In this letter, we propose a novel direct construction of three-phase Z-complementary triads with flexible lengths and various widths of the zero-correlation zone based on extended Boolean functions. The maximum width ratio of the zero-correlation zone of the construction can reach 3/4. And the proposed sequences can exist for all lengths other than powers of three. We also investigate the peak-to-average power ratio properties of the proposed ZCTs.

A set consisting of K subsets of Msequences of length L is called a complementary sequence set expressed by A(L, K, M), if the sum of the out-of-phase aperiodic autocorrelation functions of the sequences within a subset and the sum of the cross-correlation functions between the corresponding sequences in any two subsets are zero at any phase shift. Suehiro et al. first proposed complementary set A(Nn, N, N) where N and n are positive integers greater than or equal to 2. Recently, several complementary sets related to Suehiro's construction, such as N being a power of a prime number, have been proposed. However, there is no discussion about their inclusion relation and properties of sequences. This paper rigorously formulates and investigates the (generalized) logic functions of the complementary sets by Suehiro et al. in order to understand its construction method and the properties of sequences. As a result, it is shown that there exists a case where the logic function is bent when n is even. This means that each series can be guaranteed to have pseudo-random properties to some extent. In other words, it means that the complementary set can be successfully applied to communication on fluctuating channels. The logic functions also allow simplification of sequence generators and their matched filters.

Even correlation and odd correlation of sequences are two kinds of measures for their similarities. Both kinds of correlation have important applications in communication and radar. Compared with vast knowledge on sequences with good even correlation, relatively little is known on sequences with preferable odd correlation. In this paper, a generic construction of sequences with low odd correlation is proposed via interleaving technique. Notably, it can generate new sets of binary sequences with optimal odd correlation asymptotically meeting the Sarwate bound.

This letter is devoted to constructing new Type-II Z-complementary pairs (ZCPs). A ZCP of length N with ZCZ width Z is referred to in short by the designation (N, Z)-ZCP. Inspired by existing works of ZCPs, systematic constructions of (2N+3, N+2)-ZCPs and (4N+4, 7/2N+4)-ZCPs are proposed by appropriately inserting elements into concatenated GCPs. The odd-length binary Z-complementary pairs (OB-ZCPs) are Z-optimal. Furthermore, the proposed construction can generate even-length binary Z-complementary pairs (EB-ZCPs) with ZCZ ratio (i.e. ZCZ width over the sequence length) of 7/8. It turns out that the PMEPR of resultant EB-ZCPs are upper bounded by 4.

Inspired by an idea due to Levenshtein, we apply the low correlation zone constraint in the analysis of the weighted mean square aperiodic correlation. Then we derive a lower bound on the measure for quasi-complementary sequence sets with low correlation zone (LCZ-QCSS). We discuss the conditions of tightness for the proposed bound. It turns out that the proposed bound is tighter than Liu-Guan-Ng-Chen bound for LCZ-QCSS. We also derive a lower bound for QCSS, which improves the Liu-Guan-Mow bound in general.

This paper is focused on constructing even-length binary Z-complementary pairs (EB-ZCPs) with new length. Inspired by a recent work of Adhikary et al., we give a construction of EB-ZCPs with length 8N+4 (where N=2α 10β 26γ and α, β, γ are nonnegative integers) and zero correlation zone (ZCZ) width 5N+2. The maximum aperiodic autocorrelation sums (AACS) magnitude of the proposed sequences outside the ZCZ region is 8. It turns out that the generated sequences have low PAPR.

In contemporary communications, Golay, periodic and Z- complementary sequence sets play a very important role, since such sequence sets possess impulse-like or zero correlation zone (ZCZ) autocorrelation. On the other hand, the advantages of the signals over the quadrature amplitude modulation (QAM) constellation are more and more prominent. Hence, the design of such sequence sets over the QAM constellation has turned into one of the all-important issues in communications. Therefore, the construction methods of such sequence sets over the 16-QAM constellation are investigated, in this letter, and our goals are arrived at by the known quaternary Golay, periodic and Z- complementary sequence sets. Finally, many examples illuminate the validity of the proposed methods.

The present paper introduces a new approach to the construction of a sequence set with a zero-correlation zone for both periodic and aperiodic correlation functions. The proposed sequences can be constructed from a pair of Hadamard matrices of orders n0 and n1. The constructed sequence set consists of n0 n1 ternary sequences, each of length n0(m+2)(n1+Δ), for a non-negative integer m and Δ ≥ 2. The zero-correlation zone of the proposed sequences is |τ| ≤ n0m+1-1, where τ is the phase shift. The proposed sequence set consists of n0 subsets, each with a member size n1. The correlation function of the sequences of a pair of different subsets, referred to as the inter-subset correlation function, has a zero-correlation zone with a width that is approximately Δ times that of the correlation function of sequences of the same subset (intra-subset correlation function). The inter-subset zero-correlation zone of the proposed sequences is |τ| ≤ Δn0m+1, where τ is the phase shift. The wide inter-subset zero-correlation enables performance improvement during application of the proposed sequence set.

In this paper, for odd n and any k with gcd(n,k) = 1, new binary sequence families Sk of period 2n-1 are constructed. These families have maximum correlation , family size 22n+2n+1 and maximum linear span . The correlation distribution of Sk is completely determined as well. Compared with the modified Gold codes with the same family size, the proposed families have the same period and correlation properties, but larger linear span. As good candidates with low correlation and large family size, the new families contain the Gold sequences and the Gold-like sequences. Furthermore, Sk includes a subfamily which has the same period, correlation distribution, family size and linear span as the family So(2) recently constructed by Yu and Gong. In particular, when k=1, is exactly So(2).

We obtain an upper bound for the maximum aperiodic and odd correlations of the recently derived p-ary sequences from Galois rings [1]. We use the upper bound on hybrid sums over Galois rings [5], the Vinogradov method [4] and the methods of [5] and [6].

A new class of ternary sequence with a zero-correlation zone is introduced. The proposed sequence sets have a zero-correlation zone for both periodic and aperiodic correlation functions. The proposed sequences can be constructed from a pair of Hadamard matrices of size n0n0 and a Hadamard matrix of size n1n1. The constructed sequence set consists of n0 n1 ternary sequences, and the length of each sequence is (n1+1) for a non-negative integer m. The zero-correlation zone of the proposed sequences is |τ|≤ -1, where τ is the phase shift. The sequence member size of the proposed sequence set is equal to times that of the theoretical upper bound of the member size of a sequence set with a zero-correlation zone.

In order to eliminate the co-channel and multi-path interference of quasi-synchronous code division multiple access (QS-CDMA) systems, spreading sequences with low or zero correlation zone (LCZ or ZCZ) can be used. The significance of LCZ/ZCZ to QS-CDMA systems is that, even there are relative delays between the transmitted spreading sequences due to the inaccurate access synchronization and the multipath propagation, the orthogonality (or quasi-orthogonality) between the transmitted signals can still be maintained, as long as the relative delay does not exceed certain limit. In this paper, several lower bounds on the aperiodic autocorrelation and crosscorrelation of binary LCZ/ZCZ sequence set with respect to the family size, sequence length and the aperiodic low or zero correlation zone, are derived. The results show that the new bounds are tighter than previous bounds for the LCZ/ZCZ sequences.

The present letter introduces a new approach to the construction of a set of ternary arrays having a zero-correlation zone. The proposed array set has a zero-correlation zone for both periodic and aperiodic correlation functions. As such, the proposed arrays can be used as a finite-size array having a zero-correlation zone. The proposed array sets can be constructed from an arbitrary Hadamard matrix. The member size of the proposed array set is close to the theoretical upper bound.

The present paper introduces a new approach to the construction of a class of ternary sequences having a zero-correlation zone. The cross-correlation function of each pair of the proposed sequences is zero for phase shifts within the zero-correlation zone, and the auto-correlation function of each proposed sequence is zero for phase shifts within the zero-correlation zone, except for zero-shift. The proposed sequence set has a zero-correlation zone for periodic, aperiodic, and odd correlation functions. As such, the proposed sequence can be used as a finite-length sequence with a zero-correlation zone. A set of the proposed sequences can be constructed for any set of Hadamard sequences of length n. The constructed sequence set consists of 2n ternary sequences, and the length of each sequence is (n+1)2m+2 for a non-negative integer m. The periodic correlation function, the aperiodic correlation function, and the odd correlation function of the proposed sequences have a zero-correlation zone from -(2m+1-1) to (2m+1-1). The member size of the proposed sequence set is of the theoretical upper bound of the member size of a sequence having a zero-correlation zone. The ratio of the number of non-zero elements to the the sequence length of the proposed sequence is also .

We propose a new multiple access communication system based on finite field wavelet spread signature (FFWSS). In addition to the function of frequency diversity and multiple access, which are typically provided by traditional spreading codes, the FFWSS spreads data symbols in time, resulting in robustness against frequency selective slow fading. Using the FFWSS to spread a data symbol so that it is overlapped with neighboring symbols, a FFWSS-CDMA system is developed. It is observed that the ratio of the maximum nontrivial value of periodic correlation function to the code length of FFWSS is the same as that of a Sidelnikov sequence. Using RAKE-based receivers, simulation results show that the proposed FFWSS-CDMA system yields lower bit error rate (BER) than conventional DS-CDMA and MT-CDMA systems in multipath fading channels.

The periodic correlation properties of M sequences coded by channel codes are discussed. As for the channel codes, the Manchester code and the eight DC free codes in the FM family codes, which include the conventional FM code and the differential Manchester code, are adopted. The M sequences coded by the DC free codes in the FM family codes are referred to as FM coded M sequences. The periodic correlation properties of all combinations of the FM coded M sequences are checked, and the combinations which can provide almost the same or better properties as compared with those of the preferred pairs of M sequences are described. An example of code design using the FM coded M sequences for asynchronous direct sequence/spread spectrum multiple access systems is also discussed.

It is known that a family of p-ary bent sequences, whose elements take values of GF (p) with a prime p, possesses low periodic correlation properties and high linear span. Firstly such a family is shown to consist of balanced sequences in the sense that the frequency of appearances in one period is the same for each nonzero element and once less for zero element. Secondly the exact distribution of the periodic correlation values is given for the family.

An approximate equation of the odd periodic correlation distribution for the family of binary sequences is derived from the exact even periodic correlation distribution. The distribution means the probabilities of correlation values which appear among all the phase-shifted sequences in the family. It is shown that the approximate distribution is almost the same as the computational result of some family such as the Gold sequences with low even periodic correlation magnitudes, or the Kasami sequences, the bent sequences with optimal even periodic correlation properties in the sense of the Welch's lower bound. It is also shown that the odd periodic correlation distribution of the family with optimal periodic correlation properties is not the Gaussian distribution, but that of the family of the Gold sequences with short period seems to be similar to the Gaussian distribution.