Arrays with good correlation properties have emerged with promising applications in wireless communication, including ultra-wideband (UWB), two-dimensional (2- D) synchronization, and massive multiple-input multiple-output (MIMO). In this paper, we propose two efficient algorithms for designing arrays with low autocorrelation by minimizing the weighted integrated sidelobe level (WISL) and complementary ISL (CISL), respectively. We formulate these metrics as non-convex quartic problems under unimodular constraints in the frequency domain. Using the majorization-minimization (MM) framework, these problems are simplified into quadratic forms, ensuring monotonic convergence to a stationary point. Furthermore, a projection algorithm is introduced to relax unimodular constraints to peak-to-average power ratio (PAPR) constraints, enhancing the correlation performance of the optimized arrays. All proposed algorithms can be efficiently implemented using two-dimensional FFT/IFFT operations. Furthermore, a quasi-complementary array set (QCAS), generated via the proposed MM-ACISL algorithm, is applied as an omnidirectional precoding matrix in massive MIMO systems. Numerical experiments demonstrate that the proposed algorithms outperform existing methods in terms of both correlation performance and computational efficiency. Moreover, the resulting QCAS scheme effectively enables omnidirectional transmission in MIMO systems.

Low ambiguity zone (LAZ) sequences play a crucial role in modern integrated sensing and communication (ISAC) systems. In this paper, we introduce a novel class of functions known as locally perfect nonlinear functions (LPNFs). By utilizing LPNFs and interleaving techniques, we propose three new classes of both periodic and aperiodic LAZ sequence sets with flexible parameters. The proposed periodic and aperiodic LAZ sequence sets are asymptotically optimal with respect to the periodic and aperiodic lower AF bounds, respectively, which were proposed recently in [IEEE J. Sel. Areas Commun. 40 (6): 1809-1822]. Notably, the aperiodic LAZ sequence sets are the first such sequence sets in the literature that satisfy the bound. Finally, we demonstrate that the proposed sequence sets are cyclically distinct.

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.

Quasi complementary sequence sets (QCSSs) are important in modern communication systems as they are capable of supporting more users, which is desired in applications like MC-CDMA nowadays. In this paper, we first derive a tighter bound on the maximum aperiodic correlation among all constituent complementary sequence sets in QCSSs. By proposing a new combinatorial structure called quasi-Florentine rectangles, we obtain a new construction of QCSSs with large set sizes. Using Butson-type Hadamard matrices and quasi-Florentine rectangles, we propose another construction which can construct QCSSs with flexible parameters over any given alphabet size, including small alphabets. All the proposed sequences are optimal with respect to the newly proposed bound. Also, through some of the constructions, the column sequence PMEPR of the proposed QCSSs are upper bounded by 2.

Multi-instance learning (MIL) is a widely applied technique in practical applications that involve complex data structures. MIL can be broadly categorized into two types: traditional methods and those based on deep learning. These approaches have yielded significant results, especially regarding their problem-solving strategies and experiment validation, providing valuable insights for researchers in the MIL field. However, considerable knowledge is often trapped within the algorithm, leading to subsequent MIL algorithms that rely solely on the model's data fitting to predict unlabeled samples. This results in a significant loss of knowledge and impedes the development of more powerful models. In this article, we propose a novel data-driven knowledge fusion for deep MIL (DKMIL) algorithm. DKMIL adopts a completely different idea from existing deep MIL methods by analyzing the decision-making of key samples in the dataset (referred to as the data-driven) and using the knowledge fusion module designed to extract valuable information from these samples to assist the model's learning. In other words, this module serves as a new interface between data and the model, providing strong scalability and enabling prior knowledge from existing algorithms to enhance the model's learning ability. Furthermore, to adapt the downstream modules of the model to more knowledge-enriched features extracted from the data-driven knowledge fusion (DDKF) module, we propose a two-level attention (TLA) module that gradually learns shallow- and deep-level features of the samples to achieve more effective classification. We will prove the scalability of the knowledge fusion module and verify the efficiency of the proposed architecture by conducting experiments on 62 datasets across five categories.

In this paper, a general class of polyphase sequences called Generalized Zadoff-Chu (GZC) sequences is presented, which is based on a quadratic function with real-valued coefficients. The conventional ZC sequences, P3, and P4 codes are included as special cases of GZC sequences. It is shown that, with the help of grid search algorithm, the optimized GZC sequences have significantly lower PMEPR than the well-known sequences such as Golay sequences, m-sequences, P3 and P4 codes, and ZC sequences. Numerical simulations suggest that the minimum PMEPR tends to a small constant of less than 1.43 dB as the sequence length approaches infinity.

Gold functions are well-known for designing sequences with good correlation properties. This paper reveals a fascinating relationship between Gold functions and Golay-Davis-Jedwab (GDJ) Boolean functions to design sequences with low correlation and low PAPR, which is the first of its kind. The bent and semi-bent properties of the Gold functions are utilized to derive the correlation of the resultant binary spreading sequence sets, while the complementary properties of the GDJ Boolean functions are used to derive the low PAPR. Based on this idea we propose three new sets of binary spreading sequences with low PAPR and low correlation. The proposed sequence sets have the potential to be used as spreading sequences in non-orthogonal multiple access (NOMA). They have a very large set size, which in turn results in a high overloading factor as compared to the existing sequence sets with the same length and the same correlation, which are generated through systematic constructions.

Iterative Twisted Approximation (ITROX), proposed in 2012 by Soltanalian et al., is an interesting algorithm for designing sequences with desired correlation properties. However, when aperiodic correlation of unimodular complementary and Zcomplementary sets (ZCSs) are considered, the correlation magnitudes of the resultant sequence sets of the ITROX algorithm, are not as good as desired. In this work, we have proposed a new modified ITROX algorithm, which can design unimodular ZCSs. Also the correlation levels of the resultant unimodular complementary sequence sets are better as compared to the previous ITROX.

Massive machine type communication (mMTC) is one of the core components of 6G communication systems to fulfil the demand of massive connectivity of billions of Internet-of-Things (IoT) devices. Due to its various advantages, grant-free random access schemes are considered as a promising technique to implement mMTC. The key to grant-free random access is active device detection at the base station. In this paper, firstly we introduce the odd total squared correlation (OTSC) of binary signature sets, then derive a corresponding lower bound. Systematic constructions of optimal signature sets based on the known odd periodic complementary sets (OPCS), almost binary sequences, large Kasami subsets and ideal sequences are presented, which are all optimal with respect to the derived OTSC lower bound. Next, it is demonstrated that the optimal OTSC signature sets can be effectively used in massive device activity detection. Using efficient approximate message passing with minimum mean squared error (AMP-MMSE) algorithm, it is shown that the sensing matrices arising from OTSC-optimal signature sets and periodic total squared correlation (PTSC)-optimal signature sets performs better than the popular Gaussian random matrix.

Sequences with low correlation sidelobes have found a wide range of applications in communication systems and RADAR. In this work, we have proposed a computational framework of aperiodic mismatched filtering sequence pairs using iterative twisted approximation (ITROX). A mismatched-filter is a filter where the transmitting sequence and receiving sequence are different (not matched). We have used singular value decomposition (SVD) instead of eigenvalue decomposition (EVD), which is more general, to obtain the resultant sequences. Numerical simulation shows that the resultant aperiodic mismatched filtering sequences have lower sidelobes without reducing too much loss-in-processing gain.

Z-complementary code sets (ZCCSs) can support interference-free multi-carrier code-division multiple access (MC-CDMA) in quasi-synchronous channels due to their favourable correlation properties. In this letter, based on the existing optimal ZCCSs and CCCs, we propose new class of optimal ZCCSs using Kronecker product. The resultant sequence sets have enlarged set size and sequence lengths which have not been reported before.

Quasi-complementary sequence sets (QCSSs) can be seen as a generalized version of complete complementary codes (CCCs), which enables multicarrier communication systems to support more users. The contribution of this work is two-fold. First, we propose a systematic construction of Florentine rectangles. Secondly, we propose several sets of CCCs and QCSSs, using Florentine rectangles. The CCCs and QCSSs are constructed over$\mathbb {Z}_{N}$, where$N\geq 2$is any integer. The cross-correlation magnitude of any two of the constructed CCCs is upper bounded by$N$. By combining the proposed CCCs, we propose asymptotically optimal and near-optimal QCSSs with new parameters.

Since its inception in 2013, Golay complementary sequences with periodic zero autocorrelation zones (ZACZs) and cross-correlation zones (ZCCZs), or Golay-ZCZ (zero correlation zone) sequences have special importance in modern communication systems. Till date, all the proposed complementary sequences with periodic ZACZs and ZCCZs have lengths in the form$2^{m}$, where$m$is a natural number. In this paper, we extend such complementary sequences with large periodic ZACZs and ZCCZs to more flexible lengths in the form of non-power-of-two.

Cross Z-complementary pairs (CZCPs) are a special kind of Z-complementary pairs having zero autocorrelation sums around the in-phase position and end-shift position, also having zero cross-correlation sums around the end-shift position. Recent results have shown that CZCPs are very efficient in designing pilot sequences for spatial modulation enabled multiple-input multiple-output (MIMO) systems. In this paper, we propose systematic constructions of binary and quadriphase CZCPs with new lengths of the form 2M, where even-length binary Z-complementary pairs of length M exists. Interestingly, the proposed binary and quadriphase CZCPs have large CZCratio(i.e. the ratio of achieved zero correlation zone width over maximum zero correlation zone width). One of the proposed construction can also construct optimal quadriphase CZCPs using quadriphase GCPs.

The zero correlation zone (ZCZ) ratio, i.e., the ratio of the width of the ZCZ and the length of the sequence plays a major role in reducing interference in an asynchronous environment of communication systems. However, to the best of the authors knowledge, for q = 2, the highest ZCZ ratio for even-length Zcomplementary pairs which are directly constructed using generalized Boolean functions (GBFs), is 2/3. In this letter, we present a direct construction of q-ary even-length Z-complementary pairs through GBFs, which can achieve aZCZ ratio of 3/4.In general, the constructed q-ary even-length Z-complementary pairs are of length 2m-1+ 2 (m ∈ Z+), having a ZCZ width of 2m-2+ 2π(m-3)+ 1 where π is a permutation over m - 2 variables.

The construction of complementary sets (CSs) of sequences with different set size and sequence length become important due to its practical application for OFDM systems. Most of the constructions of CSs, based on generalized Boolean functions (GBFs), are of length 2α(α is a natural number). Recently some works have been reported on construction of CSs having lengths non-power of two, i.e., in the form of 2m-1+ 2v(m is natural number, 0 ≤ v <; m), N + 1 and N + 2, where N is a length for which q-ary complementary pairs exist. In this letter, we propose a construction of CSs of lengths M + N for set size 4n, using concatenation of CSs of lengths M and N, and set size 4n, where M and N are lengths for which q-ary complementary pairs exists. Also, we construct CSs of length M + P for set size 8n by concatenating CSs of lengths M and P, and set size 8n, where M and P are lengths for which q-ary complementary pairs and complementary sets of size 4 exists, respectively. The proposed constructions cover all the previous constructions as special cases in terms of lengths and lead to more CSs of new sequence lengths which have not been reported before.

In recent years, complete complementary codes (CCCs) and quasi-complementary sequence sets (QCSSs) have found many important applications in multi-carrier code-division multiple-access (MC-CDMA) systems for their good correlation properties. In this paper, we propose a generic construction of multiple sets of CCCs over ZN, consisting of sequences of length N, where N ≥ 3 is an arbitrary odd integer. Interestingly, the maximum inter-set aperiodic cross-correlation magnitude of the proposed CCCs is upper bounded by N. It turns out that the combination of the generated CCCs results in a new set of sequences to obtain asymptotically optimal and near-optimal aperiodic QCSSs. The proposed construction includes a recent optimal construction of QCSSs with prime length as a special case and leads to asymptotically optimal QCSSs with new flexible parameters.

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).

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).

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.