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.

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.

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.