直接序列扩频信号的截获分析研究
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摘要
直接序列扩频信号具有低截获概率和抗窄带干扰等特点,在军用/民用通信以及其它许多领域中有着广泛的应用。不知道伪码和其它参数,即非合作条件下,对它的截获和分析面临挑战,尤其在低信噪比情况下更是如此。
虽然过去三十年来针对非合作直扩信号的研究已经在截获和分析方面取得了很多进展,但是理论性的分析和新方法比较少,仍存在一些重要问题没有获得满意的解决。例如,对于直扩信号分析很重要的伪码周期检测和估计问题,在传统的谱相关理论下,就一直没有被严格地对待过;盲信道辨识算法用于直扩信号估计的实际性能还很少从非合作的角度分析过。
本文针对上述问题展开了深入的理论研究,同时还将研究对象扩展至长码直扩信号和软扩频信号。本文的贡献归纳起来包括以下几个方面:
1.对于短码直扩信号的伪码周期检测和估计问题,首次严格地研究了未知参数模型下的直扩信号最优检测器。在高斯混合信号模型下,推导了一致最大势不变量检测器和几种次优不变量检测器。结果展现了不变量检测器和多循环检测器之间的关系。得到的非相干加权多循环检测器可作为所有基于二阶循环平稳统计量的检测器的性能上限。而且提出的渐进局部最大势不变量(ALMPI)检测器在有限样本下比多循环检测器具有更好的性能而又没有明显增加计算复杂度。在ALMPI检测器的基础上提出了一种新的伪码周期估计器,和传统方法相比,它不需要人工判读。
2.同时从信号截获分析和盲信道辨识领域的角度综述了估计短码直扩信号的各种方法,指出了它们的理论联系和区别。首次指出即使是正确地估计了信道阶数(或有效阶数),盲信道辨识算法用于直扩信号也存在固有的鲁棒性问题。为此提出了平衡信道矩阵的概念,并提出一种新的最大化特征值乘积算法用于解决这个问题。
3.分析了长码直扩信号的信息码码宽估计问题。认识到信息码码宽估计需要克服伪码周期的干扰,同时现有方法依赖于具体使用的伪码且在低信噪比下性能不佳。为此提出了一种新的基于差分伪码解扩的信息码码宽估计方法,它在低信噪比时性能明显改善而且与伪码无关。
4.完整地研究了长码直扩信号的估计问题。针对非周期长码信号的统计性模型和确定性模型,使用加权低秩逼近优化工具,提出了迭代low-SNR UML算法和基于缺失数据模型的特征分解法,后者将非周期长码信号和短码信号统一起来,几乎达到了二阶统计量意义上的性能最优。同时对于周期长码直扩信号,考察了确定性复指数基展开的时变SIMO信道盲辨识方法用于估计多径情况下的性能,并与截获分析领域常用的特征分解方法进行了性能比较。
5.研究了软扩频信号的估计问题。对于多进制正交扩频信号,考察了它的可辨识问题,首次观察到特有的延时模糊现象,提出了一种盲同步算法,并在此基础上用期望值最大(EM)算法估计伪码。对于CCSK信号,提出了一种基于拟自相关矩阵的方法,和现有方法相比,它在低信噪比下性能有明显改善。
Direct-Sequence Spread-Spectrum (DSSS) signal has low probability of interception, anti-jamming capability and other advantages. It has widely been used in military and civil communications and many other applications. With unknown pseudo-noise (PN) sequence and other parameters, i.e., under non-cooperative context, the interception and analysis of DSSS signals is challengeable, especially under low signal-to-noise (SNR) scenarios.
Although in the past thirty years the study of non-cooperative DSSS signals has witnessed many developments in interception and analysis techniques of the DSSS signals, not so much in theoretic investigation and with new measures. However, some important problems have not been solved satisfactorily. For an example, with conventional spectral correlation theory, the detection and estimation of pseudo-noise (PN) code period, which is very important to analyze the DSSS signals, has not yet been studied rigorously. Another example is that performance analysis of the methods developed in blind channel identification has seldom been evaluated comprehensively under the non-cooperative context.
These problems are comprehensively studied from theoretical viewpoint. Other spread-spectrum signals such as long-code DSSS and the Tamed ones are considered as well. The main contributions of this dissertation include some aspects as follows:
1. For the first time, optimal detection of the DSSS signals with unknown parameters is rigorously discussed to detect and estimate the PN code period of short-code DSSS signals. With the Gaussian mixture model, the uniform most powerful invariant test and some sub-optimal invariant tests are derived. The results show the connection between the invariant tests and the multi-cycle detectors. Proposed nocoherent weighted multi-cycle detectors can be used as the performance upper-bound of all detectors based on second-order cyclostationary statistics. In the same time, proposed asymptotic locally most powerful invariant (ALMPI) test outperforms the multi-cycle detectors in the situation of finite samples and without obviously increasing computational complexity. Based on the ALMPI test, a new PN code period estimator is proposed, which needs no artificial interpretation compared with conventional approaches.
2. Simutaneously from two viewpoints, signal interception and blind channel identification, estimation of the DSSS signals is reviewed. The connection and difference between two viewpoints are spotted. When used for the estimation of short-code DSSS signals, the algorithm of blind channel identification shows to be inherently not robust even knowing the correct channel filter order (or the effective order). The principle to balance the channel matrix is proposed, and a novel MPP (maximize the product of eigenvalues) algorithm is used to solve the problem.
3. Estimation of information-code-width of long-code DSSS signals is analyzed. The results show that suppressing the interference by the PN code period is crucial and existing approach is PN code-dependent and has poor performance at low SNR. Therefore, a PN code-independent information-code-width estimator based on difference PN code despreading is proposed and demonstrates good performance at low SNR.
4. Complete study is made for the estimation of long-code DSSS signals. Using the stochastical and the deterministic models for aperiodic long-code DSSS signals, an iterative low-SNR unconditional maximum likelihood estimator and an eigen-composition algorithm for the missing-data model are proposed, respectively. Both estimators exploit the weighted low-rank approximation optimization and the latter algorithm unifies the aperiodic long-code DSSS signals and the short-code ones, which is almost optimal in the sense of the second-order statistics of received samples. The deteministic complex exponential basis expansion method for time-varying single-input-multi-output (SIMO) blind channel identification is used to estimate periodic long-code DSSS signals under multi-path scenarios and the performance is compared with conventional eigen-composition algorithms often used in the interception and analysis context.
5. Estimation of the Tamed DSSS signals is also investigated in the interception and analysis context. The identificability of M-ary orthogonal spreading spectrum (MO-SS) signals is investigated and a special phenomenon of delay ambiguity is observed. Then a blind synchronization algorithm is proposed and the Expectation Maximization (EM) algorithm is used to estimate the PN code of MO-SS signals. Moreover, an estimator based on the autocorrelation-like matrix is proposed for CCSK (Cyclic Code Shift Keying) signal, which shows obvious perfromance improvement at low SNR cases.
虽然过去三十年来针对非合作直扩信号的研究已经在截获和分析方面取得了很多进展,但是理论性的分析和新方法比较少,仍存在一些重要问题没有获得满意的解决。例如,对于直扩信号分析很重要的伪码周期检测和估计问题,在传统的谱相关理论下,就一直没有被严格地对待过;盲信道辨识算法用于直扩信号估计的实际性能还很少从非合作的角度分析过。
本文针对上述问题展开了深入的理论研究,同时还将研究对象扩展至长码直扩信号和软扩频信号。本文的贡献归纳起来包括以下几个方面:
1.对于短码直扩信号的伪码周期检测和估计问题,首次严格地研究了未知参数模型下的直扩信号最优检测器。在高斯混合信号模型下,推导了一致最大势不变量检测器和几种次优不变量检测器。结果展现了不变量检测器和多循环检测器之间的关系。得到的非相干加权多循环检测器可作为所有基于二阶循环平稳统计量的检测器的性能上限。而且提出的渐进局部最大势不变量(ALMPI)检测器在有限样本下比多循环检测器具有更好的性能而又没有明显增加计算复杂度。在ALMPI检测器的基础上提出了一种新的伪码周期估计器,和传统方法相比,它不需要人工判读。
2.同时从信号截获分析和盲信道辨识领域的角度综述了估计短码直扩信号的各种方法,指出了它们的理论联系和区别。首次指出即使是正确地估计了信道阶数(或有效阶数),盲信道辨识算法用于直扩信号也存在固有的鲁棒性问题。为此提出了平衡信道矩阵的概念,并提出一种新的最大化特征值乘积算法用于解决这个问题。
3.分析了长码直扩信号的信息码码宽估计问题。认识到信息码码宽估计需要克服伪码周期的干扰,同时现有方法依赖于具体使用的伪码且在低信噪比下性能不佳。为此提出了一种新的基于差分伪码解扩的信息码码宽估计方法,它在低信噪比时性能明显改善而且与伪码无关。
4.完整地研究了长码直扩信号的估计问题。针对非周期长码信号的统计性模型和确定性模型,使用加权低秩逼近优化工具,提出了迭代low-SNR UML算法和基于缺失数据模型的特征分解法,后者将非周期长码信号和短码信号统一起来,几乎达到了二阶统计量意义上的性能最优。同时对于周期长码直扩信号,考察了确定性复指数基展开的时变SIMO信道盲辨识方法用于估计多径情况下的性能,并与截获分析领域常用的特征分解方法进行了性能比较。
5.研究了软扩频信号的估计问题。对于多进制正交扩频信号,考察了它的可辨识问题,首次观察到特有的延时模糊现象,提出了一种盲同步算法,并在此基础上用期望值最大(EM)算法估计伪码。对于CCSK信号,提出了一种基于拟自相关矩阵的方法,和现有方法相比,它在低信噪比下性能有明显改善。
Direct-Sequence Spread-Spectrum (DSSS) signal has low probability of interception, anti-jamming capability and other advantages. It has widely been used in military and civil communications and many other applications. With unknown pseudo-noise (PN) sequence and other parameters, i.e., under non-cooperative context, the interception and analysis of DSSS signals is challengeable, especially under low signal-to-noise (SNR) scenarios.
Although in the past thirty years the study of non-cooperative DSSS signals has witnessed many developments in interception and analysis techniques of the DSSS signals, not so much in theoretic investigation and with new measures. However, some important problems have not been solved satisfactorily. For an example, with conventional spectral correlation theory, the detection and estimation of pseudo-noise (PN) code period, which is very important to analyze the DSSS signals, has not yet been studied rigorously. Another example is that performance analysis of the methods developed in blind channel identification has seldom been evaluated comprehensively under the non-cooperative context.
These problems are comprehensively studied from theoretical viewpoint. Other spread-spectrum signals such as long-code DSSS and the Tamed ones are considered as well. The main contributions of this dissertation include some aspects as follows:
1. For the first time, optimal detection of the DSSS signals with unknown parameters is rigorously discussed to detect and estimate the PN code period of short-code DSSS signals. With the Gaussian mixture model, the uniform most powerful invariant test and some sub-optimal invariant tests are derived. The results show the connection between the invariant tests and the multi-cycle detectors. Proposed nocoherent weighted multi-cycle detectors can be used as the performance upper-bound of all detectors based on second-order cyclostationary statistics. In the same time, proposed asymptotic locally most powerful invariant (ALMPI) test outperforms the multi-cycle detectors in the situation of finite samples and without obviously increasing computational complexity. Based on the ALMPI test, a new PN code period estimator is proposed, which needs no artificial interpretation compared with conventional approaches.
2. Simutaneously from two viewpoints, signal interception and blind channel identification, estimation of the DSSS signals is reviewed. The connection and difference between two viewpoints are spotted. When used for the estimation of short-code DSSS signals, the algorithm of blind channel identification shows to be inherently not robust even knowing the correct channel filter order (or the effective order). The principle to balance the channel matrix is proposed, and a novel MPP (maximize the product of eigenvalues) algorithm is used to solve the problem.
3. Estimation of information-code-width of long-code DSSS signals is analyzed. The results show that suppressing the interference by the PN code period is crucial and existing approach is PN code-dependent and has poor performance at low SNR. Therefore, a PN code-independent information-code-width estimator based on difference PN code despreading is proposed and demonstrates good performance at low SNR.
4. Complete study is made for the estimation of long-code DSSS signals. Using the stochastical and the deterministic models for aperiodic long-code DSSS signals, an iterative low-SNR unconditional maximum likelihood estimator and an eigen-composition algorithm for the missing-data model are proposed, respectively. Both estimators exploit the weighted low-rank approximation optimization and the latter algorithm unifies the aperiodic long-code DSSS signals and the short-code ones, which is almost optimal in the sense of the second-order statistics of received samples. The deteministic complex exponential basis expansion method for time-varying single-input-multi-output (SIMO) blind channel identification is used to estimate periodic long-code DSSS signals under multi-path scenarios and the performance is compared with conventional eigen-composition algorithms often used in the interception and analysis context.
5. Estimation of the Tamed DSSS signals is also investigated in the interception and analysis context. The identificability of M-ary orthogonal spreading spectrum (MO-SS) signals is investigated and a special phenomenon of delay ambiguity is observed. Then a blind synchronization algorithm is proposed and the Expectation Maximization (EM) algorithm is used to estimate the PN code of MO-SS signals. Moreover, an estimator based on the autocorrelation-like matrix is proposed for CCSK (Cyclic Code Shift Keying) signal, which shows obvious perfromance improvement at low SNR cases.
引文
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