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There are a number of situations in which several signals are simultaneously recorded in complex systems, which exhibit long-term power-law cross-correlations. This paper presents two-dimensional multifractal cross-correlation analysis based on the partition function (2D-MFXPF), two-dimensional multifractal cross-correlation analysis based on the detrended fluctuation analysis (2D-MFXDFA) and two-dimensional multifractal cross-correlation analysis based on the detrended moving average analysis (2D-MFXDMA). We apply these methods to pairs of two-dimensional multiplicative cascades (2D-MC) to do a comparative study. Then, we apply the two-dimensional multifractal cross-correlation analysis based on the detrended fluctuation analysis (2D-MFXDFA) to real images and unveil intriguing multifractality in the cross correlations of the material structures. At last, we give the main conclusions and provide a valuable reference on how to choose the multifractal algorithms in the potential applications in the field of SAR image classification and detection. [ABSTRACT FROM AUTHOR]

This study explored a novel method based on eigenvalue decomposition (EVD) and independent component analysis (ICA) to separate the multi-component radar signal in the single channel. By exploiting the generalized periodicity of the radar signal, the proposed method structures the multi-dimensional matrix from the observed signal in single-channel through EVD, then applies ICA to the matrix to determine the basic waveform of each component, and finally reconstructs the component signals. Simulation results confirmed the effectiveness of the proposed method and compared it with other methods, although the performance of proposed approach is a bit worse than some other method when processing radar signals, the most outstanding advantage of the proposed approach is that it does not require any other known conditions, and it can recover the component signals with a satisfactory level, so it can yet be regarded as an effective method. [ABSTRACT FROM AUTHOR]

This paper proposes an approach of single channel source separation and parameter estimation of multi-component PRBCPM-SFM (pseudo-random binary code phase modulated sinusoidal frequency modulation) signal. By transforming all components to SFM signals through square calculation, we may then apply singular value decomposition to determine the generalized period and the modulation frequency of the SFM signal. The modulation index and carrier frequency are determined by searching for discrete points and optimizing calculations. The initial phase can be determined by calculating the inner product. Finally, given that the pseudo-random binary code is a real signal, the PN (Pseudo-noise) sequence and the amplitude can be estimated. Our proposed method can estimate the SNR by using the method of subspace-based decomposition, and the estimated SNR can be used to adaptively stop separation. Experimental results demonstrate the algorithm's performance. [ABSTRACT FROM AUTHOR]

Abstract: The time-singularity multifractal spectrum distribution (MFSD) has been proposed recently as a generalized singularity spectrum in a time varying framework. In this paper, we aim at putting forward a new algorithm i.e. MFSD based on detrending moving average (DMA-MFSD) to determine MFSD, which is also a generalization of multifractal detrending moving average (MF-DMA) method. We relate DMA-MFSD method to the MFSD based on the standard partition function, and prove that both approaches are equivalent for fractal time series with compact support. The performance of the DMA-MFSD methods with different moving windows is studied using synthetic fractional Gaussian noise (fGn), binomial multiplicative cascades (BMC) with analytical solutions and real sea clutter data. We find that the estimated DMA-MFSD is in good accordance with the detrended fluctuation analysis based multifractal spectrum distribution (DFA-MFSD) and the theoretical analysis. Overall, the backward DMA-MFSD method has the best performance, which provides the most accurate estimates of the time-singularity MFSD, while the centered DMA-MFSD method performs worse. In addition we find that the backward DMA-MFSD algorithm even outperforms the DFA-MFSD method in the computational complexity and precision. [Copyright &y& Elsevier]

Signal recognition technology is a currently active area in both civilian and military applications. Recently, deep learning has aroused extensive attempts in radar signal recognition due to its remarkable capability of automatic feature extraction. However, existing radar signal recognition networks overly depend on the probability-based decision model, resulting in poor robustness. This paper develops a novel deep metric learning frame to enhance the robustness of the recognition system. First, a multiscale atrous pyramid network (MAPNet) is proposed to efficiently learn high-resolution and distinct feature representation. Second, a variance loss is designed to constrain the intra-class feature distribution in metric space. Third, according to the distribution of training signals in metric space, recognition results are recalibrated to provide explicit rejection probabilities for unknowns. Extensive experiments and evaluations demonstrate that the proposed model can accurately classify known signals while robustly identifying unknown signals. The signal database and model can be freely accessed at https://github.com/bryantky/MAPNet. [ABSTRACT FROM AUTHOR]

Fractal reconstruction (FR) and multifractal reconstruction (MFR) can be considered as the inverse problem of singularity spectrum analysis, and it is challenging to reconstruct fractal signal in accord with multifractal spectrum (MFS). Due to the multiple solutions of fractal reconstruction, the traditional methods of FR/MFR, such as FBM based method, wavelet based method, random wavelet series, fail to reconstruct fractal signal deterministically, and besides, those methods neglect the power spectral distribution in the singular domain. In this paper, we propose a novel MFR method based singularity power spectrum (SPS). Supposing the consistent uniform covering of multifractal measurement, we control the traditional power law of each scale of wavelet coefficients based on the instantaneous singularity exponents (ISE) or MFS, simultaneously control the singularity power law based on the SPS, and deduce the principle and algorithm of MFR based on SPS. Reconstruction simulation and error analysis of estimated ISE, MFS and SPS show the effectiveness and the improvement of the proposed methods compared to those obtained by the Fraclab package. [ABSTRACT FROM AUTHOR]

The interference environment faced by Ultra-wideband (UWB) cognitive radar has the characteristics of wide bandwidth and extensive dynamic range. For that, a higher sampling rate is required for spectrum sensing. The current coprime sampling scheme can significantly reduce the sampling rate and show a high degree of freedom. However, the virtual co-array generated by coprime sampling has certain missing elements, leading to errors and the lack of spectral estimation information. This paper proposes a delayed coprime sampling scheme to supplement missing elements in virtual co-arrays to increase degrees of freedom. The regularity of the holes and the selection of suitable delay factors are also presented. The simulation results show that the proposed method can further improve the degree of freedom and theoretically achieve the maximum degree of freedom of a fixed sample. The precision of the spectrum estimation is also improved since the data generated by the proposed method can be used to estimate the existing elements in the virtual co-array. [ABSTRACT FROM AUTHOR]