The present paper introduces the construction of quadriphase sequences having a zero-correlation zone. For a zero-correlation zone sequence set of N sequences, each of length l, the cross-correlation function and the side lobe of the autocorrelation function of the proposed sequence set are zero for the phase shifts τ within the zero-correlation zone z, such that |τ|≤z (τ ≠ 0 for the autocorrelation function). The ratio $rac{N(z+1)}{ell}$ is theoretically limited to one. When l=N(z+1), the sequence set is called an optimal zero-correlation sequence set. The proposed zero-correlation zone sequence set can be generated from an arbitrary Hadamard matrix of order n. The length of the proposed sequence set can be extended by sequence interleaving, where m times interleaving can generate 4n sequences, each of length 2m+3n. The proposed sequence set is optimal for m=0,1 and almost optimal for m>1.

The present paper introduces a novel construction of structured ternary sequences having a zero-correlation zone (ZCZ) for both periodic and aperiodic correlation functions. The cross-correlation function and the side lobe of the auto-correlation function of the proposed sequence set are zero for phase shifts within the ZCZ. The proposed ZCZ sequence set can be generated from an arbitrary Hadamard matrix of order n. The sequence set of order 0 is identical to the r-th row of the Hadamard matrix. For m≥0, the sequence set of order (m+1) is constructed from the sequence set of order m by sequence concatenation and interleaving. The sequence set of order m has 2m subsets of size n. The length of the sequence is equal to n4m+2m+1(2m-1); The phase shift of the ZCZ for the whole sequence set is from -(2m-1) to (2m-1). The sequence set of order 0 is coincident with the rows of the given Hadamard sequence with no ZCZ. The subsets can be associated with a perfect binary tree of height m with 2m leaves. The r-th sequence subset consists of from the nr-th sequence to the ((n+1)r-1)-th sequence. The r-th subset is assigned to the r-th leaf of the perfect binary tree. For a longer distance between the corresponding leaves to the r-th and s-th sequences, the ZCZ of the r-th and s-th sequences is wider. This tree-structured width of ZCZ of a pair of the proposed sequences enables flexible design in applications of the proposed sequence set. The proposed sequence is suitable for a heterogeneous wireless network, which is one of the candidates for the fifth generation of radio access networks.

This paper presents a method of generating sets of orthogonal and zero-correlation zone (ZCZ) periodic real-valued sequences of period 2n, n ≥ 1. The sequences admit a fast correlation algorithm and the sets of sequences achieve the upper bound on family size. A periodic orthogonal sequence has the periodic autocorrelation function with zero sidelobes, and a set with orthogonal sequences whose mutual periodic crosscorrelation function at zero shift is zero. Similarly, a ZCZ set is the set of the sequences with zero-correlation zone. In this paper, we derive the real-valued periodic orthogonal sequences of period 2n from a real-valued Huffman sequence of length 2ν+1, ν being a positive integer and ν ≥ n, whose aperiodic autocorrelation function has zero sidelobes except possibly at the left and right shift-ends. The orthogonal and ZCZ sets of real-valued periodic orthogonal sequences are useful in various systems, such as synchronous code division multiple access (CDMA) systems, quasi-synchronous CDMA systems and digital watermarkings.

This paper presents constructions of two kinds of sets of sequences with a zero correlation zone, called ZCZ code, which can reach the upper bound of the member size of the sequence set. One is a ZCZ code which can be constructed by a unitary matrix and a perfect sequence. Especially, a ternary perfect sequence with elements 1 and zero can be used to construct the proposed ZCZ code. The other is a ZCZ code of pairs of ternary sequences and binary sequences which can be constructed by an orthogonal matrix that includes a Hadamard matrix and an orthogonal sequence pair. As a special case, an orthogonal sequence pair, which consists of a ternary sequence and a binary sequence, can be used to construct the proposed ZCZ code. These codes can provide CDMA systems without co-channel interference.

The optical ZCZ code is a set of pairs of binary and bi-phase sequences with zero correlation zone. An optical M-ary direct sequence spread spectrum (M-ary/DS-SS) system using this code can detect a desired sequence without interference of undesired sequences. However, the bank of matched filters in a receiver circuit may fall into large scale. In this paper, we propose the compact construction of a bank of matched filters for an M-ary/DS-SS system using an optical ZCZ code. This filter bank can decrease the number of 2-input adders from O(N2) to O(N) and delay circuits from O(N2) to O(Nlog 2 N), respectively, and is implemented on a field programmable gate array (FPGA) corresponding to 400,000 logic gates.

The present paper introduces a novel type of structured ternary sequences having a zero-correlation zone (zcz) for both periodic and aperiodic correlation functions. The cross-correlation function and the side lobe of the auto-correlation function of the proposed sequence set are zero for phase shifts within the zcz. The proposed zcz sequence set can be generated from an arbitrary pair of an Hadamard matrix of order lh and a binary/ternary perfect sequence of length lp. The sequence set of order 0 is identical to the r-th row of the Hadamard matrix. For m ≥ 0, the sequence set of order (m+1) is constructed from the sequence set of order m by sequence concatenation and interleaving. The sequence set has lp subsets of size 2lh. The periodic correlation function and the aperiodic correlation function of the proposed sequence set have a zcz from -(2m+1-1) to 2m+1-1. The periodic correlation function and the aperiodic correlation function of the sequences of the i-th subset and k-th subset have a zcz from -2m+2-(lh+1)((j-k) mod lp) to -2m+2-(lh+1)((j-k) mod lp). The proposed sequence is suitable for a heterogeneous wireless network, which is one of the candidates for the fifth-generation mobile networks.

The spreading technique can improve system performance since it mitigates the influence of deeply faded subcarrier channels. Proposals for implementing orthogonal frequency division multiplexing (OFDM) systems include frequency symbol spreading (FSS) based on the Walsh-Hadamard transform (WHT) and the discrete Fourier transform (DFT). In a single carrier frequency division multiplexing (SC-FDMA), good performance is obtained by the interleaved subcarrier allocation. Moreover, in a multiple-input multiple-output (MIMO), interleaving the operation of the different transmit antennas is also effective. By combining these techniques, in this paper, we propose the different antenna interleaved allocation with the full and divided WHT/DFT spreading for a high time resolution carrier interferometry (HTRCI) MIMO-OFDM.

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.

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.

This paper presents two kinds of new ZCZ codes consisting of trios of two binary sequences and a bi-phase sequence, which can reach the upper bound on the ZCZ codes. From the viewpoint of sequence design, it is shown that they can provide the most effective ASK-CDMA system, which can remove co-channel interference.

The present paper introduces a novel method for the construction of sequences that have a zero-correlation zone. For the proposed sequence set, both the cross-correlation function and the side lobe of the autocorrelation function are zero for phase shifts within the zero-correlation zone. The proposed scheme can generate a set of sequences, each of length 16n2, from an arbitrary Hadamard matrix of order n and a set of 4n trigonometric function sequences of length 2n. The proposed construction can generate an optimal sequence set that satisfies, for a given zero-correlation zone and sequence period, the theoretical bound on the number of members. The peak factor of the proposed sequence set is equal to √2.

In this paper, we propose new generation methods of two-dimensional (2D) optical zero-correlation zone (ZCZ) sequences with the high peak autocorrelation amplitude. The 2D optical ZCZ sequence consists of a pair of a binary sequence which takes 1 or 0 and a bi-phase sequence which takes 1 or -1, and has a zero-correlation zone in the two-dimensional correlation function. Because of these properties, the 2D optical ZCZ sequence is suitable for optical code-division multiple access (OCDMA) system using an LED array having a plurality of light-emitting elements arranged in a lattice pattern. The OCDMA system using the 2D optical ZCZ sequence can be increased the data rate and can be suppressed interference by the light of adjacent LEDs. By using the proposed generation methods, we can improve the peak autocorrelation amplitude of the sequence. This means that the BER performance of the OCDMA system using the sequence can be improved.

In this paper, we propose a new structure for a compact matched filter bank for a mutually orthogonal zero-correlation zone (MO-ZCZ) sequence set consisting of ternary sequence pairs obtained by Hadamard and binary ZCZ sequence sets; this construction reduces the number of two-input adders and delay elements. The matched filter banks are implemented on a field-programmable gate array (FPGA) with 51,840 logic elements (LEs). The proposed matched filter bank for an MO-ZCZ sequence set of length 160 can be constructed by a circuit size that is about 8.6% that of a conventional matched filter bank.

The present paper introduces a new approach to the construction of a sequence set with a zero-correlation zone (ZCZ), which is referred to as a ZCZ sequence set. The proposed sequence construction generates a ZCZ sequence set from a ZCZ sequence set. The proposed method can generate an almost optimal ZCZ sequence set, the member size of which approaches the theoretical bound, when an almost optimal ZCZ sequence is used for the sequence construction. The proposed sequence set consists of NO subsets, where a ZCZ sequence set Z(LO, NO, ZO is used in sequence construction. The correlation function of the sequences of a pair of different subsets, referred to as the inter-subset correlation function, has a ZCZ with a width that is about times that of the correlation function of sequences of the same subset (intra-subset correlation function) for integers Λ ≥ 1, T, and m ≥ 0. Wide inter-subset zero-correlation enables improved performance during application of the proposed sequence set.

ZCZ sets are families of sequences, whose periodic auto/cross-correlation functions have zero correlation zone at the both side of the zero-shift. They can provide approximately synchronized CDMA systems without intra-cell interference for cellular mobile communications. This paper presents ternary ZCZ sets achieving a mathematical bound, and investigates the average interference parameters for the sets in order to evaluate inter-cell interference. It is shown that they can provide AS-CDMA systems with efficiency frequency usage.

In this paper, we propose a new structure for a compact matched filter bank (MFB) for an optical zero-correlation zone (ZCZ) sequence set with Zcz=2z. The proposed MFB can reduces operation elements such as 2-input adders and delay elements. The number of 2-input adders decrease from O(N2) to O(N log2 N), delay elements decrease from O(N2) to O(N). In addition, the proposed MFBs for the sequence of length 32, 64, 128 and 256 with Zcz=2,4 and 8 are implemented on a field programmable gate array (FPGA). As a result, the numbers of logic elements (LEs) of the proposed MFBs for the sequences with Zcz=2 of length 32, 64, 128 and 256 are suppressed to about 76.2%, 84.2%, 89.7% and 93.4% compared to that of the conventional MFBs, respectively.

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.

Factorization of Hadamard matrices can provide fast algorithm and facilitate efficient hardware realization. In this letter, constructions of factorizable multilevel Hadamard matrices, which can be considered as special case of unitary matrices, are inverstigated. In particular, a class of ternary Hadamard matrices, together with its application, is presented.

This paper presents a ZCZ code which are combinedly used for spreading sequences and a synchronization symbol in quasi-synchronous CDMA systems using PSK, ASK or BFSK. Furthermore a simple matched filter is presented, which simultaneously calculates correlations with any sequences in the ZCZ code.

The present paper introduces a new approach to the construction of a sequence set with a zero-correlation zone (ZCZ). This sequence set is referred to as a ZCZ sequence set. The proposed sequence construction generates a ZCZ sequence set from a perfect sequence pair or a single perfect sequence. The proposed method can generate an optimal ZCZ sequence set, the member size of which reaches the theoretical bound.