非线性通信信号处理方法研究
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摘要
近二十年来,非线性科学,尤其是混沌科学在通信与电子工程领域中得到了广泛的关注。在其诸多应用中,最典型最重要的应用之一是基于混沌理论来构造多种多样的通信系统,如混沌跳频通信系统,基于非线性动力系统同步的通信系统以及混沌直扩通信系统等。尽管这些领域的研究工作已经开展了多年,但其中仍然存在很多有待进一步深入研究的问题,并且随着这些领域中研究工作的逐渐深入,也带来了很多新的富有挑战性的问题,如针对混沌通信的对抗等。本论文的工作在混沌通信以及混沌通信对抗这两个方面均有所涉及,所研究的主要内容及其创新点包括:
1.为了对抗具有高跳速的混沌跳频通信系统,作者提出了两种新的混沌时间序列单步预测算法,包括基于Bernstein多项式以及基于Legendre多项式的自适应预测算法,这两种模型均具有良好的建模能力,能对各种典型的混沌序列进行建模和预测,由于采用了收敛速度较快的递推最小二乘算法,这两种方法的建模速度也较快,适合于对短数据进行实时预测的场合;此外,当混沌跳频通信系统的跳速很高时,仅作单步预测则干扰机的工作范围十分有限,因此需要作多步预测以扩大干扰机的有效工作范围。针对这一问题,作者对基于一维迭代混沌映射构造的跳频码提出了一种改善多步预测效果的算法,其思想是对传统预测方法的预测轨道进行修正,将一条预测轨道修正为两条预测序列,如果同时按照两条修正的预测序列进行跳频干扰,将得到比按照传统方法给出的一条预测轨道进行跳频干扰更好的效果。
2.为了增强基于非线性动力系统同步的通信系统的抗噪声性能或保密性能,作者提出了若干种新颖的非线性动力系统同步方案,这些方案包括:非线性时滞动力系统的一类广泛的同步模型以及非线性耦合动力系统的切响应模型。前者涵盖了非常广泛的动力系统,由之可以构造出具有不同动力学行为的同步系统,如一般延迟响应系统以及一般预测响应系统,这两种系统中均含有一个待定函数,选择不同的函数就将得到不同类型的系统,作者对这两种系统分别选择了一个特殊的函数,并对得到的两个特殊系统做了详细的研究,它们分别是减速延迟响应系统与加速预测响应系统,它们均有着与传统同步系统截然不同的全新的变速同步性质,并且理论分析证明它们在大多数情况下都对噪声的干扰以及参数失配有着良好的鲁棒性,此外作者还构造了一种快速收敛的一般延迟响应系统,以减少其达到同步的过渡时间;后者,即切响应模型,也有着全新的动力学行为,该模型使得响应系统的状态逐渐接近驱动系统状态的一阶导数,并且在渐近意义下,可以把响应系统的相空间视为驱动系统相空间的非线性扭曲,这种同步方式比完全同步更加复杂。以上两类同步系统均可用于基于非线性动力系统同步的通信系统以增强其抗噪声或保密的性能。
3.为了破译利用一维迭代混沌映射产生扩频码的混沌直扩通信系统,作者提出的思路分为两个步骤:(1)从接收数据中恢复出信息码1与-1各自对应的动力学规律;(2)判决接收到的两个相邻时刻数据点背后所遵循的动力学规律。在论文中,首先对步骤(2)进行了研究,提出了一种新的混沌直扩通信的信息码半盲估计算法,该算法在混沌动力学方程已知但精确混沌扩频序列未知的条件下,把信息码的估计问题转换为对接收的两个相邻时刻数据背后的潜在动力学规律进行判决的问题,利用概率统计理论推导了判决表达式,仿真表明,即使缺少了精确扩频码以及扩频增益等信息,利用该方法也可在负信噪比的环境中有效估计出信息码,且估计性能总体上随着信噪比的提高而改善。
4.上述第3点中的步骤(1)是最具挑战性的问题,但目前还没有完全解决,作者针对一个相关的稍简单的问题进行了研究,以期为此工作的进一步研究打下基础。作者研究了含噪混沌序列的动力学规律的提取问题,该问题与步骤(1)中的问题的区别在于没有考虑信息码的引入所带来的影响。解决的基本思路是将一维迭代混沌映射的定义域均匀划分为充分小的区间,然后取每个小区间的中点为代表点,最后估计出混沌映射的函数在定义域内的代表点处的取值。该算法首先将观测的相邻时刻的两个含噪混沌序列值描述为一个二维随机向量的观测值,然后利用这个二维随机向量落入特殊区域的概率及其特殊的条件数学期望建立起待估计值的线性方程组,最后采用正则化方法求解线性方程组以得到稳定的数值解。算法除了估计出混沌映射的函数在定义域内的代表点处的取值外,也给出了混沌的自然不变密度在代表点处的取值。仿真表明,该方法即使在负信噪比的环境中也能有效工作并且当参数选择恰当时,方法对一维迭代混沌映射的变化以及信噪比的变化具有一定的鲁棒性。该算法除了为继续进行第3点中的步骤(1)的研究提供了一个基础外,也具有独立的科研意义,即给出了一种从低信噪比的含噪混沌序列中估计动力学方程以及自然不变密度这些重要信息的方法。
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.
1.为了对抗具有高跳速的混沌跳频通信系统,作者提出了两种新的混沌时间序列单步预测算法,包括基于Bernstein多项式以及基于Legendre多项式的自适应预测算法,这两种模型均具有良好的建模能力,能对各种典型的混沌序列进行建模和预测,由于采用了收敛速度较快的递推最小二乘算法,这两种方法的建模速度也较快,适合于对短数据进行实时预测的场合;此外,当混沌跳频通信系统的跳速很高时,仅作单步预测则干扰机的工作范围十分有限,因此需要作多步预测以扩大干扰机的有效工作范围。针对这一问题,作者对基于一维迭代混沌映射构造的跳频码提出了一种改善多步预测效果的算法,其思想是对传统预测方法的预测轨道进行修正,将一条预测轨道修正为两条预测序列,如果同时按照两条修正的预测序列进行跳频干扰,将得到比按照传统方法给出的一条预测轨道进行跳频干扰更好的效果。
2.为了增强基于非线性动力系统同步的通信系统的抗噪声性能或保密性能,作者提出了若干种新颖的非线性动力系统同步方案,这些方案包括:非线性时滞动力系统的一类广泛的同步模型以及非线性耦合动力系统的切响应模型。前者涵盖了非常广泛的动力系统,由之可以构造出具有不同动力学行为的同步系统,如一般延迟响应系统以及一般预测响应系统,这两种系统中均含有一个待定函数,选择不同的函数就将得到不同类型的系统,作者对这两种系统分别选择了一个特殊的函数,并对得到的两个特殊系统做了详细的研究,它们分别是减速延迟响应系统与加速预测响应系统,它们均有着与传统同步系统截然不同的全新的变速同步性质,并且理论分析证明它们在大多数情况下都对噪声的干扰以及参数失配有着良好的鲁棒性,此外作者还构造了一种快速收敛的一般延迟响应系统,以减少其达到同步的过渡时间;后者,即切响应模型,也有着全新的动力学行为,该模型使得响应系统的状态逐渐接近驱动系统状态的一阶导数,并且在渐近意义下,可以把响应系统的相空间视为驱动系统相空间的非线性扭曲,这种同步方式比完全同步更加复杂。以上两类同步系统均可用于基于非线性动力系统同步的通信系统以增强其抗噪声或保密的性能。
3.为了破译利用一维迭代混沌映射产生扩频码的混沌直扩通信系统,作者提出的思路分为两个步骤:(1)从接收数据中恢复出信息码1与-1各自对应的动力学规律;(2)判决接收到的两个相邻时刻数据点背后所遵循的动力学规律。在论文中,首先对步骤(2)进行了研究,提出了一种新的混沌直扩通信的信息码半盲估计算法,该算法在混沌动力学方程已知但精确混沌扩频序列未知的条件下,把信息码的估计问题转换为对接收的两个相邻时刻数据背后的潜在动力学规律进行判决的问题,利用概率统计理论推导了判决表达式,仿真表明,即使缺少了精确扩频码以及扩频增益等信息,利用该方法也可在负信噪比的环境中有效估计出信息码,且估计性能总体上随着信噪比的提高而改善。
4.上述第3点中的步骤(1)是最具挑战性的问题,但目前还没有完全解决,作者针对一个相关的稍简单的问题进行了研究,以期为此工作的进一步研究打下基础。作者研究了含噪混沌序列的动力学规律的提取问题,该问题与步骤(1)中的问题的区别在于没有考虑信息码的引入所带来的影响。解决的基本思路是将一维迭代混沌映射的定义域均匀划分为充分小的区间,然后取每个小区间的中点为代表点,最后估计出混沌映射的函数在定义域内的代表点处的取值。该算法首先将观测的相邻时刻的两个含噪混沌序列值描述为一个二维随机向量的观测值,然后利用这个二维随机向量落入特殊区域的概率及其特殊的条件数学期望建立起待估计值的线性方程组,最后采用正则化方法求解线性方程组以得到稳定的数值解。算法除了估计出混沌映射的函数在定义域内的代表点处的取值外,也给出了混沌的自然不变密度在代表点处的取值。仿真表明,该方法即使在负信噪比的环境中也能有效工作并且当参数选择恰当时,方法对一维迭代混沌映射的变化以及信噪比的变化具有一定的鲁棒性。该算法除了为继续进行第3点中的步骤(1)的研究提供了一个基础外,也具有独立的科研意义,即给出了一种从低信噪比的含噪混沌序列中估计动力学方程以及自然不变密度这些重要信息的方法。
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.
引文
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