New Sets of Optimal Odd-length Binary Z-Complementary Pairs

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 $2^{\alpha} \pm 1$, where $\alpha$ is a positive integer. In this paper, we construct optimal OB-ZCPs of generic lengths $2^\alpha 10^\beta 26^\gamma +1$ (where $\alpha,~ \beta, ~ \gamma$ are non-negative integers and $\alpha \geq 1$) 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 $4 \times 10^{\beta-1} +1$, $12 \times 26^{\gamma -1}+1$ and $12 \times 10^\beta 26^{\gamma -1}+1$ through proper insertions of GCPs of lengths $10^\beta,~ 26^\gamma, \text{and } 10^\beta 26^\gamma$, respectively. Our proposed OB-ZCPs have applications in communications and radar (as an alternative to GCPs)

New sets of Non-Orthogonal Spreading Sequences With Low Correlation and Low PAPR Using Extended Boolean Functions

Extended Boolean functions (EBFs) are one of the most important tools in cryptography and spreading sequence design in communication systems. In this paper, we use EBFs to design new sets of spreading sequences for non-orthogonal multiple access (NOMA), which is an emerging technique capable of supporting massive machine-type communications (mMTC) in 5G and beyond. In this work, first $p$-ary complementary sequences are constructed using EBFs and then, these sequences are used to design new sets of non-orthogonal spreading sequence sets having very low coherence and peak to average power ratio (PAPR). The proposed spreading sequence sets are capable of supporting a large number of active devices simultaneously. In fact, for a $p$-ary spreading sequence set, we theoretically achieve an overloading factor of $2p$, where $p$ is an odd prime. Specifically, for $p=3$, we achieve an overloading factor of $6$, which cannot be achieved through the existing constructions till date

New sets of even-length binary Z-complementary pairs with asymptotic ZCZ ratio of 3/4

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 +2 10β 26γ +2 (where α, β, and γ are nonnegative integers) and ZCZ widths 3 × 2α 10β 26γ +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).NRF (Natl Research Foundation, S’pore