices with regard to the availability of wide range of sequence lengths.

We investigate spectrally-constrained sequences (SCSs), which are applicable to the communication and radar systems operating over non-contiguous carriers or frequency slots. Typical examples of such systems are overlay cognitive radio or cognitive radar networks. First, we derive the periodic- and aperiodic-correlation lower bounds for single-channel SCSs and multi-channel SCSs by convex optimization in the frequency domain. Each of these bounds reduces to a Welch bound when the number of forbidden carriers is set to zero. We then propose systematic constructions of optimal unimodular single-channel SCSs with the aid of cyclic difference sets and the theory of maximal-length shift register sequences.

Owing to their ideal correlation properties, complete complementary codes (CCC) have found numerous applications in wireless engineering, in particular they have been employed to support interference-free multi-carrier code-division multiple access systems with improved spectral efficiency. In this paper, we propose a simple construction of CCCs of length Nn(n e N) based on paraunitary matrices of size N × N. This algorithm can generate CCCs from N-shift cross-orthogonal sequence sets for n > 1. Then, we introduce an easy implementation of the proposed algorithm by multiplexers and read-only memories (ROMs), i.e., a multiplier-free implementation. As multipliers are avoided, substantial reduction of construction complexity for CCCs is obtained as compared to the existing works.

Generalized Levenshtein bound (GLB) is a lower bound on the maximum aperiodic correlation sum of quasi-complementary sequence set (QCSS) which refers to a set of two-dimensional matrices with low non-trivial aperiodic auto- and cross-correlation sums. GLB is an indefinite fractional quadratic function of a “simplex” weight vector w and three additional parameters associated with QCSS. We present a novel approach to analytically conduct fractional quadratic optimization for the tightening of the GLB. Our key idea is to apply the frequency-domain decomposition of the relevant circulant matrix (i.e., the numerator term of GLB) to convert the non-convex problem into a convex one. We derive a new weight vector which asymptotically leads to a tighter GLB (over the Welch bound) for all possible (K, M) cases, where K, M denote the set size, the number of channels, of QCSS, respectively.

In this paper, a novel multiple-input multiple-output (MIMO) transmission scheme, termed as receive antenna selection (RAS)-aided spatial modulation MIMO (SM-MIMO), is proposed for millimeter-wave (mmWave) communications. It employs the spatial modulation (SM) concept and the RAS technique to tackle the costs of the multiple radio frequency (RF) chains at both link ends. Moreover, we develop a pair of RAS algorithms for the proposed mmWave RAS-SM scheme based on the capacity maximization (max-capacity) and the bit-error rate (BER) minimization criteria, which are formulated as two combinatorial optimization problems. The theoretical gradients of the capacity and the BER with respect to RAS variables are derived and the convexities of these problems are discussed. Furthermore, a novel iterative algorithm through jointly designing the log-barrier algorithm (LbA) and the simplified conjugate gradient method is proposed for RAS optimization. Our simulation results show that the proposed RAS-SM schemes are capable of achieving considerable performance gains over conventional norm-based and eigenvalue-based schemes in mmWave MIMO channels, while avoiding an overwhelming complexity imposed by exhaustive search.

We present a novel transform for periodic complementary sets (PCSs) over two-valued alphabets from a large set of difference families. This is achieved by generalizing Golomb's idea in 1992, which was for transformed perfect sequences with zero autocorrelations only. Based on the properties of difference family, a sufficient condition for such two-valued PCSs is derived. Systematic constructions of two-valued periodic complementary pairs are presented. It is shown that many lengths for which binary PCSs do not exist become admissible for our proposed two-valued PCSs.

A pair of sequences is called a periodic complementary pair (PCP) if the periodic autocorrelations of the constituent sequences sum up to zero for all nonzero time shifts. Owing to the scarcity of PCPs, we investigate optimal binary periodic almost-complementary pairs (BP-ACPs), each displaying correlation property closest to that of PCP. We show that an optimal BP-ACP of even length N has zero out-of-phase periodic autocorrelation sums (PACSs) except at the time shift of N/2, where the corresponding PACS has minimum magnitude of 4. We also show that for any arbitrary odd N, all the out-of-phase PACSs of an optimal BP-ACP should have identical magnitude of 2. A number of optimal BP-ACPs from analytical constructions as well as computer search are presented. In addition, our proposed optimal BP-ACPs for the even-length case lead to two new families of base-two almost difference families.

A pair of sequences is said to be an almost-complementary pair (ACP) if they have zero aperiodic autocorrelation sums except at only one position over all the positive/negative time-shifts. Having correlation property very close to that of Golay complementary pairs (GCPs), ACPs may be used as an alternative to GCPs in many applications in communications and radar. For high-rate code-keying OFDM communication, we construct novel 16-QAM ACPs from three new classes of quadratic offsets, leading to three large sets of 16-QAM almost-complementary sequences with maximum peak-to-mean envelope power ratio (PMEPR) of 2.4.

A sequence is said to be spectrally-constrained if it has to satisfy a spectral map consisting of several non-contiguous nulled frequency-slots. Such sequences play a key role in emerging spectrally-constrained systems such as cognitive radio and cognitive radar. In this paper, we study two types of spectrally-constrained sequences (SCSs), one with low periodic auto-correlation function (PACF) sidelobe, the other with zero auto-correlation zone (ZACZ). By deriving a correlation lower bound, we show that Type-I SCSs are optimal with minimum total PACF sidelobe energy provided that uniform power allocation is applied to all active (non-nulled) frequency-slots. We also propose optimal Type-II SCSs, each having maximum ZACZ width, for certain spectral map patterns.

Transform domain communication system (TDCS) is a multi- carrier cognitive radio (CR) technique which uses cyclic code shift keying (CCSK) for overlay opportunistic spectrum access. Specifically, at any given time, a TDCS system cyclically shifts a fundamental modulation waveform (i.e., a CR sequence satisfying a dynamic spectrum hole constraint) according to specific input data symbol. In practical TDCS system, an interesting research problem is how to design CR sequence with inter-carrier interference (ICI) resilience, where ICI is caused by carrier frequency offset (CFO) or Doppler spread. In this paper, we present a novel family of CR sequences which are able to achieve ICI self-cancellation in TDCS. Analysis and simulations validate that our proposed CR sequence is effective for ICI suppression in TDCS. A future work of this research is to optimize the peak-to-mean power ratio of such CR sequences.

Complete complementary codes (CCC) refer to a set of two-dimensional matrices, which have zero non-trivial aperiodic auto- and cross- correlation sums. A modern application of CCC is in interference-free multicarrier code-division multiple-access (MC-CDMA) communications. In this paper, we first show that in asynchronous “fractional-delay” uplink channels, CCC-MC-CDMA systems suffer from orthogonality loss, which may lead to huge interference increase when a conventional correlator based receiver is deployed. Then, by exploiting the correlation properties of CCC, we present a fractional-delay-resilient receiver which is comprised of a chip-spaced correlating array. Analysis and simulations validate the interference-free achievability of the proposed CSCA receiver in strong interference scenarios.

In this paper, we present a direct construction of zero-correlation zone (ZCZ) sequence sets (each associated with a graph) from the second order cosets of the first-order generalized Reed-Muller codes. This settles an open problem introduced by Rathinakumar and Chaturvedi in their 2008 paper.

To support interference-free quasi-synchronous code-division multiple-access (QS-CDMA) communication with low spectral density profile in a cognitive radio (CR) network, it is desirable to design a set of CDMA spreading sequences with zero-correlation zone (ZCZ) property. However, traditional ZCZ sequences (which assume the availability of the entire spectral band) cannot be used because their orthogonality will be destroyed by the spectrum hole constraint in a CR channel. To date, analytical construction of ZCZ CR sequences remains open. Taking advantage of the Kronecker sequence property, a novel family of sequences (called "quasi-ZCZ" CR sequences) which displays zero cross-correlation and near-zero auto-correlation zone property under arbitrary spectrum hole constraint is presented in this paper. Furthermore, a novel algorithm is proposed to jointly optimize the peak-to-average power ratio (PAPR) and the periodic auto-correlations of the proposed quasi-ZCZ CR sequences. Simulations show that they give rise to single-user bit-error-rate performance in CR-CDMA systems which outperform traditional non-contiguous multicarrier CDMA and transform domain communication systems; they also lead to CR-CDMA systems which are more resilient than non-contiguous OFDM systems to spectrum sensing mismatch, due to the wideband spreading.

For an even-period binary Z-complementary pair (EB-ZCP), if it is not a Golay complementary pair (GCP), we show that Z ≤ N-2, where N and Z denote the sequence length and the zero correlation zone (ZCZ) width, respectively. This result partially answers the Fan-Yuan-Tu conjecture in 2007. In addition, we present a construction of EB-ZCPs with large ZCZ widths, where N=2m+1+2mand Z=2m+1. Interestingly, each of the proposed EB-ZCPs features zero out-of-phase aperiodic auto-correlation sums except for the time-shift of ±2m+1, thus displaying a very close correlation property to that of GCPs.

Owing to the zero non-trivial aperiodic correlation sum properties, complete complementary codes (CCC) have been applied to asynchronous multi-carrier code-division multiple-access (MC-CDMA) communications in order to provide zero interference performance. When each complementary code is arranged to be a matrix, the peak-to-mean envelope power ratio (PMEPR) of the CCC-MC-CDMA system is determined by the column sequences of the complementary matrices. The existing CCC have the column sequence PMEPR of M, where M denotes the number of subcarriers in a CCC-MC-CDMA system. In practice, M is generally large and a PMEPR approaching this value is unacceptable. To solve this problem, a new class of CCC using generalized Boolean functions and with a column sequence PMEPR of at most 2 is proposed in this paper.

Levenshtein improved the famous Welch bound on aperiodic correlation for binary sequences by utilizing some properties of the weighted mean square aperiodic correlation. Following Levenshtein's idea, a new correlation lower bound for quasi-complementary sequence sets (QCSSs) over the complex roots of unity is proposed in this paper. The derived lower bound is shown to be tighter than the Welch bound for QCSSs when the set size is greater than some value. The conditions for meeting the new bound with equality are also investigated.

A pair of sequences is called a Golay complementary pair (GCP) if their aperiodic autocorrelation sums are zero for all out-of-phase time shifts. Existing known binary GCPs only have even-lengths in the form of 2α10β26γ(where \(α, β, γ) are nonnegative integers). To fill the gap left by the odd-lengths, we investigate the optimal odd-length binary (OB) pairs, which display the closest correlation property to that of GCPs. Our criteria of closeness is that each pair has the maximum possible zero-correlation zone (ZCZ) width and minimum possible out-of-zone aperiodic autocorrelation sums. Such optimal pairs are called optimal OB Z-complementary pairs (OB-ZCP) in this paper. We show that each optimal OB-ZCP has maximum ZCZ width of (N+1)/2, and minimum out-of-zone aperiodic sum magnitude of 2, where N denotes the sequence length (odd). Systematic constructions of such optimal OP-ZCPs are proposed by insertion and deletion of certain binary GCPs, which settle the 2011 Li-Fan-Tang-Tu open problem positively. The proposed optimal OB-ZCPs may serve as a replacement for GCPs in many engineering applications, where odd sequence lengths are preferred. In addition, they give rise to a new family of base-two almost difference families, which are useful in studying partially balanced incomplete block design.

The Levenshtein bound on aperiodic correlation, which is a function of the weight vector, is tighter than the Welch bound for sequence sets over the complex roots of unity when$M\geq 4$and$n\geq 2$, where$M$denotes the set size and$n$the sequence length. Although it is known that the tightest Levenshtein bound is equal to the Welch bound for$M\in\{1,2\}$, it is unknown whether the Levenshtein bound can be tightened for$M=3$, and Levenshtein, in his paper published in 1999, postulated that the answer may be negative. A new weight vector is proposed in this paper, which leads to a tighter Levenshtein bound for$M=3$,$n\geq 3$and$M\geq 4$,$n\geq 2$. In addition, the explicit form of the weight vector (which is derived by relating the quadratic minimization to the Chebyshev polynomials of the second kind) in Levenshtein's paper is given. Interestingly, this weight vector also yields a tighter Levenshtein bound for$M=3$,$n\geq 3$and$M\geq 4$,$n\geq\sqrt{M}$, a fact not noticed by Levenshtein.

In this paper we introduce the optimal odd-period binary Z-complementary pairs (OB-ZCPs), which display properties similar to Golay complementary pairs. These pairs have the maximum possible zero-correlation-zone (ZCZ) of width (N + 1)/2, where N denotes the sequence length, and the minimum possible magnitude of 2 for each out-of-zone aperiodic auto-correlation sum. Furthermore, we show that the optimal OB-ZCPs correspond to sets of almost difference families and present some of their interesting properties.

The Levenshtein bound, as a function of the weight vector, is only known to be tighter than the Welch bound on aperiodic correlation for K ≥ 4, N ≥ 2, where K and N denoting the set size and the sequence length, respectively. A quadratic weight vector is proposed in this paper which leads to a tighter Levenshtein bound for K ≥ 4, N ≥ 2 and K = 3, N ≥ 4. The latter case was left open by Levensthein.

There have been five constructions (Cases I to V) of 64-QAM Golay complementary sequences (GCSs), of which the Cases IV and V constructions were identified by Chang in 2010. The Generalized Cases I-III constructions for 4q-QAM (q ≥ 1) GCSs were additionally proposed by Li. In this paper, the Generalized Case IV and Generalized Case V constructions for 4q-QAM (q > =3) GCSs are proposed using selected Gaussian integer pairs, each of which contains two distinct Gaussian integers with identical magnitude and which are not conjugate with each other.

Levenshtein improved the Welch bound on aperiodic correlation by weighting the cyclic shifts of the sequences over complex roots-of-unity. Although many works have been concerned on meeting the Welch bound with equality, no such effort has been reported for the Levenshtein bound. We show that the Levenshtein bound with equality is met if and only if the non-trivial aperiodic correlations have identical amplitude for all time-shifts, and the sequences form a novel class of complementary set whose aperiodic correlation is defined as the conventional aperiodic correlation modulated by a simplex weighting vector.

The Welch bound for aperiodic correlation for binary sequence set was improved by Levenshtein by weighting the cyclic shifts of the sequence vectors. Taking Levenshtein's idea, a new lower bound for quasi-complementary sequence set (QCSS) over the complex roots-of-unity is derived in this paper. It is shown to be tighter than the Welch bound for QCSS in one of the following cases: 1) K = 4M − 1, M ≥ 2 and equation; 2) K ≥ 4M, M ≥ 2 and N ≥ 2. where K,M,N respectively denotes the set size, number of channels, elementary sequence length of QCSS.

The correlation lower bounds, as well as the set size upper bounds, of low-correlation-zone complementary sequences are presented in this paper. They can be treated as an extension of Tang-Fan-Matsufuji bounds in and , which considered only the conventional (non-complementary) low-correlation-zone sequence sets.