Specific emitter identification (SEI) techniques are often used in civilian and military spectrum-management operations, and they are also applied to support the security and authentication of wireless communication. In this letter, a new SEI method based on the natural measure of the one-dimensional component of the chaotic system is proposed. We find that the natural measures of the one-dimensional components of higher dimensional systems exist and that they are quite diverse for different systems. Based on this principle, the natural measure is used as an RF fingerprint in this letter. The natural measure can solve the problems caused by a small amount of data and a low sample rate. The Kullback-Leibler divergence is used to quantify the difference between the natural measures obtained from diverse emitters and classify them. The data obtained from real application are exploited to test the validity of the proposed method. Experimental results show that the proposed method is not only easy to operate, but also quite effective, even though the amount of data is small and the sample rate is low.
A computationally quick and conceptually simple method to recover time delay of the chaotic system from scalar time series is developed in this paper. We show that the orbits in the incomplete two-dimensional reconstructed phase-space will show local clustering phenomenon after the component reordering procedure proposed in this work. We find that information captured by the incomplete two-dimensional reconstructed phase-space is related to the time delay τ_{0} present in the system, and will be transferred to the reordered component by the procedure of component reordering. We then propose the segmented mean variance (SMV) from the reordered component to identify the time delay τ_{0} of the system. The proposed SMV shows clear maximum when the embedding delay τ of the incomplete reconstruction matches the time delay τ_{0} of the chaotic system. Numerical data generated by a time-delay system based on the Mackey-Glass equation operating in the chaotic regime are used to illustrate the effectiveness of the proposed SMV. Experimental results show that the proposed SMV is robust to additive observational noise and is able to recover the time delay of the chaotic system even though the amount of data is relatively small and the feedback strength is weak. Moreover, the time complexity of the proposed method is quite low.
The specific emitter identification (SEI) technique determines the unique emitter of a given signal by using some external feature measurements of the signal. It has recently attracted a great deal of attention because many applications can benefit from it. This work addresses the SEI problem using two methods, namely, the normalized visibility graph entropy (NVGE) and the normalized horizontal visibility graph entropy (NHVGE) based on treating emitters as nonlinear dynamical systems. Firstly, the visibility graph (VG) and the horizontal visibility graph (HVG) are used to convert the instantaneous amplitude, phase and frequency of received signals into graphs. Then, based on the information captured by the VG and the HVG, the normalized Shannon entropy (NSE) calculated from the corresponding degree distributions are utilized as the rf fingerprint. Finally, four emitters from the same manufacturer are utilized to evaluate the performance of the two methods. Experimental results demonstrate that both the NHVGE-based method and NVGE-based method are quite effective and they perform much better than the method based on the normalized permutation entropy (NPE) in the case of a small amount of data. The NVGE-based method performs better than the NHVGE-based method since the VG can extract more information than the HVG does. Moreover, our methods do not distinguish between the transient signal and the steady-state signal, making it practical.
Detection and identification of chaotic signal is very important in the chaotic time series analysis. It is not easy to distinguish chaotic time series from stochastic processes since they share some similar natures. The detection methods to capture and utilize the structure of state-space dynamics can be very effective. In practice, it is very hard to obtain full information about the structure, and accurate phase-space reconstruction from scalar time series data is also a real challenge. However, the chaotic signals also show fundamental dynamical structure in the incomplete two-dimensional phase-space for the reason that they are generated by the deterministic chaotic systems or maps. Based on the fact that the distribution of chaotic signals is quite different from that of the noise signals in the incomplete two-dimensional phase-space, a novel detection method, which depends on the component permutation of the incomplete two-dimensional phase-space, is proposed. The incomplete two-dimensional phase-space is first obtained through the time series. Then, the first component is sorted in the ascending order, and the second component is permutated accordingly. The permutated component shows more structure characteristics for chaotic signals because of the relation between these two components. But this phenomenon does not appear in the noise because these components are independent of each other. And then, the permutated component is segmented into several groups properly. Finally, the sample mean and sample variance of different groups are calculated to obtain the sequence of sample mean (SSM) and the sequence of sample variance (SSV). Meanwhile, by calculating the variance of the SSM and the mean of the SSV, the test statistic is obtained. Furthermore, it is proved that this test statistic follows the F distribution under the null hypothesis of Gaussian noise. The proposed method is first adopted for detecting the several chaotic signals under different data lengths in Gaussian noise conditions. The simulation results show that the proposed method can detect chaotic signals effectively under low signal-to-noise ratio and it also has a good robustness against noise compared with the permutation entropy test. The time consumptions of the proposed method under different data lengths are evaluated and also compared with the results of permutation entropy test, showing that the proposed method can detect chaotic signals quickly, and the time complexity is much lower than that of the permutation entropy test. The theoretical analysis and simulation results demonstrate that the proposed method not only outperforms the permutation entropy test with lower complexity, but also has a better robustness against noise.
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