Research On Methodology Of Weak Signal Detection Based On Duffing Oscillator

Weak signal detection has been widely used in numerous fields such as communication, radar and sonar. With the increasing needs of weak signal detection, it has been a research hot spot. In order to detect the underlying signals in high levels of noise rapidly and accurately, scholars explore and develop the new theory and methods of weak signal detection. There are some limitations of the traditional time domain signal detecting methods, so it is very difficult to make the signal to noise ratio(SNR) threshold further lower. Recent advances in nonlinear theory provide a novel viewpoint to recognize problem, analyze problem and resolve problem. In particular, specific chaotic system is sensitive to weak signal and immune to noise, which suggests advantages of using chaos in weak signal detection application. The idea to use chaos theory to detect weak signal appeared in the beginning of 90's in 20th, which extends the engineering application of chaos theory and impels the development of weak signal detection theory. Compared with conventional schemes, chaos-based detection methods have a lower SNR threshold. Hence, the research on chaotic weak signal detection method is of significance in theory and application.In this scenario and supported by the nation natural fund project, our research work focused on two aspects, namely study on detection and estimation methods of weak signal detection by using Duffing oscillator and study on the application of Duffing oscillator in the process of communication signals. In more detail, this dissertation deals with the following aspects:At first of all, dynamic behavior of a soften spring Duffing oscillator is analyzed theoretically and numerically, upon which the majority of this work is founded.Secondly, we study the techniques of state transition detection in chaos-based weak signal detection method. A quantitative description of spectrum characteristic is presented to automatically recognize the state transition from chaotic state to the large-scale periodic state of Duffing oscillator. Meanwhile, a zone partition approach, which aims at the real time signals processing, is proposed. Through partition, the trajectory on two-dimensional phase plan is transformed into one-dimensional time signal, which is used to indicate the state transition online.Thirdly, the detecting weak signal method is researched based on the Duffing chaotic system. The principle and some aspects for practical application about weak signal detection based on chaotic critical state of Duffing oscillator are discussed deeply. Furthermore, detection method that can eliminate the dependence on phase difference between the weak signal and the driving signal are presented.Fourthly, the detecting weak signal method is researched based on the Duffing periodic system. A new signal estimation method is presented to determine the amplitude and phase of a weak sinusoidal signal by using the sensitive dependence on parameters of the Duffing oscillator, which is kept in a periodic motion nearby the critical bifurcation. The theoretical analysis and the numerical results verify that this approach is effective and feasible.Finally, the use of Duffing oscillator in the context of practical communication application is investigated. We study the chaotic approach to detect the modulated signals, and analyze the effect of carrier deviation. Further, we propose a BPSK/DPSK detector based on Duffing periodic oscillator. By using Monte Carlo techniques, the bit error performance of the detector is evaluated under additive Gaussian noise. We also compare the bit error rate(BER) of the proposed detector with traditional detection schemes and investigate the effect of the parameters on the BER. Simulation results show that the proposed detector is feasible for communication modulated signal detection.In summary, the application of Duffing oscillator to weak signal detection is investigated. To improve efficiency and realize on-line detection, two choices for state transition detection are given respectively. To eliminate the dependence on phase difference of single Duffing oscillator, detection approach independent on phase difference is presented. In view of unknown phase of the signal, we have proposed a new method to determine the amplitude and phase of a weak signal. Based on the periodic region of Duffing oscillator, a new approach for detecting modulated signals is given. Our findings with computer simulations indicate that chaos-based weak signal detection method is feasible. The methodology developed in this dissertation is valuable for weak signal detection and provides the basics of a communication detector using nonlinear oscillator. It is expected that the results will find direct applications in communication, radar and sonar engineering in the near future.