| Over the past two decades, the nonlinear science, especially the science of chaos has attracted a lot attention in the fields of communication and electronic engineering. Among many applications of chaotic theory, one of the most typical and important applications is the construction of various communication systems based on chaotic theory. These kinds of communication systems involve, for example, the frequency hopping communication system based on chaos, the communication system based on synchronization of nonlinear dynamical systems and the chaotic direct-sequence spread-spectrum (CD3S) communication system. Though the research in these areas has been conducted for many years, quite a lot of problems still need to be further studied. Besides, in-depth study in these fields has also given rise to many new and challenging problems such as chaotic communication countermeasure. This dissertation deals with chaotic communication as well as chaotic communication countermeasure simultaneously. The main research topics and the related new results are listed as follows.1. For the countermeasure of the high-speed frequency hopping communication system based on chaos, two new approaches of one-step-ahead prediction of chaotic time series are proposed. They are adaptive approaches based on Bernstein polynomial and Legendre polynomial respectively. Since both polynomial models have good modeling capabilities, the proposed approaches can model and predict various typical chaotic series. Due to the use of recursive least-squares algorithm with fast convergence, the speeds of modeling of these two approaches are fast. This makes the approaches can be applied to predict short record time series in real time. When the frequency hop rate of frequency hopping communication system is very high, the effective interference range of a jammer is fairly limited if only one-step-ahead prediction is made. Therefore, multi-step-ahead prediction is needed to expand the effective interference range of a jammer. Under this background, a method is suggested to improve the prediction precision of multi-step-ahead prediction for the frequency-hopping sequence generated by a one-dimensional chaotic map. The basic idea of this method is to modify the single predicted trajectory of the traditional method appropriately to obtain two predicted sequences. Interfering with the frequency hopping communication system according to these two predicted sequences provides better performance than utilizing the single predicted trajectory of the traditional method to interfere.2. To enhance the anti-noise performance or the security of communication system based on synchronization of nonlinear dynamical systems, some new synchronization schemes of nonlinear dynamical systems are proposed. These schemes are a broad class of synchronization schemes of nonlinear time-delay dynamical systems and the tangent response scheme in coupled nonlinear systems. The former covers a very wide range of dynamical systems and synchronization schemes capable of generating various dynamical behaviors can be constructed according to it. For example, the general lag response scheme and the general anticipating response scheme are such schemes. For each of these two general schemes, various specific schemes can be obtained by choosing a function to be determined in them. The decelerative lag response scheme, a specific case of the general lag response scheme, and the accelerative anticipating response scheme, a specific case of the general anticipating response scheme are studied in detail. They have new property of speed-changing synchronization which is completely different from the traditional synchronization schemes. Theoretical analyses demonstrate that, in most cases, they are robust against the disturbances as well as parameter mismatches. Further, a general lag response scheme with the property of fast convergence is proposed to reduce the transient time before synchronization is achieved. The later, i.e., the tangent response scheme in coupled nonlinear systems makes the state of the response system asymptotically approach the first-order derivative of the state of the driver, which is a completely new dynamical behavior. In the asymptotic sense, the state space of the response system can be viewed as a distorted version of the one of the drive system, which makes the synchronization mode of this scheme more complex than the one of complete synchronization scheme. The above-mentioned two synchronization schemes can be used to enhance the anti-noise performance or the security of communication system based on synchronization of nonlinear dynamical systems.3. For breaking a CD3S communication system whose spreading sequence is generated by a one-dimensional chaotic map, a two-step method is proposed, where step (1) is to recover the dynamical rules corresponding to information symbol 1 and -1 respectively from the receiving data and step (2) is to decide the underlying dynamical rule of two receiving data at adjacent times. In this dissertation, the step (2) is studied first. A new semi-blind estimation algorithm for information symbols of CD3S communication is proposed. Under the condition that the chaotic dynamical rule is known and the exact chaotic spreading sequence is unknown, the proposed algorithm changes the problem of estimation of information symbols into the problem of decision of the underlying dynamical rule of two receiving data at adjacent times. A decision expression is derived according to the theory of probability and statistics. Numerical simulations demonstrate that, though the exact spreading sequence and the spreading gain are unknown, the proposed algorithm can estimate information symbols effectively even when the signal-to-noise ratio (SNR) is negative and generally, the higher the SNR is, the better this algorithm performs.4. The step (1) mentioned in point 3 above is the most challenging problem, which has not been solved completely yet. A related but relatively simpler problem is studied to lay the foundation for a further investigation of the step (1). This related problem is to estimate the dynamical rule from noisy chaotic series. The difference between this problem and the one in the step (1) lies in that the information symbols are not considered here. The basic idea to solve this problem is first to divide the domain of the one-dimensional chaotic map into subintervals of uniform length which is sufficiently small, second to take the midpoint of every subinterval as a representative point, and third to estimate the function values of the chaotic map at these representative points. The procedure of the proposed algorithm is outlined as follows: first regard two observations at adjacent times in the noisy chaotic series as an observation of a two-dimensional random vector; then establish the linear equations of the values to be estimated by utilizing the probability that the random vector falls into a special area and a special conditional expectation of the random vector; finally the regularization methods are applied to stabilize the numerical solutions of the linear equations. The proposed algorithm estimates the function values of the chaotic map at the representative points as well as the values of the natural invariant density at the same representative points. Numerical simulations demonstrate that this algorithm works effectively even when the SNR is negative and it is robust to changes of one-dimensional chaotic map and changes of SNR when the parameters are chosen appropriately. This algorithm lays the foundation for a further investigation of the step (1) and besides that, it has independent significance for providing a method for the estimation of the dynamical rule and the natural invariant density from noisy chaotic series when the SNR is low.
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