## 1 Introduction  
An active acoustic decoy which can simulate a target echo provides very important countermeasures to active acoustic torpedoes and active sonar. Basically, the active acoustic decoy comprises several monostatic hydrophones, and once the hydrophones receive the incident sonar pulse, the monostatic hydrophones transmit an acoustic wave with a certain phase, magnitude, Doppler frequency shift, time delay, and signal broadening that characterize the target echo [1; 2; 3; 4]. This kind of active acoustic decoy can simulate a series of an echo's characteristic parameters, such as the relative positions of the main echo highlights, relative magnitude of echo highlights, and scale features of the target, and it is a great challenge for active sonar target classification. Many algorithms have been developed for underwater acoustic target tracking [5; 6; 7; 8], but discriminating the real underwater target echo from the synthetic echo is still a key challenge to identifying an underwater target. The echo of an underwater target is the incident signal modulated by material, structure, and shape parameters, so the echo envelope structure is the characterization of the target's geometric scattering and elastic scattering in a time domain [9; 10; 11; 12]. Therefore, the envelope structure of an underwater echo contains the information which closely relates to the physical parameters of the target. In a high-frequency acoustic scattering wave, the echo's energy is dominated by a geometrical scattering wave, the geometrical scattering highlights are always present in the high-amplitude fluctuation of an echo envelope, while the elastic scattering highlights are present in the fast and weak fluctuation of the envelope [13]. For the high-amplitude fluctuation of an echo envelope, the envelope's structural features can be characterized by the number of echo highlights, relative magnitude, and relative spacing [14; 15; 16; 17; 18]. A statistical quantitative model of echo highlights has been established for a complex target, which quantitatively characterizes the echo highlights [19]. For the weak fluctuation of the echo envelope, which contains the elastic scattering, for an actual echo signal, the features of weak fluctuation echo envelope are hard to extract and use [13]. In previous work, echo envelope fluctuation features were studied in a frequency domain, and the envelope modulation rate of underwater target's scattering signal is characterized. Theoretical and experimental research has indicated that the maximum envelope modulation frequency of a complex target increases when the incident frequency increases [20]. Based on the maximum envelope modulation frequency, a method for discriminating the real target from the synthetic target was proposed and tested [21]. The maximum envelope modulation frequency was obtained by using a threshold for the strong influence of low-frequency envelope modulation. The extraction of maximum frequency is always affected by the threshold, and the correct choice of the threshold is often not easy for actual sea data. Consequently, in order to deeply understand the mechanism of echo envelope modulation and to properly describe the echo envelope fluctuation, the authors studied the features of echo envelope fluctuation in a time domain, and they proposed a novel method for the discrimination of a real underwater target echo from a synthetic echo. Compared with previous work, the strong influence of a low-frequency echo envelope fluctuation was reduced, the fine structure of a high fluctuation envelope was enhanced, and the processing of the features extracted from a high-frequency modulation was straightforward. The major contributions of this paper are as follows:  
* This paper focuses on the characterization and extraction of echo fluctuation features from an underwater complex target. Based on practical engineering applications, it presents a method for discrimination of a real echo from a synthetic echo underwater.