In the massive machine-type communication scenario, aiming at the problems of active user detection and channel estimation in the grant-free non-orthogonal multiple access (NOMA) system, new sets of non-orthogonal spreading sequences are proposed by using the zero/low correlation zone sequence set with low correlation among multiple sets. The simulation results show that the resulting sequence set has low coherence, which presents reliable performance for channel estimation and active user detection based on compressed sensing. Compared with the traditional Zadoff-Chu (ZC) sequences, the new non-orthogonal spreading sequences have more flexible lengths, and lower peak-to-average power ratio (PAPR) and smaller alphabet size. Consequently, these sequences will effectively solve the problem of high PAPR of time domain signals and are more suitable for low-cost devices in massive machine-type communication.

This paper shows an optimal spreading sequence in the Weyl sequence class, which is similar to the set of the Oppermann sequences for asynchronous CDMA systems. Sequences in Weyl sequence class have the desired property that the order of cross-correlation is low. Therefore, sequences in the Weyl sequence class are expected to minimize the inter-symbol interference. We evaluate the upper bound of cross-correlation and odd cross-correlation of spreading sequences in the Weyl sequence class and construct the optimization problem: minimize the upper bound of the absolute values of cross-correlation and odd cross-correlation. Since our optimization problem is convex, we can derive the optimal spreading sequences as the global solution of the problem. We show their signal to interference plus noise ratio (SINR) in a special case. From this result, we propose how the initial elements are assigned, that is, how spreading sequences are assigned to each users. In an asynchronous CDMA system, we also numerically compare our spreading sequences with other ones, the Gold codes, the Oppermann sequences, the optimal Chebyshev spreading sequences and the SP sequences in Bit Error Rate. Our spreading sequence, which yields the global solution, has the highest performance among the other spreading sequences tested.

The present paper proposes two new methods for constructing polyphase asymmetric zero-correlation zone (A-ZCZ) sequence sets. In previous studies, the authors proposed methods for constructing quasi-optimal polyphase A-ZCZ sequence sets using perfect sequences and for constructing optimal polyphase A-ZCZ sequence sets using discrete Fourier transform (DFT) matrices. However, in these methods, the total number of sequences in an A-ZCZ sequence set cannot exceed the period of the perfect sequence or the dimension of the DFT matrix used for constructing the A-ZCZ sequence set. We now propose two extended versions of these methods. The proposed methods can generate a quasi-optimal or optimal polyphase A-ZCZ sequence set where the total number of sequences exceeds the period of the perfect sequence or the dimension of the DFT matrix. In other words, the proposed methods can generate new A-ZCZ sequence sets that cannot be obtained from the known methods.

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.

Recently, asymmetric zero-correlation zone (A-ZCZ) sequence sets that are composed of several sequence subsets have been proposed. In A-ZCZ sequence sets, the zero-cross-correlation zone (ZCCZ) length between different sequence subsets is larger than the zero-correlation zone (ZCZ) length in each sequence subset. However, the ZCCZ length between different sequence subsets was not precisely shown in previous studies. The present letter shows precisely the ZCCZ length between different sequence subsets. This information is useful for estimating the magnitude of inter-cell interference when designing approximately synchronized code-division multiple-access (AS-CDMA) systems.

The even-shift orthogonal sequence whose out-of-phase aperiodic autocorrelation function takes zero at any even shifts is generalized to multi-dimension called even-shift orthogonal array (E-array), and the logic function of E-array of power-of-two length is clarified. It is shown that E-array can be constructed by complementary arrays, which mean pairs of arrays that the sum of each aperiodic autocorrelation function at the same phase shifts takes zero at any shift except zero shift, as well as the one-dimensional case. It is also shown that the number of mates of E-array with which the cross correlation function between E-arrays takes zero at any even shifts is equal to the dimension. Furthermore it is investigated that E-array possesses good aperiodic autocorrelation that the rate of zero correlation values to array length approaches one as the dimension becomes large.

The present paper proposes a new method for constructing polyphase asymmetric zero-correlation zone (A-ZCZ) sequence sets. The proposed method can generate A-ZCZ sequence sets that cannot be obtained from methods proposed by other researchers and is a generalized version of our previously proposed method. An A-ZCZ sequence set can be regarded as a ZCZ sequence set. The newly obtained A-ZCZ sequence sets include quasi-optimal ZCZ sequence sets of which the zero-cross-correlation zone (ZCCZ) length between different sequence subsets is larger than the mathematical upper bound of conventional ZCZ sequence sets. A new method for extending the A-ZCZ sequence sets is also presented in the present paper.

In non-cooperative scenarios, the estimation of direct sequence spread spectrum (DS-SS) signals has to be done in a blind manner. In this letter, we consider the spreading sequence estimation problem for DS-SS signals. First, the maximum likelihood estimate (MLE) of spreading sequence is derived, then a semidefinite relaxation (SDR) approach is proposed to cope with the exponential complexity of performing MLE. Simulation results demonstrate that the proposed approach provides significant performance improvements compared to existing methods, especially in the case of low numbers of data samples and low signal-to-noise ratio (SNR) situations.

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.

Performance of band-limited baseband synchronous CDMA using orthogonal Independent Component Analysis (ICA) spreading sequences is investigated. The orthogonal ICA sequences have an orthogonality condition in a synchronous CDMA like the Walsh-Hadamard sequences. Furthermore, these have useful correlation properties like the Gold sequences. These sequences are obtained easily by using the ICA which is one of the brain-style signal processing algorithms. In this study, the ICA is used not as a separator for received signal but as a generator of spreading sequences. The performance of the band-limited synchronous CDMA using the orthogonal ICA sequences is compared with the one using the Walsh-Hadamard sequences. For limiting bandwidth, a Root Raised Cosine filter (RRC) is used. We investigate means and variances of correlation outputs after passing the RRC filter and the Bit Error Rates (BERs) of the system in additive white Gaussian noise channel by numerical simulations. It is found that the BER in the band-limited system using the orthogonal ICA sequences is much lower than the one using the Walsh-Hadamard sequences statistically.

A performance of the complex chaotic spreading sequences with constant power is investigated in a chip-synchronous complex CDMA with a complex scrambling. We estimate a signal-to-interference ratio (SIR) and a bit error rate (BER). An exact invariant measure of the complex chaotic spreading sequence can be obtained. Therefore, the SIR can be calculated analytically. The result can be used as one of the criteria for evaluating the performance of the complex CDMA using the chaotic spreading sequences.

The present paper introduces the construction of a class of sequence sets with zero-correlation zones called zero-correlation zone sequence sets. The proposed zero-correlation zone sequence set can be generated from an arbitrary perfect sequence and an arbitrary Golay complementary sequence pair. The proposed construction is a generalization of the zero-correlation zone sequence construction previously reported by the present author. The proposed sequence set can successfully provide CDMA communication without co-channel interference.

The present paper describes a method for the construction of a zero-correlation zone sequence set from a perfect sequence. Both the cross-correlation function and the side-lobe of the auto-correlation function of the proposed sequence sets are zero for phase shifts within the zero-correlation zone. These sets can be generated from an arbitrary perfect sequence, the length of which is the product of a pair of odd integers ((2n+1)(2k+1) for k ≥ 1 and n ≥ 0). The proposed sequence construction method can generate an optimal zero-correlation zone sequence set that achieves the theoretical bounds of the sequence member size given the size of the zero-correlation zone and the sequence period. The peak in the out-of-phase correlation function of the constructed sequences is restricted to be lower than the half of the power of the sequence itself. The proposed sequence sets could successfully provide CDMA communication without co-channel interference, or, in an ultrasonic synthetic aperture imaging system, improve the signal-to-noise ratio of the acquired image.

This paper extends previous analytical approaches for the study of CDMA systems to the relevant case of multipath environments where users can operate at different bit rates. This scenario is of interest for the Wideband CDMA strategy employed in UMTS, and the model permits the performance comparison of classic and more innovative spreading signals. The method is based on the characteristic function approach, that allows to model accurately the various kinds of interferences. Some numerical examples are given with reference to the ITU-R M.1225 Recommendations, but the analysis could be extended to different channel descriptions.

We propose a novel asynchronous direct-sequence code-division multiple access (DS-CDMA) using feedback-controlled spreading sequences (FCSSs) (FCSS/DS-CDMA). At the receiver of FCSS/DS-CDMA, the code-orthogonalizing filter (COF) produces a spreading sequence, and the receiver returns the spreading sequence to the transmitter. Then the transmitter uses the spreading sequence as its updated version. The performance of FCSS/DS-CDMA is evaluated over time-dispersive channels. The results indicate that FCSS/DS-CDMA greatly suppresses both the intersymbol interference (ISI) and multiple access interference (MAI) over time-invariant channels. FCSS/DS-CDMA is applicable to the decentralized multiple access.

We design M(≥3)-phase spreading sequences of Markov chains optimal in terms of bit error probabilities in asynchronous SSMA (spread spectrum multiple access) communication systems. To this end, we obtain the distributions of the normalized MAI (multiple access interference) for such systems and find a necessary and sufficient condition that the distributions become independent of the phase shifts.

The present paper introduces the construction of a class of sequence sets with zero-correlation zones called zero-correlation zone sequence sets. The proposed zero-correlation zone sequence set can be generated from an arbitrary perfect sequence, the length of which is longer than 4. The proposed sets of ternary sequences, which can be constructed from an arbitrary perfect sequence, can successfully provide CDMA communication without co-channel interference. In an ultrasonic synthetic aperture imaging system, the proposed sequence set can improve the signal-to-noise ratio of the acquired image.

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.

We study asynchronous SSMA communication systems using binary spreading sequences of Markov chains and prove the CLT (central limit theorem) for the empirical distribution of the normalized MAI (multiple-access interference). We also prove that the distribution of the normalized MAI for asynchronous systems can never be Gaussian if chains are irreducible and aperiodic. Based on these results, we propose novel theoretical evaluations of bit error probabilities in such systems based on the CLT and compare these and conventional theoretical estimations based on the SGA (standard Gaussian approximation) with experimental results. Consequently we confirm that the proposed theoretical evaluations based on the CLT agree with the experimental results better than the theoretical evaluations based on the SGA. Accordingly, using the theoretical evaluations based on the CLT, we give the optimum spreading sequences of Markov chains in terms of bit error probabilities.

This paper proposes a new class of polyphase ZCZ (zero-correlation zone) sequence sets which satisfy a mathematical upper bound. The proposed ZCZ sequence sets are obtained from DFT matrices and unitary matrices. In addition, this paper discusses the cross-correlation property between different ZCZ sequence sets which belong to the proposed class.