Two-dimensional (2-D) Golay complementary array sets (GCASs) have found important applications in massive multiple-input multiple-output (MIMO) systems equipped with a uniform rectangular array (URA), which are employed as precoding matrices to produce omnidirectional transmission. In this letter, new constructions of 2-D GCASs based on 2-D multivariable functions are presented. Compared with the existing constructions in the literature, the proposed constructions can be represented by explicit function forms that are more convenient to use in practical applications. Furthermore, 2-D GCASs with new parameters are obtained. Finally, numerical results show that the proposed 2-D GCASs are useful in massive MIMO systems.

Quasi-complementary sequence sets (QCSSs) have the advantage of supporting more users in multi-carrier CDMA systems. Recently, a generic construction of QCSSs from difference sets was developed by Liu et al. In this letter, the idea of Liu et al. is extended, and constructions of QCSSs from both difference sets and almost difference set are proposed. These constructions produce QCSSs asymptotically achieving the theoretical bound. The QCSSs presented in this letter have new parameters not covered in the literature.

An (M; K; N; δmax)-quasi-complementary sequence set (QCSS) is referred to as a set of M two-dimensional matrices of order K × N with periodic tolerance δmax. In a multicarrier codedivision multiple-access (MC-CDMA) communication system, the set size M of a QCSS is equal to the maximum number of users it can support and the periodic tolerance δmax 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 associated with some known integer sets.

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 (MC-CDMA) communication system to achieve low-interference performance. Compared with perfect complementary sequence sets (PCSSs), 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.

Complementary sequences have been applied to multi-carrier code-division multiple-access (MC-CDMA) wireless communication systems. In this paper, multiple complementary sequence sets are constructed. The presented multiple complementary sequence sets have the following properties: 1) each set is a complete complementary code (CCC) with parameters $(p,p,p)$ -CCC; 2) the maximum inter-set aperiodic cross-correlation amplitude is $p$ ; 3) an aperiodic quasi-complementary sequence set (QCSS) with asymptotically near optimal correlation amplitude will be obtained by combining these complementary sequence sets together, which is not covered in the literature.

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.