Good Autocorrelation Research Articles

The 4-adic complexity of new quaternary sequences with good autocorrelation

The 4-adic complexity of new quaternary sequences with good autocorrelation

Genetic Approach to Improve Cryptographic Properties of Balanced Boolean Functions Using Bent Functions

Recently, balanced Boolean functions with an even number n of variables achieving very good autocorrelation properties have been obtained for 12≤n≤26. These functions attain the maximum absolute value in the autocorrelation spectra (without considering the zero point) less than 2n2 and are found by using a heuristic search algorithm that is based on the design method of an infinite class of such functions for a higher number of variables. Here, we consider balanced Boolean functions that are closest to the bent functions in terms of the Hamming distance and perform a genetic algorithm efficiently aiming to optimize their cryptographic properties, which provides better absolute indicator values for all of those values of n for the first time. We also observe that among our results, the functions for 16≤n≤26 have nonlinearity greater than 2n−1−2n2. In the process, our search strategy produces balanced Boolean functions with the best-known nonlinearity for 8≤n≤16.

Chaotic logistic map sequences with good auto-correlation properties

In this work, chaotic sequences with good auto-correlation properties are presented. The studied sequences are synthesized by means of the logistic map function and, been chaotic but fully deterministic, become a good alternative for well-known sequences, for example the Zadoff-Chu sequences, especially for small size sequences commonly used for frame synchronization purposes in digital communications systems. A new auto-correlation goodness metric is proposed, and it is employed as objective function in order to maximize the correlation goodness for short synchronization sequences synthesized by means the logistic map function.

OPTIMAL SIGNAL-CODE CONSTRUCTIONS FOR INCREASE EFFICIENCY OF 5G AND 6G MOBILE INFOCOMMUNICATION RADIO SYSTEMS

The article discusses methods of increasing the efficiency of information communication radio systems of mobile communication, which includes increasing spectral efficiency and energy efficiency when used for telecommunication radio equipment. A comparison of block error coefficient values for f-OFDM, W-OFDM and OFDM methods with mixed numerology of uplink and downlink subscriber channels of access to information resources of the telecommunications network was made. As a result of the study of compression methods using several carriers, the dominant compression method for mobile communication systems, in particular, the CP-OFDM method due to its high efficiency of spectrum use, scalability and flexibility due to the introduction of a cyclic prefix, has been determined. It is proved that the CP-OFDM compression method is free from the Doppler range shift problem, thus the range and Doppler shift estimations can be considered as independent tasks in CP-OFDM. In addition, CP-OFDM parameters such as carrier distance, guard interval size, frame length, and pilot shape can be tailored to optimize the performance and robustness of detection and data transmission. However, such advantages are based on perfect synchronization (time and frequency) between the transmitter and receiver – although perfect synchronization may not be possible, especially for bistatic scanning, where the transmitter and receiver of the scan signal are not adjacent. In this case, the cyclic prefix may not provide any advantage for quality scanning, and multiple unprefixed waveforms may be considered. The main disadvantage of rejecting the prefix is the difficulty of data detection (due to intersymbol interference), which must be eliminated. Another important challenge for scanning, where energy efficiency is extremely important, is the large PAPR of multi-carrier (prefixed or unprefixed) signals. Single-carrier compression methods, which are based on the expansion of the code area of common radar signals and communication, in which the radar characteristics are affected by sequence autocorrelation, have been studied. However, the long spreading code, which leads to good autocorrelation, reduces the spectrum utilization efficiency for communication systems. In this case, the estimation of the Doppler effect is not trivial and requires more complex algorithms. The justification of the choice of the signal modulation scheme in 5/6G radio systems has been made.

5G PRS-Based Sensing: A Sensing Reference Signal Approach for Joint Sensing and Communication System

The emerging joint sensing and communication (JSC) technology is expected to support new applications and services, such as autonomous driving and extended reality (XR), in the future wireless communication systems. Pilot (or reference) signals in wireless communications usually have good passive detection performance, strong anti-noise capability and good auto-correlation characteristics, hence they bear the potential for applying in radar sensing. In this paper, we investigate how to apply the positioning reference signal (PRS) of the 5th generation (5 G) mobile communications in radar sensing. This approach has the unique benefit of compatibility with the most advanced mobile communication system available so far. Thus, the PRS can be regarded as a sensing reference signal to simultaneously realize the functions of radar sensing, communication and positioning in a convenient manner. Firstly, we propose a PRS based radar sensing scheme and analyze its range and velocity estimation performance, based on which we propose a method that improves the accuracy of velocity estimation by using multiple frames. Furthermore, the Crámer-Rao lower bound (CRLB) of the range and velocity estimation for PRS based radar sensing and the CRLB of the range estimation for PRS based positioning are derived. Our analysis and simulation results demonstrate the feasibility and superiority of PRS over other pilot signals in radar sensing. Finally, some suggestions for the future 5G-Advanced and 6th generation (6 G) frame structure design containing the sensing reference signal are derived based on our study.

Effective and efficient gradient based methods for low-bit discrete-phase sequence designs

We devise effective and efficient gradient based methods to design low-bit, including binary (one-bit per sample, or 1b) and quaternary (two-bit per sample, or 2b), discrete-phase sequences without or with low correlation zone (LCZ) requirements. We determine proper step sizes needed by the gradient based algorithms to monotonically decrease the optimization metric via efficient line search techniques for aperiodic and periodic low-bit discrete-phase sequence designs. Moreover, we introduce approximate gradient based approaches to reduce the autocorrelation sidelobes when the desired LCZ is relatively large. Numerical examples are provided to show that the proposed gradient based algorithms can outperform the state-of-the-art algorithms for designing 1b and 2b sequences with good autocorrelation properties.

Computational Search of Long Skew-symmetric Binary Sequences with High Merit Factors

In this paper, we present a computational search for best-known merit factors of longer binary sequences with an odd length. Finding low autocorrelation binary sequences with optimal or suboptimal merit factors is a very difficult optimization problem. An improved version of the heuristic algorithm is presented and tackled to search for aperiodic binary sequences with good autocorrelation properties. High-performance computations with the execution of our stochastic algorithmto search skew-symmetric binary sequences with high merit factors. After experimental work, as results, we present new binary sequences with odd lengths between 201 and 303 that are skew-symmetric and have the merit factor F greater than 8.5. Moreover, an example of a binary sequence having F > 8 has been found for all odd lengths between 201 and 303. The longest binary sequence with F > 9 found to date is of length 255.

Non-Binary PRN-Chirp Modulation: A GNSS Fast Acquisition Signal Waveform

In this letter, we propose a new non-binary modulation which allows both Global Navigation Satellite Systems (GNSS) synchronization and the demodulation of non-binary symbols, without the need of a pilot signal, with the aim to provide a fast first position, velocity and time fix. The waveform is constructed as the product of i) a pseudo-random noise sequence with good auto-correlation and cross-correlation properties, and ii) a chirp spread spectrum family, which allows to demodulate non-binary symbols even if the signal phase is unknown. In order to demodulate the data, a bank of non-coherent matched filters is proposed. Because of the particular modulation structure, the receiver is capable to demodulate the navigation message faster while allowing the basic GNSS signal processing functionalities. Illustrative results are provided to support the discussion.

Distributed Acoustic Sensing System Based on Inserting-Zero Golay Coding With Ultra-Weak Fiber Bragg Gratings

A distributed acoustic sensing (DAS) system based on ultra-weak fiber Bragg grating (UWFBG) array is proposed and experimentally demonstrated by Inserting-Zero (IZ) Golay coding. The system uses 1.5 km UWFBG as the sensing fiber, and extracts phase information through heterodyne detection and IQ demodulation. The Golay coding pulse sequence are used as the modulation signal to improve the system signal-to-noise ratio (SNR), which is benefited from the good autocorrelation characteristics of Golay code. The experimental results display that the DAS system based on Golay coding can effectively reduce the noise level, and the SNR of the system increases by 4.6 dB compared with the individual pulse system. Every bit of Golay coding sequence is inserting one bit “0” can decrease the inter-symbol crosstalk (ISC), and the SNR is further improved by 2.7 dB, and reaches 62.2 dB at 100 Hz. The proposed system has a good response ability of distributed sensing and a good linear characteristic with the coefficient of 0.9966.

Linear complexity over $${\mathbb {F}_{{q}}}$$ and 2-adic complexity of a class of binary generalized cyclotomic sequences with good autocorrelation

Linear complexity over $${\mathbb {F}_{{q}}}$$ and 2-adic complexity of a class of binary generalized cyclotomic sequences with good autocorrelation

Index Modulation With Circularly-Shifted Chirps for Dual-Function Radar and Communications

In this study, we propose index modulation (IM) with circularly-shifted chirps (CSCs) (CSC-IM) for dual-function radar and communication (DFRC) systems. The proposed scheme encodes the information bits with the CSC indices and the phase-shift keying (PSK) symbols. It allows the receiver to exploit the frequency selectivity naturally in fading channels by combining IM and wideband CSCs. It also leverages the fact that a CSC is a constant-envelope signal to achieve a controllable peak-to-mean envelope power ratio (PMEPR). For radar functionality, CSC-IM maintains the good autocorrelation (AC) properties of a chirp by ensuring that the transmitted CSCs are separated apart sufficiently in the time domain through index separation (IS). We investigate the impact of IS on spectral efficiency (SE) and obtain the corresponding mapping functions. For theoretical results, we derive the union bound (UB) of the block error rate (BLER) for arbitrary chirps and the Cramer-Rao lower bounds (CRLBs) for the range and reflection coefficients for the matched filter (MF)- based estimation. We also prove that complementary sequences (CSs) can be constructed through CSCs by linearly combining the Fourier series of CSCs. Finally, through comprehensive comparisons, we demonstrate the efficacy of the proposed scheme for DFRC scenarios.

Cognitive waveform design with desired spectrum-autocorrelation properties

This paper proposes a novel cognitive waveform design methodology aimed at shaping a specified spectrum and achieving good autocorrelation properties in terms of the spectrum band notch and local autocorrelation peak sidelobe level (A-PSL). To this end, the Pareto optimization framework is introduced that minimizes the lp-norm of multi-objective functions both encompassing the stopband energy and local A-PSL. In addition, along with energy and peak-to-average power ratio constraints to ensure hardware compatibility, the out-of-band (OOB) spectrum energy and the rest autocorrelation sidelobe level are restricted to resist the OOB strong interference (also prevent spectrum leakage) and enhance multiple target detectability, respectively. To tackle the resultant nonconvex nonsmooth (in general NP-hard) design problem, an iterative majorization minimization proximal method of multipliers (MM-PMM) algorithm is developed along with each iteration involving multiple subproblems which are solved through a majorization method or closed-form solutions. In particular, resorting to Wiener-Khintchine theorem, the developed algorithm is efficiently implemented via the fast fourier transform and element-wise arithmetic. Extensive numerical examples highlight that the synthesized waveform shares the desired spectrum-autocorrelation properties and is capable of enhancing the weak target detection and anti-jamming performance in comparison with some counterparts.

Autoregressive Modeling and Prediction of the Activity of Antihypertensive Peptides.

Naturally derived bioactive peptides with antihypertensive activities serve as promising alternatives to pharmaceutical drugs. There are few relevant reports on the mapping relationship between the EC50 value of antihypertensive peptide activity (AHTPA-EC50) and its corresponding amino acid sequence (AAS) at present. In this paper, we have constructed two group series based on sorting natural logarithm of AHTPA-EC50 or sorting its corresponding AAS encoding number. One group possesses two series, and we find that there must be a random number series in any group series. The random number series manifests fractal characteristics, and the constructed series of sorting natural logarithm of AHTPA-EC50 shows good autocorrelation characteristics. Therefore, two non-linear autoregressive models with exogenous input (NARXs) were established to describe the two series. A prediction method is further designed for AHTPA-EC50 prediction based on the proposed model. Two dynamic neural networks for NARXs (NARXNNs) are designed to verify the two series characteristics. Dipeptides and tripeptides are used to verify the proposed prediction method. The results show that the mean square error (MSE) of prediction is about 0.5589 for AHTPA-EC50 prediction when the classification of AAS is correct. The proposed method provides a solution for AHTPA-EC50 prediction.

A high frequency endoscopic ultrasound imaging method combining chirp coded excitation and compressed sensing

Insufficient imaging penetration and large data acquisition are two of the major challenges of high-frequency ultrasound imaging. Based on the good autocorrelation properties of chirp signal and the feasibility of using compressed sensing theory to reconstruct high-quality ultrasound images with low sampling requirements, this paper proposed a chirp coded excitation combined with compressed sensing (CCE-CS) technique for high-frequency endoscopic ultrasound (HFEUS) imaging. The feasibility of the method was verified by a brief theoretical analysis, and the relevant parameters were selected and analyzed according to the actual engineering situation. Simulated phantoms and in-vitro tissue experiments were used to evaluate the performance of the CCE-CS. Simulation results demonstrate that CCE-CS is capable of reducing the impact of reconstruction errors and improving imaging quality through comparison with conventional methods. The reduction of reconstruction data had less impact on penetration depth, resolution and general contrast general contrast-to-noise ratio (gCNR), and the reconstructed image was closer to the original image with a maximum improvement of 37% in peak signal-to-noise ratio (PSNR). Moreover, comparisons were conducted on the digestive tract of swine, and the results show that CCE-CS is also feasible in the in-vitro environment. These results demonstrated that CCE-CS method has good potential for application to improve the imaging quality of HFEUS while reducing the sampling rate.

Ternary perfect sequences with three-valued cross-correlation

<p style='text-indent:20px;'>The calculation of the cross-correlation between a sequence with good autocorrelation and its decimated sequence has been a longstanding research problem in the field of sequence design. The objective of this paper is to determine the cross-correlation between a class of well-known ternary sequences with perfect autocorrelation and its <inline-formula><tex-math id="M1">\begin{document}$ 2 $\end{document}</tex-math></inline-formula>-decimation. Based on the theory of quadratic forms and exponential sums over finite fields, it is shown that the cross-correlation function takes on three low values.</p>

On Properties of Periodic Binary Sequences in the Presence of System Non-Linearities

Phase-modulated continuous-wave (PMCW) radar systems possess inherent interference mitigation capabilities and can be useful for many civilian applications including autonomous driving. For PMCW radar systems, binary sequences with good autocorrelation properties are used as probing sequences due to their low cost to generate in practical hardware systems. However, the non-linearity (NL) suffered by practical PMCW radar systems can produce undesirable cross-products and distort the receiver matched filter outputs. The purpose of this paper is to investigate the properties of the well-known periodic binary almost perfect autocorrelation sequences (APAS) under NL conditions, including even-order and odd-order NL conditions. We also consider designing long binary periodic sequences with low autocorrelation sidelobes within a low correlation zone (LCZ) using a computational algorithm. The computationally optimized sequences (COS) do not suffer from sequence length restrictions and offer much higher diversity than their APAS counterparts. We compare COS with APAS under NL conditions. We show that both types of sequences can be used to avoid ghost peaks in the range profiles under NL conditions.

Estimate of 4-adic complexity of unified quaternary sequences of length $ 2p $

<p style='text-indent:20px;'>We derive the 4-adic complexity of unified quaternary sequences with period <inline-formula><tex-math id="M2">\begin{document}$ 2p $\end{document}</tex-math></inline-formula>. These sequences with good autocorrelation properties are proposed by Ke et al. in 2020. We estimate the 4-adic complexity of aforementioned sequences and show that any of them has high 4-adic complexity, which is good enough to resist the attack of the rational approximation algorithm.</p>

On the search for short chaotic logistic map sequences with good auto-correlation properties

This work presents short chaotic sequences with good auto correlation properties. The studied sequences are synthesized by means of the logistic map function, and being chaotic but fully deterministic, become a good alternative to well-known

UNIPOL: Unimodular sequence design via a separable iterative quartic polynomial optimization for active sensing systems

Sequences having better autocorrelation properties play a crucial role in enhancing the performance of active sensing systems. Hence, sequences with good autocorrelation properties are very much in demand. In this paper, we addressed the problem of designing a unimodular sequence having better side-lobe levels. We formulated it as a constrained optimization problem comprising the Integrated Side-lobe Level (ISL) metric and then proposed an effective algorithm (named UNIPOL - UNImodular sequence design via a separable iterative quartic POLynomial optimization) where we perform the polynomial optimization at every iteration. The novelty of the paper comes from deriving a quartic majorization function that is separable in the sequence variables and that can be minimized parallelly. To evaluate the performance of our proposed algorithm we perform the numerical experiments for different sequence lengths and confirm that our proposed algorithm is one of the fastest algorithms to attain an actual optimum minimizer of the ISL metric.

SLOPE: A monotonic algorithm to design sequences with good autocorrelation properties by minimizing the peak sidelobe level

Sequences with low autocorrelation sidelobes has applications in various fields like wireless communications, radar, sonar, cryptography to name a few. In this paper, we propose an approach to construct sequences, in particular unimodular sequences, by directly minimizing the peak sidelobe level (PSL) metric. The underlying optimization problem involved is a minimax problem which is in general difficult to tract. We address this issue and propose an iterative algorithm named Sequence with LOw Peak sidelobE level (SLOPE) based on the technique of Majorization Minimization, which can be implemented efficiently using the Fast Fourier Transform tool. Further, we also discuss the extension of SLOPE to incorporate energy, peak-to-average-power ratio (PAPR) and spectral constraints on the sequence. We show through numerical simulations that the proposed algorithm can generate sequences of considerably longer lengths with lower peak sidelobe level when compared to the state-of-the-art algorithms and in the end we also evaluate the performance of the sequences designed via SLOPE in the context of channel estimation application.