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.

In this paper, we study the properties of the sum-of-squares indicator of vectorial Boolean functions. Firstly, we give the upper bound of $sum_{uin mathbb{F}_2^n,vin mathbb{F}_2^m}mathcal{W}_F^3(u,v)$. Secondly, based on the Walsh-Hadamard transform, we give a secondary construction of vectorial bent functions. Further, three kinds of sum-of-squares indicators of vectorial Boolean functions are defined by autocorrelation function and the lower and upper bounds of the sum-of-squares indicators are derived. Finally, we study the sum-of-squares indicators with respect to several equivalence relations, and get the sum-of-squares indicator which have the best cryptographic properties.

In this paper, some properties of Boolean functions via the unitary transform and c-correlation functions are presented. Based on the unitary transform, we present two classes of secondary constructions for c-bent4 functions. Also, by using the c-correlation functions, a direct link between c-autocorrelation function and the unitary transform of Boolean functions is provided, and the relationship among c-crosscorrelation functions of arbitrary four Boolean functions can be obtained.

We consider both-ends-fixed k-ary necklaces and enumerate all such necklaces of length n from the viewpoints of symbolic dynamics and β-expansions, where n and k(≥ 2) are natural numbers and β(> 1) is a real number. Recently, Sawada et al. proposed an efficient construction of k-ary de Bruijn sequence of length kn, which for each n ≥ 1, requires O(n) space but generates a single k-ary de Bruijn sequence of length kn in O(1)-amortized time per bit. Based on the enumeration of both-ends-fixed k-ary necklaces of length n, we evaluate auto-correlation values of the k-ary de Bruijn sequences of length kn constructed by Sawada et al. We also estimate the asymptotic behaviour of the obtained auto-correlation values as n tends to infinity.

This article proposes to apply the auto-correlation function (ACF), bispectrum analysis, and convolutional neural networks (CNN) to implement radar emitter identification (REI) based on intrapulse features. In this work, we combine ACF with bispectrum for signal feature extraction. We first calculate the ACF of each emitter signal, and then the bispectrum of the ACF and obtain the spectrograms. The spectrum images are taken as the feature maps of the radar emitters and fed into the CNN classifier to realize automatic identification. We simulate signal samples of different modulation types in experiments. We also consider the feature extraction method directly using bispectrum analysis for comparison. The simulation results demonstrate that by combining ACF with bispectrum analysis, the proposed scheme can attain stronger robustness to noise, the spectrograms of our approach have more pronounced features, and our approach can achieve better identification performance at low signal-to-noise ratios.

In this letter, we will prove that chaotic binary sequences generated by the tent map and Walsh functions are i.i.d. (independent and identically distributed) and orthogonal to each other.

This paper proposes statistical analysis of phase-only correlation (POC) functions under the phase fluctuation of signals due to additive Gaussian noise. We derive probability density function of phase-spectrum differences between original signal and its noise-corrupted signal with additive Gaussian noise. Furthermore, we evaluate the expectation and variance of the POC functions between these two signals. As the variance of Gaussian noise increases, the expectation of the peak of the POC function monotonically decreases and variance of the POC function monotonically increases. These results mathematically guarantee the validity of the POC functions used for similarity measure in matching techniques.

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.

This paper proposes statistical analysis of phase-only correlation functions between two signals with stochastic phase-spectra following bivariate circular probability distributions based on directional statistics. We give general expressions for the expectation and variance of phase-only correlation functions in terms of joint characteristic functions of the bivariate circular probability density function. In particular, if we assume bivariate wrapped distributions for the phase-spectra, we obtain exactly the same results between in case of a bivariate linear distribution and its corresponding bivariate wrapped distribution.

Sequences that attain the smallest possible absolute sidelobes (SPASs) of periodic autocorrelation function (PACF) play fairly important roles in synchronization of communication systems, Large scale integrated circuit testing, and so on. This letter presents an approach to construct 16-QAM sequences of even periods, based on the known quaternary sequences. A relationship between the PACFs of 16-QAM and quaternary sequences is established, by which when quaternary sequences that attain the SPASs of PACF are employed, the proposed 16-QAM sequences have good PACF.

Many autocorrelation-based frequency estimation algorithms have been proposed. However, some of them cannot construct a strict linear prediction (LP) property among the adjacent autocorrelation lags, which affects the estimators' performance. To improve the precision of frequency estimation, two novel autocorrelation based frequency estimation methods of the real sinusoid signal in additive white Gaussian noise (AWGN) are proposed in this paper. Firstly, a simple method is introduced to transform the real sinusoid signal into the noncircular signal. Secondly, the autocorrelation of the noncircular signal is analyzed and a strict LP property is constructed among the adjacent autocorrelation lags of the noncircular signal. Thirdly, the least squares (LS) and reformed Pisarenko harmonic decomposer (RPHD) frameworks are employed to improve estimation accuracy. The simulation results match well with the theoretical values. In addition, computer simulations demonstrate that the proposed algorithm provides high estimation accuracy and good noise suppression capability.

Let d=2pm-1 be the Niho decimation over $mathbb{F}_{p^{2m}}$ satisfying $gcd(d,p^{2m}-1)=3$, where m is an odd positive integer and p is a prime with p ≡ 2(mod 3). The cross-correlation function between the p-ary m-sequence of period p2m-1 and its every d-decimation sequence with short period $rac{p^{2m}-1}{3}$ is investigated. It is proved that for each d-decimation sequence, the cross-correlation function takes four values and the corresponding correlation distribution is completely determined. This extends the results of Niho and Helleseth for the case gcd(d, p2m-1)=1.

As one functionality of the wireless distributed network (WDN) enabling flexible wireless networks, it is supposed that a dynamic spectrum access is applied to OFDM systems for superior radio resource management. As a basic technology for such WDN, our study deals with the OFDM signal detection based on its cyclostationary feature. Previous relevant studies mainly relied on software simulations based on the Monte Carlo method. This paper analytically clarifies the relationship between the design parameters of the detector and its detection performance. The detection performance is formulated by using multiple design parameters including the transfer function of the receive filter. A hardware experiment with radio frequency (RF) signals is also carried out by using the detector consisting of an RF unit and FPGA. Thereby, it is verified that the detection characteristics represented by the false-alarm and non-detection probabilities calculated by the analytical formula agree well with those obtained by the hardware experiment. Our analysis and experiment results are useful for the parameter design of the signal detector to satisfy required performance criteria.

To overcome the false lock or detection missing problems caused by the multiple peaks of the auto-correlation function (ACF) of Binary Offset Carrier (BOC) modulated signal, an acquisition algorithm based on unit correlation for BOC(n,n) signal is proposed in this paper. The local BOC signal is separated into two unit signals, an odd one and an even one. Then a reconstruction of the unit correlation functions between the unit signals and the received BOC signal is performed and M sections of reconstructed correlation function are accumulated according to the non-coherent method, so that this novel acquisition algorithm can not only eliminate the multiple secondary peaks, but also retain the advantage of the narrow correlation main peak. Simulation results show that the acquisition sensitivity of the proposed algorithm is increased 3dBHz compared with the ASPeCT method, and the computation cost is only 41.46% of the ASPeCT method when M=2.

This paper presents study results regarding the analytical method for performance characteristics and application scheme, which cover a feature detection scheme using a Cyclic Prefix (CP) that is attached to an OFDM signal. The detection scheme is especially important when used as a sensing technology in advanced systems such as Device-to-Device (D-to-D) or Internet of Things (IoT). Herein, we present several basic performance characteristics of the signal processing involved in feature detection, namely, the Output S/N (Signal-to-Noise power ratio) and probability density functions of the OFDM signal and the noise measured at the output of the feature detector. The Output S/Nis described by an analytical expression and is also examined by conducting a software simulation. An analytical approach is investigated by modeling the spectral density of the OFDM signal and input noise and by executing the mathematical operations such as convolutional integration on the combination of OFDM signal and noise. The analytical results coincide closely with the simulation results. As for the applications to mobile communication system, some methods of the feature detection schemes are addressed. These are an estimation method for the Input C/N (Carrier-to-Noise power ratio) and a system discrimination scheme, especially under the assumption that two OFDM systems using different CP lengths are simultaneously operated in the same frequency. Furthermore, under the condition that two OFDM signals are transmitted in an asynchronous manner, a scheme to estimate their timing offset and signal power ratio is also described.

This paper proposes the statistical analysis of phase-only correlation functions between two real signals with phase-spectrum differences. For real signals, their phase-spectrum differences have odd-symmetry with respect to frequency indices. We assume phase-spectrum differences between two signals to be random variables. We next derive the expectation and variance of the POC functions considering the odd-symmetry of the phase-spectrum differences. As a result, the expectation and variance of the POC functions can be expressed by characteristic functions or trigonometric moments of the phase-spectrum differences. Furthermore, it is shown that the peak value of the POC function monotonically decreases and the sidelobe values monotonically increase as the variance of the phase-spectrum differences increases.

This paper proposes statistical analysis of phase-only correlation functions with phase-spectrum differences following wrapped distributions. We first assume phase-spectrum differences between two signals to be random variables following a linear distribution. Next, based on directional statistics, we convert the linear distribution into a wrapped distribution by wrapping the linear distribution around the circumference of the unit circle. Finally, we derive general expressions of the expectation and variance of the POC functions with phase-spectrum differences following wrapped distributions. We obtain exactly the same expressions between a linear distribution and its corresponding wrapped distribution.

An algorithm that finds a set of real-valued approximately-zero correlation zone (AZCZ) sequences is proposed on the basis of the concept of feedback-controlled direct-sequence code-division multiple access (FC/DS-CDMA). It is known that ordinary algorithms can construct low correlation zone (LCZ) and zero correlation zone (ZCZ) sequence sets in which the choices of the number of sequences, sequence length, and LCZ or ZCZ length are limited. It is shown that the proposed algorithm finds AZCZ sequence sets by a numerical method under arbitrary conditions. The properties of AZCZ sequence sets are evaluated in terms of the autocorrelation and cross-correlation functions. It is shown that the periodic autocorrelation and cross-correlation functions take small values within a designated AZCZ. It is also shown that we can construct approximately-perfect sequences that have approximately ideal autocorrelation functions and new sequence sets that have multiple AZCZs using the proposed algorithm.

To analyze the structure of a set of high-dimensional perfect sequences over a composition algebra over R, we developed the theory of Fourier transforms of the set of such sequences. We define the discrete cosine transform and the discrete sine transform, and we show that there exists a relationship between these transforms and a convolution of sequences. By applying this property to a set of perfect sequences, we obtain a parameterization theorem. Using this theorem, we show the equivalence between the left perfectness and right perfectness of sequences. For sequences of real numbers, we obtain the parameterization without restrictions on the parameters.

This paper proposes statistical analysis of phase-only correlation functions based on linear statistics and directional statistics. We derive the expectation and variance of the phase-only correlation functions assuming phase-spectrum differences of two input signals to be probability variables. We first assume linear probability distributions for the phase-spectrum differences. We next assume circular probability distributions for the phase-spectrum differences, considering phase-spectrum differences to be circular data. As a result, we can simply express the expectation and variance of phase-only correlation functions as linear and quadratic functions of circular variance of phase-spectrum differences, respectively.