This paper presents a new construction method for binary cross Z-complementary pairs (CZCPs) with mutually orthogonal mates. Our approach, which utilizes Boolean functions, achieves a cross Z-complementary ratio (CZCratio) of 6/7. These CZCP mates can be used in generalized spatial modulation (SM) systems to enhance the channel estimation performance, thanks to their zero auto- and cross-correlation zone properties at the front-/tail-ends. We show that our method demonstrates the ability to generate new binary CZCP mates with improved CZCratioand flexible sequence lengths. Through numerical studies, we illustrate that the constructed mutually orthogonal CZCP mates can enhance the channel estimation performance in generalized SM systems.

In this paper, we first propose a new design strategy of 2D Z-complementary array quads (2D-ZCAQs) with feasible array sizes. A 2D-ZCAQ consists of four distinct unimodular arrays satisfying zero 2D auto-correlation sums for non-trivial 2D time-shifts within certain zone. Then, we obtain the upper bounds on the column sequence peak-to-mean envelope power ratio (PMEPR) of the constructed 2D-ZCAQs by using specific auto-correlation properties of some seed sequences. The constructed 2D-ZCAQs with bounded column sequence PMEPR can be used as a potential alternative to 2D Golay complementary array sets for practical applications.

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.

In this paper, we present a novel design strategy of DNA codes with length 3n over the non-chain ring ℤ4+uℤ4+u2ℤ4with 64 elements and u3=1, where n denotes the length of a code over R. We first study and analyze a distance conserving map defined over the ring R into the length-3 DNA sequences. Then, we derive some conditions on the generator matrix of a linear code over R, which leads to a DNA code with reversible, reversible-complement, homopolymer 2-run-length, and3wn-GC-content constraints for integer w (0 ≤ w ≤ 3n). Finally, we propose a new construction of DNA codes using Reed-Muller type generator matrices. This allows us to obtain DNA codes with reversible, reversible-complement, homopolymer 2-run-length, and -GC-content constraints.

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.

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.

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.