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.

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.

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.

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.

In the conventional iterative superimposed pilot-assisted channel estimation (SI-PACE), simple averaging of the instantaneous channel estimates obtained by using the pilot over several single-carrier (SC) blocks (called the frame in this paper) is taken in order to reduce the interference from data symbols. Therefore, the conventional SI-PACE has low tracking ability against fading time variations. To solve the tracking problem, Wiener filtering (WF)-based averaging can be used instead of simple averaging. However, WF incurs high computational complexity. Furthermore, the estimation error of the fading autocorrelation function significantly degrades the channel estimation accuracy. In order to improve the channel estimation accuracy while keeping the computational complexity low, a new iterative SI-PACE using sliding WF (called iterative SWFSI-PACE) is proposed. The channel estimation is done by sliding a WF having a shorter filter size than the measurement interval. The bit error rate (BER) and throughput performances of SC-FDE using iterative SWFSI-PACE are investigated by computer simulation to show that the proposed scheme achieves good BER and throughput performances while keeping the computational complexity low irrespective of the fading rate (or maximum Doppler frequency).

Binary sequence pairs as a class of mismatched filtering of binary sequences can be applied in radar, sonar, and spread spectrum communication system. Binary sequence pairs with two-level periodic autocorrelation function (BSPT) are considered as the extension of usual binary sequences with two-level periodic autocorrelation function. Each of BSPT consists of two binary sequences of which all out-phase periodic crosscorrelation functions, also called periodic autocorrelation functions of sequence pairs, are the same constant. BSPT have an equivalent relationship with difference set pairs (DSP), a new concept of combinatorial mathematics, which means that difference set pairs can be used to research BSPT as a kind of important tool. Based on the equivalent relationship between BSPT and DSP, several families of BSPT including perfect binary sequence pairs are constructed by recursively constructing DSP on the integer ring. The discrete Fourier transform spectrum property of BSPT reveals a necessary condition of BSPT. By interleaving perfect binary sequence pairs and Hadamard matrix, a new family of binary sequence pairs with zero correlation zone used in quasi-synchronous code multiple division address is constructed, which is close to the upper theoretical bound with sequence length increasing.

Multi-dimensional (MD) periodic complementary array sets (CASs) with impulse-like MD periodic autocorrelation function are naturally generalized to (one dimensional) periodic complementary sequence sets, and such array sets are widely applied to communication, radar, sonar, coded aperture imaging, and so forth. In this letter, based on multi-dimensional perfect arrays (MD PAs), a method for constructing MD periodic CASs is presented, which is carried out by sampling MD PAs. It is particularly worth mentioning that the numbers and sizes of sub-arrays in the proposed MD periodic CASs can be freely changed within the range of possibilities. In particular, for arbitrarily given positive integers M and L, two-dimensional periodic polyphase CASs with the number M2 and size L L of sub-arrays can be produced by the proposed method. And analogously, pseudo-random MD periodic CASs can be given when pseudo-random MD arrays are sampled. Finally, the proposed method's validity is made sure by a given example.

In this letter, Doppler spread estimation in different Doppler spectra is investigated and some efficient methods are proposed to calculate the maximum Doppler frequency from autocorrelation function easily.

In this letter, we first investigate the bias of Doppler shift estimator based on autocorrelation function (ACF). Then we derive a signal-to-noise ratio (SNR) independent condition for Doppler shift estimation and achieve this condition by a adaptive process. Moreover, we present theoretical analysis about the convergency of our adaptive Doppler shift estimator, and derive a close-form expression for its mean square error (MSE). We verify the proposed estimator by computer simulation, the results of which are in agreement with the analysis, i.e., the proposed method achieves a good SNR-independent performance in a wide range of velocities and SNRs.

This paper analyses the autocorrelation function of return waveforms in high precision radar altimeters employing chirp-pulse transmit signal under the condition of near-nadir deviations of the antenna boresight axis. It is shown that in case of ultra wideband transmit signals providing very high time resolution the correlation function can be approximated by a product of two separate functions of time.

This letter proposes a low-complexity single frequency estimator for flat fading channels. The simplified estimator decreases the number of computations in the calculation of the autocorrelation function (AF) when compared to AF-based conventional estimators. The simplified estimator yields a comparable estimation performance to the existing estimators, while retaining the same frequency range.

A time domain (TD) speech enhancement technique to improve SNR in noise-contaminated speech is proposed. Additional supplementary scheme is applied to estimate the degree of noise of noisy speech. This is estimated from a function, which is previously prepared as the function of the parameter of the degree of noise. The function is obtained by least square (LS) method using the given degree of noise and the estimated parameter of the degree of noise. This parameter is obtained from the autocorrelation function (ACF) on frame-by-frame basis. This estimator almost accurately estimates the degree of noise and it is useful to reduce noise. The proposed method is based on two-stage processing. In the first stage, subtraction in time domain (STD), which is equivalent to ordinary spectral subtraction (SS), is carried out. In the result, the noise is reduced to a certain level. Further reduction of noise and by-product noise residual is carried out in the second stage, where blind source separation (BSS) technique is applied in time domain. Because the method is a single-channel speech enhancement, the other signal is generated by taking the noise characteristics into consideration in order to apply BSS. The generated signal plays a very important role in BSS. This paper presents an adaptive algorithm for separating sources in convolutive mixtures modeled by finite impulse response (FIR) filters. The coefficients of the FIR filter are estimated from the decorrelation of two mixtures. Here we are recovering only one signal of interest, in particular the voice of primary speaker free from interfering noises. In the experiment, the different levels of noise are added to the clean speech signal and the improvement of SNR at each stage is investigated. The noise types considered initially in this study consist of the synthesized white and color noise with SNR set from 0 to 30 dB. The proposed method is also tested with other real-world noises. The results show that the satisfactory SNR improvement is attained in the two-stage processing.

In this paper, we introduce a new method for depth perception from a 2D natural scene using scale variation of patterns. As the surface from a 2D scene gets farther away from us, the texture appears finer and smoother. Texture gradient is one of the monocular depth cues which can be represented by gradual scale variations of textured patterns. To extract feature vectors from textured patterns, higher order local autocorrelation functions are utilized at each scale step. The hierarchical linear discriminant analysis is employed to classify the scale rate of the feature vector which can be divided into subspaces by recursively grouping the overlapped classes. In the experiment, relative depth perception of 2D natural scenes is performed on the proposed method and it is expected to play an important role in natural scene analysis.

In this letter we first introduce a new generalized cyclotomic sequence of order four with respect to pq, then we calculate the linear complexity and minimal polynomial of this sequence. Our results show that the new binary sequence is quite good from the linear complexity viewpoint.

Video service is slated to be a major application of emerging high-speed communications networks of the future. In particular, full-motion video is designed to take advantage of the high bandwidths that will become affordably available with the advent of B-ISDN. A salient feature of compressed video sources is that they give rise to autocorrelated traffic streams, which are difficult to model with traditional modeling techniques. In this paper, we describe a new methodology, called TES (Transform-Expand-Sample) , for modeling general autocorrelated time series, and we apply it to traffic modeling of compressed video. The main characteristic of this methodology is that it can model an arbitrary marginal distribution and approximate the autocorrelation structure of an empirical sample such as traffic measurements. Furthermore, the empirical marginal (histogram) and leading autocorrelations are captured simultaneously. Practical TES modeling is computationally intensive and is effectively carried out with software support. A computerized modeling environment, called TEStool, is briefly reviewed. TEStool supports a heuristic search approach for fitting a TES model to empirical time series. Finally, we exemplify our approach by two examples of TES video source models, constructed from empirical codec bitrate measurements: one at the frame level and the other at the group-of-block level. The examples demonstrate the efficacy of the TES modeling methodology and the TEStool modeling environment.