Frame synchronization detection before data transmission is an important module which directly affects the lifetime and coexistence of underwater acoustic communication (UAC) networks, where linear frequency modulation (LFM) is a frame preamble signal commonly used for synchronization. Unlike terrestrial wireless communications, strong bursty noise frequently appears in UAC. Due to the long transmission distance and the low signal-to-noise ratio, strong short-distance bursty noise will greatly reduce the accuracy of conventional fractional fourier transform (FrFT) detection. We propose a multi-segment verification fractional fourier transform (MFrFT) preamble detection algorithm to address this challenge. In the proposed algorithm, 4 times of adjacent FrFT operations are carried out. And the LFM signal identifies by observing the linear correlation between two lines connected in pair among three adjacent peak points, called ‘dual-line-correlation mechanism’. The accurate starting time of the LFM signal can be found according to the peak frequency of the adjacent FrFT. More importantly, MFrFT do not result in an increase in computational complexity. Compared with the conventional FrFT detection method, experimental results show that the proposed algorithm can effectively distinguish between signal starting points and bursty noise with much lower error detection rate, which in turn minimizes the cost of retransmission.

In this study, a blind carrier frequency offset (CFO) estimation method is proposed using the time-frequency symmetry of the transmitted signals of a weighted Fourier transform (WFrFT) communication system. Blind CFO estimation is achieved by focusing on the property that results in matching the signal waveforms before and after the Fourier transform when the WFrFT parameter is set to a certain value. Numerical simulations confirm that the proposed method is more resistant to Rayleigh fading than the conventional estimation methods.

Parameter estimation theorems for LFM signals have been developed due to the advantages of fractional Fourier transform (FrFT). The traditional estimation methods in the fractional Fourier domain (FrFD) are almost based on two-dimensional search which have the contradiction between estimation performance and complexity. In order to solve this problem, we introduce the orthogonal matching pursuit (OMP) into the FrFD, propose a modified optimization method to estimate initial frequency and final frequency of fractional bandlimited LFM signals. In this algorithm, the differentiation fractional spectrum which is used to form observation matrix in OMP is derived from the spectrum analytical formulations of the LFM signal, and then, based on that the LFM signal has approximate rectangular spectrum in the FrFD and the correlation between the LFM signal and observation matrix yields a maximal value at the edge of the spectrum (see Sect.3.3 for details), the edge spectrum information can be extracted by OMP. Finally, the estimations of initial frequency and final frequency are obtained through multiplying the edge information by the sampling frequency resolution. The proposed method avoids reconstruction and the traditional peak-searching procedure, and the iterations are needed only twice. Thus, the computational complexity is much lower than that of the existing methods. Meanwhile, Since the vectors at the initial frequency and final frequency points both have larger modulus, so that the estimations are closer to the actual values, better normalized root mean squared error (NRMSE) performance can be achieved. Both theoretical analysis and simulation results demonstrate that the proposed algorithm bears a relatively low complexity and its estimation precision is higher than search-based and reconstruction-based algorithms.

In this paper, a scramble phase assisting weighted-type fractional Fourier transform (SPA-WFRFT) based system is proposed to guarantee the communication's security. The original transmitting signal is divided into two parts. The first part is modulated by WFRFT and subsequently makes up the constellation beguiling. The other part is used to generate the scramble phase and also to assist in the encryption of the WFRFT modulated signal dynamically. The novel constellation optimal model is built and solved through the genetic algorithm (GA) for the constellation beguiling. And the double pseudo scheme is implemented for the scramble phase generation. Theoretical analyses show that excellent security performances and high spectral efficiency can be attained. Final simulations are carried out to evaluate the performances of the SPA-WFRFT based system, and demonstrate that the proposed system can effectively degrade the unauthorized receivers' bit error rate (BER) performance while maintaining its own communication quality.

We propose a novel bit error rate (BER) analysis model of weighted-type fractional Fourier transform (WFRFT)-based systems with WFRFT order offset Δα. By using the traditional BPSK BER analysis method, we deduce the equivalent signal noise ratio (SNR), model the interference in the channel as a Gaussian noise with non-zero mean, and provide a theoretical BER expression of the proposed system. Simulation results show that its theoretical BER performance well matches the empirical performance, which demonstrates that the theoretical BER analysis proposed in this paper is reliable.

This letter investigates the circularity of fractional Fourier transform (FRFT) coefficients containing noise only, and proves that all coefficients coming from white Gaussian noise are circular via the discrete FRFT. In order to use the spectrum kurtosis (SK) as a Gaussian test to check if linear frequency modulation (LFM) signals are present in a set of FRFT points, the effect of the noncircularity of Gaussian variables upon the SK of FRFT coefficients is studied. The SK of the α th-order FRFT coefficients for LFM signals embedded in a white Gaussian noise is also derived in this letter. Finally the signal detection algorithm based on FRFT and SK is proposed. The effectiveness and robustness of this algorithm are evaluated via simulations under lower SNR and weaker components.

This letter describe target classification from the synthesized active sonar returns from targets. A fractional Fourier transform is applied to the sonar returns to extract shape variation in the fractional Fourier domain depending on the highlight points and aspects of the target. With the proposed features, four different targets are classified using two neural network classifiers.

This letter deals with angular position classification using the synthesized active sonar returns from targets. For the synthesis of active sonar returns, we synthesized active sonar returns based on ray tracing algorithm for 3D highlight models. Then, a fractional Fourier transform (FrFT) was applied to the sonar returns to extract the angular position information depending on the target aspect by utilizing separation capability of the time-delayed combination of linear frequency modulated (LFM) signals in the FrFT domain. With the FrFT-based features, three different target angular positions were classified using neural networks.

Combining the strong anti-interference advantages of OFDM technology and the time-frequency analysis features of fractional Fourier transform (FFT), we apply OFDM as the coding modulation technology for digital watermarking. Based on the Arnold scrambling and OFDM coding, an innovative DFRFT digital watermarking algorithm is proposed. First, the watermark information is subjected to the Arnold scrambling encryption and OFDM coding transform. Then it is embedded into the FFT domain amplitude. The three parameters of scrambling iterations number, t, FFT order, p, and the watermark information embedded position, L, are used as keys, so that the algorithm has high safety. A simulation shows that the algorithm is highly robust against noise, filtering, compression, and other general attacks. The algorithm not only has strong security, but also makes a good balance between invisibility and robustness. But the possibility of using OFDM technique in robust image watermarking has drawn a very little attention.

The separation time-overlapping ultrasound signals is necessary to obtain accurate estimate of transit time and material properties. In this letter, a method to determine the optimal transform order of fractional Fourier transform (FRFT) for decomposition of overlapping ultrasonic signals is proposed. The optimal transform order is obtained by minimizing the mean square error (MSE) between the output and the reference signal. Furthermore, windowing in FRFT domain is discussed. Numerical simulation results show the performances of the proposed method in separating signals overlapping in time.

In this paper, Integration of Fractional Gaussian Window transform (IFRGWT) is proposed for the parameter estimation of linear FM (LFM) signal; the proposal is based on the integration of the Fractional Fourier transform modified by Gaussian Window. The peak values can be detected by adjusting the standard deviation of Gaussian function and locating the optimal rotated angles. And also the parameters of the signal can be estimated well. As an application, detection and parameter estimation of multiple LFM signals are investigated in low signal-to-noise ratios (SNRs). The analytic results and simulations clearly demonstrate that the method is effective.