DS及DS/CDMA信号的估计方法研究
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摘要
直扩（DS）信号及直扩码分多址（DS/CDMA）信号的估计方法研究是宽带微弱信号检测与估计以及通信对抗领域的一个重要研究课题。近30多年来，已发展了诸多的DS信号估计方法。这些估计方法大都基于常规信号检测与估计理论，但DS信号是宽带微弱信号，其并不符合常规的信号处理理论，因此当观察信号的信噪比较低时，这些估计方法的估计性能恶化，甚至得不到正确的估计结果。虽然DS信号在军事和民用中应用较为广泛，但直到80年代初，有关研究人员才明确地开始对DS信号的估计进行研究。从当前的研究发展状况来看，DS及DS/CDMA信号的估计方法研究进展缓慢，概念性的研究较为多见，而具体估计方法的研究还远不够全面、成熟。考虑到在未知信号伪码（PN码）序列的情况下对DS及DS/CDMA信号进行估计的挑战性，有必要对DS及DS/CDMA信号的估计做进一步的研究，以获得有效的DS及DS/CDMA信号的估计方法。
读博期间，作者围绕DS及DS/CDMA信号的估计方法展开研究。本文的主要工作是在先验知识未知的情况下，先对DS及DS/CDMA信号的参数进行估计，并在已获知信号参数的情况下，再对信号的PN码序列进行估计。本文提出了用于信号参数估计的功率谱二次处理算法、谱相关算法和时域相关算法，提出了能用于信号信息码与PN码同步起止时刻、PN码序列估计的矩阵分解算法和神经网络（N.N.）算法等等。在提出算法的同时，还考虑了如何增强算法的性能，因此贯穿本文的另一条主线是研究如何提高算法压制噪声的性能以适应实际的情况。
本文的主要工作和创新之处包括：
（1）对DS及DS/CDMA信号模型进行了研究，指出了基带DS及DS/CDMA信号的估计可以分为参数估计（PN码周期、PN码片宽度以及信息码与PN码同步的起止时刻的估计）和波形估计（PN码序列的估计）。
（2）在对DS及DS/CDMA信号功率谱研究的基础上，提出了一种用于估计该类信号PN码周期的功率谱二次处理算法，该算法具有结构简单、快速，并容易作到较低的信噪比容限等优点。
（3）在对DS及同步DS/CDMA信号周期谱（谱相关）研究的基础上，论证了应用DS信号的周期谱（谱相关）可以得到该信号PN码片宽度的估计，提出了一种用于估计同步DS/CDMA信号PN码片宽度的谱相关算法，并作到了较低的信噪比容限。
（4）综合了DS及DS/CDMA信号处理的时域相关方法，表明了通过改变时域相关函数的时延可以同时作出对DS及DS/CDMA信号PN码周期和DS及同步DS/CDMA信号PN码片宽度的估计，提出了用于估计DS/CDMA信号PN码周期的时域相关算法（当相关时延较大可以和PN码周期比拟时），还提出了用于估计同步DS/CDMA信号PN码片宽度的时域相关算法（当相关时延较小可以和PN码片宽度比拟时）。
（5）针对DS及DS/CDMA信号PN码序列估计的问题，提出了用于信号PN码序列估计的数据矩阵和相关矩阵的奇异值分解算法以及相关矩阵的特征分解算法。相关矩阵的奇异值分解算法是按任意确定的随机起点，以PN码周期对信号进行分段以形成数据向量观察集，用累加平均的信号相关矩阵奇异值分解的算法来估计出信号的PN码序列。我们证明了在对信号相关矩阵实施奇异值分解时，由最大和次大奇异值对应
的左奇异向量形成的序列是能完整地恢复出信号的PN码序列的。该相关矩阵的奇异值分解算法在用于估计DS及DS/CDMA信号PN码序列时可以获得较低的信噪比容限。
（6）受DS及DS/CDMA信号主动解扩思想的启发，在PN码序列估计的矩阵分解算法基础上，提出了用于DS及DS/CDMA信号PN码序列估计的神经网络算法，同时证明了矩阵的主分量分析和特征分析的等价性。对已知信息码与PN码同步起止时刻的DS信号，提出了用于信号PN码估计的无监督主分量提取神经网络算法，并且证明了它的收敛性。对未知信息码与PN码同步起止时刻的DS及DS/CDMA信号，提出了用于信号PN码序列估计的冗余去除的无监督多主分量提取神经网络算法。
（7）针对如何使估计算法适应更低信噪比的观察信号和提高计算输出的信噪比问题，本文提出了多通道分集和线性累加平均相结合的方法。进一步，还提出了将本文所提算法用于DS及DS/CDMA信号估计的多个系统化框图。
与现有的其它DS及DS/CDMA信号估计方法相比，上述信号估计方法的优点在于无须知道观察信号的PN码序列，与信号PN码序列的线性复杂度无关，在估计到了信号的PN码序列以后，可以用和主动解扩一样的方法对观察信号进行解扩处理，从而最终实现对DS及DS/CDMA信号的盲解扩。而且上述的这些估计方法优缺点互为补充，仿真实验表明，总体上这些方法可以作到较低的信噪比容限。
The problem of estimating direct sequence spread spectrum (DS) signals and direct sequence code division multiple access (DS/CDMA) signals direct from the received signals has been of great research interest with the development of the field of wide-band weak signal processing and the field of communication antagonism. For the last several decades, a class of DS&DS/CDMA signal estimation methods has been developed. The methods are almost based upon the theory of conventional signal detection and estimation. However the DS&DS/CDMA signals are wide-band weak signals, they aren't in conformity with the theory of conventional signal processing, so when the signal to noise ratios of the received signals becomes lower, the performance of the methods take a turn for the worse, the methods don't work. Though DS&DS/CDMA signals are widely used in military and civil, until recently study on the DS&DS/CDMA signal estimation appeared in the literature. Presently, the development of DS&DS/CDMA signal estimation is very slow, it is almost in study of conception and the study of concrete method is far from comprehensive and mature. Due to the challenge of DS&DS/CDMA signal estimation without knowledge of the pseudo-noise (PN) sequence, the study of DS&DS/CDMA signal estimation is necessary, so that we can obtain efficient method of DS&DS/CDMA signal estimation.
The main contributions of this dissertation include two aspects. One is parameter estimation of the DS&DS/CDMA signal, include period estimation and chip interval estimation of the PN sequence etc., the other is PN sequence estimation of the DS&DS/CDMA signals.
Several valuable and important results which bring forth new ideas are achieved and listed as follows:
1、 Based upon the study of models of the DS&DS/CDMA signals, we obtain the parameters of base-band DS&DS/CDMA signals for estimation are as follows: the period and the chip interval of PN sequence, the moment of de-synchronization between observation window and symbols. Besides, we obtain waveform for estimation: the PN sequence itself.
2、 Based upon the study of the power spectrum of DS&DS/CDMA signals, a power spectrum reprocessing approach is presented to estimate the period of PN sequence.
3、 Based upon the study of the cyclic spectrum of DS&DS/CDMA signals, a spectral correlation approach is presented to estimate the chip interval of PN sequence.
After synthesizing the DS&DS/CDMA signal estimation methods of time-domain correlation, we obtain two approaches. When the correlation time-delay can compare to the period of PN sequence, a time-domain correlation approach is presented to estimate the period of DS&DS/CDMA signals. When the correlation time-delay can compare to the chip interval of PN sequence, another time-domain
4、 correlation approach is presented to estimate the chip interval of DS&DS/CDMA signals.
5、 In order to solve the estimation problem of PN sequence itself, we presented a matrix decomposition approach to estimate the PN sequence itself. Through decomposition of the correlation matrix of DS&DS/CDMA signal, we can estimate the PN sequence from the largest and the second largest left singular vector.
6、 In order to solve the estimation problem of PN sequence itself, based upon the idea of the correlation matrix decomposition, we present the neural networks (N.N.) approach to estimate the PN sequence itself. Here, the N.N. approaches include: the principal component analysis and the principal components analysis N.N. . When the moment of the de-synchronization is known, we can use the principal component analysis N.N. to extract the first principal component of the DS&DS/CDMA signal, we can estimate the PN sequence from the first principal component. When the moment of the de-synchronization is unknown, we can use the principal components analysis N.N. to extract the first and the second principal components of the DS&DS/CDMA signals, we can estimate the PN sequence itself from them too.
Compare with the existed DS&DS/CDMA signal estimation methods, an advant
读博期间，作者围绕DS及DS/CDMA信号的估计方法展开研究。本文的主要工作是在先验知识未知的情况下，先对DS及DS/CDMA信号的参数进行估计，并在已获知信号参数的情况下，再对信号的PN码序列进行估计。本文提出了用于信号参数估计的功率谱二次处理算法、谱相关算法和时域相关算法，提出了能用于信号信息码与PN码同步起止时刻、PN码序列估计的矩阵分解算法和神经网络（N.N.）算法等等。在提出算法的同时，还考虑了如何增强算法的性能，因此贯穿本文的另一条主线是研究如何提高算法压制噪声的性能以适应实际的情况。
本文的主要工作和创新之处包括：
（1）对DS及DS/CDMA信号模型进行了研究，指出了基带DS及DS/CDMA信号的估计可以分为参数估计（PN码周期、PN码片宽度以及信息码与PN码同步的起止时刻的估计）和波形估计（PN码序列的估计）。
（2）在对DS及DS/CDMA信号功率谱研究的基础上，提出了一种用于估计该类信号PN码周期的功率谱二次处理算法，该算法具有结构简单、快速，并容易作到较低的信噪比容限等优点。
（3）在对DS及同步DS/CDMA信号周期谱（谱相关）研究的基础上，论证了应用DS信号的周期谱（谱相关）可以得到该信号PN码片宽度的估计，提出了一种用于估计同步DS/CDMA信号PN码片宽度的谱相关算法，并作到了较低的信噪比容限。
（4）综合了DS及DS/CDMA信号处理的时域相关方法，表明了通过改变时域相关函数的时延可以同时作出对DS及DS/CDMA信号PN码周期和DS及同步DS/CDMA信号PN码片宽度的估计，提出了用于估计DS/CDMA信号PN码周期的时域相关算法（当相关时延较大可以和PN码周期比拟时），还提出了用于估计同步DS/CDMA信号PN码片宽度的时域相关算法（当相关时延较小可以和PN码片宽度比拟时）。
（5）针对DS及DS/CDMA信号PN码序列估计的问题，提出了用于信号PN码序列估计的数据矩阵和相关矩阵的奇异值分解算法以及相关矩阵的特征分解算法。相关矩阵的奇异值分解算法是按任意确定的随机起点，以PN码周期对信号进行分段以形成数据向量观察集，用累加平均的信号相关矩阵奇异值分解的算法来估计出信号的PN码序列。我们证明了在对信号相关矩阵实施奇异值分解时，由最大和次大奇异值对应
的左奇异向量形成的序列是能完整地恢复出信号的PN码序列的。该相关矩阵的奇异值分解算法在用于估计DS及DS/CDMA信号PN码序列时可以获得较低的信噪比容限。
（6）受DS及DS/CDMA信号主动解扩思想的启发，在PN码序列估计的矩阵分解算法基础上，提出了用于DS及DS/CDMA信号PN码序列估计的神经网络算法，同时证明了矩阵的主分量分析和特征分析的等价性。对已知信息码与PN码同步起止时刻的DS信号，提出了用于信号PN码估计的无监督主分量提取神经网络算法，并且证明了它的收敛性。对未知信息码与PN码同步起止时刻的DS及DS/CDMA信号，提出了用于信号PN码序列估计的冗余去除的无监督多主分量提取神经网络算法。
（7）针对如何使估计算法适应更低信噪比的观察信号和提高计算输出的信噪比问题，本文提出了多通道分集和线性累加平均相结合的方法。进一步，还提出了将本文所提算法用于DS及DS/CDMA信号估计的多个系统化框图。
与现有的其它DS及DS/CDMA信号估计方法相比，上述信号估计方法的优点在于无须知道观察信号的PN码序列，与信号PN码序列的线性复杂度无关，在估计到了信号的PN码序列以后，可以用和主动解扩一样的方法对观察信号进行解扩处理，从而最终实现对DS及DS/CDMA信号的盲解扩。而且上述的这些估计方法优缺点互为补充，仿真实验表明，总体上这些方法可以作到较低的信噪比容限。
The problem of estimating direct sequence spread spectrum (DS) signals and direct sequence code division multiple access (DS/CDMA) signals direct from the received signals has been of great research interest with the development of the field of wide-band weak signal processing and the field of communication antagonism. For the last several decades, a class of DS&DS/CDMA signal estimation methods has been developed. The methods are almost based upon the theory of conventional signal detection and estimation. However the DS&DS/CDMA signals are wide-band weak signals, they aren't in conformity with the theory of conventional signal processing, so when the signal to noise ratios of the received signals becomes lower, the performance of the methods take a turn for the worse, the methods don't work. Though DS&DS/CDMA signals are widely used in military and civil, until recently study on the DS&DS/CDMA signal estimation appeared in the literature. Presently, the development of DS&DS/CDMA signal estimation is very slow, it is almost in study of conception and the study of concrete method is far from comprehensive and mature. Due to the challenge of DS&DS/CDMA signal estimation without knowledge of the pseudo-noise (PN) sequence, the study of DS&DS/CDMA signal estimation is necessary, so that we can obtain efficient method of DS&DS/CDMA signal estimation.
The main contributions of this dissertation include two aspects. One is parameter estimation of the DS&DS/CDMA signal, include period estimation and chip interval estimation of the PN sequence etc., the other is PN sequence estimation of the DS&DS/CDMA signals.
Several valuable and important results which bring forth new ideas are achieved and listed as follows:
1、 Based upon the study of models of the DS&DS/CDMA signals, we obtain the parameters of base-band DS&DS/CDMA signals for estimation are as follows: the period and the chip interval of PN sequence, the moment of de-synchronization between observation window and symbols. Besides, we obtain waveform for estimation: the PN sequence itself.
2、 Based upon the study of the power spectrum of DS&DS/CDMA signals, a power spectrum reprocessing approach is presented to estimate the period of PN sequence.
3、 Based upon the study of the cyclic spectrum of DS&DS/CDMA signals, a spectral correlation approach is presented to estimate the chip interval of PN sequence.
After synthesizing the DS&DS/CDMA signal estimation methods of time-domain correlation, we obtain two approaches. When the correlation time-delay can compare to the period of PN sequence, a time-domain correlation approach is presented to estimate the period of DS&DS/CDMA signals. When the correlation time-delay can compare to the chip interval of PN sequence, another time-domain
4、 correlation approach is presented to estimate the chip interval of DS&DS/CDMA signals.
5、 In order to solve the estimation problem of PN sequence itself, we presented a matrix decomposition approach to estimate the PN sequence itself. Through decomposition of the correlation matrix of DS&DS/CDMA signal, we can estimate the PN sequence from the largest and the second largest left singular vector.
6、 In order to solve the estimation problem of PN sequence itself, based upon the idea of the correlation matrix decomposition, we present the neural networks (N.N.) approach to estimate the PN sequence itself. Here, the N.N. approaches include: the principal component analysis and the principal components analysis N.N. . When the moment of the de-synchronization is known, we can use the principal component analysis N.N. to extract the first principal component of the DS&DS/CDMA signal, we can estimate the PN sequence from the first principal component. When the moment of the de-synchronization is unknown, we can use the principal components analysis N.N. to extract the first and the second principal components of the DS&DS/CDMA signals, we can estimate the PN sequence itself from them too.
Compare with the existed DS&DS/CDMA signal estimation methods, an advant
引文
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