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.

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.

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.

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 .