This paper proposes a novel Flag sequence set design withpeak-curtainauto-ambiguity functions (AAF) and near-zero cross-ambiguity functions (CAF) in a specific delay-Doppler zone. This property allows for the rapid identification of ambiguity function (AF) peaks by prioritizing the search within thecurtainregion, thereby achieving low-complexity delay-Doppler estimation. In view of the high AF sidelobes of existing Flag sequence sets, we propose the construction of Flag sequence sets within the region of interest using alternating optimization (AO)-Newton's method. The weighted peak sidelobe level (WPSL) is used to evaluate the performance of the Flag sequences. For the first time, this method abandons the separate design of thecurtainsequence andpeaksequence to instead directly design the flag sequence as a unified whole. Experimental results demonstrate that the proposed algorithm exhibits excellent convergence, and in subsequent multi-input multi-output (MIMO) radar multi-target detection, it outperforms baseline methods in detecting both strong and weak targets.

Quasi-complementary sequence sets (QCSSs) have attracted sustained research interests due to the ability to support more users compared to complete complementary codes (CCCs) in multi-carrier code division multiple access (MC-CDMA) systems. In this paper, two classes of aperiodic QCSSs are constructed over the finite rings, which have new parameters in terms of the length of constituent sequences and set size respectively. Most notably, the length of constituent sequences of QCSS derived from the first construction is$ p^{n} + 1$, where p is a prime and n is a positive integer, which has not been covered in the literature. In the second construction, the set size of the proposed binary QCSS is$2^{n+1}$larger than the existing binary QCSS. In addition, both the proposed aperiodic QCSSs are asymptotically optimal with respect to the correlation lower bound.

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 design of omnidirectional precoding has been widely studied for massive multiple-input multiple-output (MIMO) systems. For the base station (BS) equipped with a uniform rectangular array (URA), the current state-of-the-art scheme uses two-dimensional (2-D) Golay complementary array pairs (GCAPs)/Golay complementary array sets (GCASs) as precoding matrices to achieve omnidirectional transmission. However, the existing constructions of 2-D GCAP/GCAS-based precoding can just be implemented using the analog phase shifter network with fully-connected structure (FCS), and the existing parameters of 2-D GCAPs constructed from function-based methods are limited. More specifically, the array sizes are in the form of a power-of-two. In this paper, utilizing the truncation technique, we presented three constructions of new 2-D GCAPs with non-power-of-two array sizes from 2-D generalized Boolean functions (GBFs), which have never been reported in the literature. The proposed constructions include 2-D GCAPs with power-of-two array sizes as a special case, with flexible parameters. Moreover, we further provide a theoretical connection between 2-D GBFs and precoding matrices, such that the omnidirectional precoding scheme based on the proposed 2-D GCAPs is applicable to both FCS and partially-connected structure (PCS). Finally, simulation results demonstrate that the precoding scheme is useful in massive MIMO omnidirectional transmission systems.

Controlling the peak-to-mean envelope power ratio (PMEPR) of multi-carrier code division multiple access (MC-CDMA) transmissions is a notoriously important problem. In this letter, a direct construction of multiple complete complementary codes (CCCs) with inter-set zero cross-correlation zone (ZCCZ) is proposed based on multivariable functions. The presented construction has an advantage over the previous works with regard to the new flexible parameters and low column sequence PMEPR, which may give an extra benefit in fulfilling different requirements and managing PMEPR in MC-CDMA systems with multiple cells. In addition, it turns out that the combination of the constructed CCCs results in a new optimal Z-complementary code set (ZCCS).

Mutually orthogonal complementary sets (MOCSs) have found a number of practical applications in wireless communications and radar owing to their perfect aperiodic auto-correlation and cross-correlation properties. Recently, toward the challenge of designing MOCSs with non-power-of-two lengths, direct constructions were presented by Wu et al. using generalized Boolean functions (GBFs). In this letter, a new construction of MOCSs is proposed based on GBFs, which leads to MOCSs with flock size 2k+1and length 2m+ 2t, whose set size is 1/2 of the flock size, where integers 0 ≤ t <; k ≤ m. In addition, the constructed MOCSs can yield column sequence peak-to-mean envelope power ratio (PMEPR) of at most 2.

Z-complementary code sets (ZCCSs), extended from complete complementary codes (CCCs), have ideal correlations within a zone around the in-phase position named zero correlation zone (ZCZ). In this article, two classes of aperiodic ZCCSs with good cross-correlation subsets are investigated. They are multiple CCCs with inter-set zero cross-correlation zone (ZCCZ) property and multiple aperiodic ZCCSs with ideal inter-set aperiodic cross-correlation property respectively, the latter is referred to as an aperiodic inter-group complementary (IGC) code set and each ZCCS is called a group. First of all, based on polyphase paraunitary (PU) matrices and special permutation matrices, a construction of multiple polyphase CCCs with an inter-set ZCCZ is proposed. The obtained multiple CCCs have potential applications in interference-free multi-cell environments to support a large number of users. In addition, a construction of aperiodic polyphase IGC code sets is presented from polyphase PU matrices. We remark that different groups of the derived IGC code sets yield different constituent sequence lengths, thus they could provide a variety of quality of service (QoS) in quasi-synchronous multi-cell multi-rate communication systems. To the best of our knowledge, the aforementioned constructions of ZCCSs with good cross-correlation subsets based on PU matrices have not been reported in the literature.

Recently, quasi-complementary sequence sets (QCSSs) including low correlation zone complementary sequence sets (LCZ-CSSs), and low correlation complementary sequence sets (LC-CSSs) have raised lots of concerns. According to the theoretical bounds, the set size of a QCSS is much larger than that of a traditional perfect complementary sequence set (PCSS). As a result, it is believed that QCSSs have potential applications in multi-carrier code-division multiple-access (MC-CDMA) systems to support more users. As binary sequences are desired in practice because of easier realization, we consider the design of binary QCSSs with large set size in this letter. A construction of aperiodic binary LCZ-CSSs is proposed, which leads to aperiodic binary LCZ-CSSs with asymptotically optimal parameters. Additional, aperiodic binary LC-CSSs with asymptotically optimal parameters can also be derived from the proposed construction.

Spectrally-constrained sequences (SCSs) with good correlation properties, and low spectral power under the spectral constraint have found many practical applications in communication, and radar systems operating over non-contiguous carriers or frequency slots. In this letter, a construction of single-channel spectrally-null-constrained sequence (SNCS) families with good correlation is proposed. Following the proposed construction, a single-channel polyphase SNCS family with period N(N + 1), and family size (p - 1) can be obtained, which has zero power leakage underthe spectral constraint{1 + a(N + 1) : a ∈ ℤN}, where N is an odd integer, and p is the minimum prime factor of N. Note that the maximum periodic correlation magnitude of the derived single-channel SNCS family is (N + 1), which asymptotically achieves the correlation lower bound as p increasing.

Complete complementary codes (CCCs) have found a number of practical applications in wireless communications owing to their perfect aperiodic auto-correlation and cross-correlation properties. In particular, an important application of CCCs is in interference-free multi-carrier code-division multiple-access (MC-CDMA) systems. The available number of complementary codes determines the system capacity. To enlarge the system capacity, this paper focuses on constructing multiple CCCs with inter-set zero cross-correlation zone (ZCCZ) property based on generalized Boolean functions (GBFs). To the best of our knowledge, such multiple CCCs have not been reported in the literature. The obtained multiple CCCs can provide advantages in applications to MC-CDMA systems with multiple cells. As a byproduct, optimal aperiodic Z-complementary code sets (ZCCSs) with low peak-to-mean envelope power ratio (PMEPR) can be derived by combining these CCCs.

Zero correlation zone (ZCZ) sequences have received much research attention in many practical applications, such as quasi‐synchronous code‐division multiple‐access systems and MIMO systems. In this study, three constructions of multiple polyphase ZCZ sequence sets with low inter‐set cross‐correlation property are proposed. The resultant periodic ZCZ sequence sets are optimal with respect to the theoretical bound and have new parameters uncovered in the literature. Consequently, a great deal of flexibility may be provided in the choice of periodic optimal ZCZ sequence sets with good inter‐set cross‐correlation property for their applications.

Complementary sequences have been applied to multi-carrier code-division multiple-access wireless communication systems. In this letter, multiple complementary sequence sets are constructed. The presented multiple complementary sequence sets have the following properties: first, each set is a complete complementary code (CCC) with parameters (p,p,p)-CCC; second, the maximum inter-set aperiodic cross-correlation amplitude is p; and finally, an aperiodic quasi-complementary sequence set with asymptotically near optimal correlation amplitude will be obtained by combining these complementary sequence sets together, which is not covered in the literature.

Codebooks with small inner product correlation have wide applications in many fields, such as direct spread code-division multiple access communications, signal processing, and compressed sensing. It is extremely hard to produce optimal codebooks with respect to the Welch bound or the Levenstein bound. This letter focuses on constructing asymptotically optimal codebooks with additive characters of finite fields. Following the proposed constructions, two classes of asymptotically optimal codebooks with respect to the Welch bound are obtained. In addition, the resulting codebooks could have a small alphabet size.

An (M, K, N, δmax)-quasi-complementary sequence set (QCSS) is referred to as a set of M two-dimensional matrices of size K × N with maximum periodic correlation magnitude δmax. It can be applied to a multi-carrier code-division multiple-access communication system to achieve low-interference performance. Compared with perfect complementary sequence sets, QCSSs with maximum periodic correlation magnitudes achieving or asymptotically achieving the correlation lower bounds have the advantage of supporting more users. In this paper, two constructions of periodic QCSSs from additive characters and multiplicative characters of finite fields are developed. In the first construction, new QCSSs with constituent sequence length N = p are proposed by using cyclic classes, where p is a prime. In the second construction, QCSSs with constituent sequence length N = q - 1 and N = r2- 1 are presented by employing almost difference sets and special sets proposed by Katz, respectively, where q > 5 is an odd prime power and r is a prime power. Notably, the parameters of QCSSs derived from the second construction are flexible and have not been covered in the literature. In addition, all the proposed periodic QCSSs are asymptotically optimal with respect to the correlation lower bounds.

Mutually orthogonal complementary codes have found many practical applications in wireless communications owing to their perfect correlation properties. However, the set size of a mutually orthogonal complementary code set (MOCCS) is upper bounded by the number of constituent sequences in each complementary code. As a result, the number of users in the communication system is limited. To overcome this limitation, quasi-complementary sequence sets (QCSSs) were proposed, which include low correlation zone complementary sequence sets (LCZ-CSSs) and low correlation complementary sequence sets (LC-CSSs). In this paper, aperiodic quasi-complementary sequences are our main interest. Constructions of aperiodic LC-CSSs and aperiodic LCZ-CSSs over the complex roots of unity are proposed. With these constructions, asymptotically optimal aperiodic QCSSs can be obtained.

An$(\boldsymbol {M},\boldsymbol {K},\boldsymbol {N},\delta _{\max })$-quasi-complementary sequence set (QCSS) is referred to as a set of$\boldsymbol {M}$2-D matrices of order$\boldsymbol {K}\times \boldsymbol {N}$with periodic tolerance$\delta _{\max }$. In a multicarrier code-division multiple-access (MC-CDMA) communication system, the set size$\boldsymbol {M}$of a QCSS is equal to the maximum number of users it can support, and the periodic tolerance$\delta _{\max }$determines the interference performance. For the application of a QCSS, it is desirable that the set size should be as large as possible, and the periodic tolerance should be as small as possible. In this paper, a framework of a periodic QCSS is proposed from additive and multiplicative characters associated with a specific integer set. It is then discovered that the parameters of the obtained QCSS are determined by the employed integer set. From this discovery, new classes of periodic QCSSs with large set sizes and low periodic tolerances are constructed and associated with some known integer sets.

Based on p ‐ary pseudorandom sequences, this study proposes a construction of degree‐ k Gaussian integer sequences of period by utilising k th power residue symbol satisfying , where p is an odd prime and positive integers . The periodic autocorrelation values are 0 at shifts of the resultant sequences. Specially, there is exactly one non‐zero out‐of‐phase periodic autocorrelation value of the resultant sequences for . The non‐zero elements of the sequences are balanced and can be predefined flexibly. Moreover, the maximum energy efficiency of the proposed sequences is close to for sufficiently large m .