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.

The present paper introduces a novel construction of ternary sequences having a zero-correlation zone. The cross-correlation function and the side-lobe of the auto-correlation function of the proposed sequence set is zero for the phase shifts within the zero-correlation zone. The proposed sequence set consists of more than one subset having the same member size. The correlation function of the sequences of a pair of different subsets, referred to as the inter-subset correlation function, has a wider zero-correlation zone than that of the correlation function of sequences of the same subset (intra-subset correlation function). The wide inter-subset zero-correlation enables performance improvement during application of the proposed sequence set. The proposed sequence set has a zero-correlation zone for periodic, aperiodic, and odd correlation functions.

This paper discusses factorization of bent function type complex Hadamard matrices of order pn with a prime p. It is shown that any bent function type complex Hadamard matrix has symmetrical factorization, which can be expressed by the product of n matrices of order pn with pn+1 non-zero elements, a matrix of order pn with pn non-zero ones, and the n matrices, at most. As its application, a correlator for M-ary spread spectrum communications is successfully given, which can be simply constructed by the same circuits with reduced multiplicators, before and behind.

This paper presents a quadriphase sequence pair, whose aperiodic auto-correlation functions for non-zero shifts and cross-one for any shift take pure imaginary values. Functions for pairs of length 2n are formulated, which map the vector space of order n over GF(2) to Z4. It is shown that they are bent for any n, such that their Fourier transforms take all the unit magnitude.

A polyphase sequence set with orthogonality consisting complex elements with unit magnitude, can be expressed by a unitary matrix corresponding to the complex Hadamard matrix or the discrete Fourier transform (DFT) matrix, whose rows are orthogonal to each other. Its matched filter bank (MFB), which can simultaneously output the correlation between a received symbol and any sequence in the set, is effective for constructing communication systems flexibly. This paper discusses the compact design of the MFB of a polyphase sequence set, which can be applied to any sequence set generated by the given logic function. It is primarily focused on a ZCZ code with q-phase or more elements expressed as A(N=qn+s, M=qn-1, Zcz=qs(q-1)), where q, N, M and Zcz respectively denote, a positive integer, sequence period, family size, and a zero correlation zone, since the compact design of the MFB becomes difficult when Zcz is large. It is shown that the given logic function on the ring of integers modulo q generating the ZCZ code gives the matrix representation of the MFB that M-dimensional output vector can be represented by the product of the unitary matrix of order M and an M-dimensional input vector whose elements are written as the sum of elements of an N-dimensional input vector. Since the unitary matrix (complex Hadamard matrix) can be factorized into n-1 unitary matrices of order M with qM nonzero elements corresponding to fast unitary transform, a compact MFB with a minimum number of circuit elements can be designed. Its hardware complexity is reduced from O(MN) to O(qM log q M+N).