直接序列扩频信号的盲解扩研究
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摘要
直接序列扩频(Direct Sequence Spread Spectrum, DSSS)信号具有抗多径、抗干扰、低截获概率、多址复用等优点,在军事和民用通信领域有着广泛的应用。对于非合作方如通信侦察、无线电频谱监测及非法通信电台的定位跟踪等,需要在未知扩频序列条件下实现信号的解扩以完成传输信息的恢复,因此开展DSSS信号的盲解扩研究具有重要的意义。
尽管过去在DSSS信号盲解扩方面已经取得了很多进展,但由于缺乏深入的理论分析,使得问题的解决手段比较单一,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,对于扩频波形估计的理论下界一直没有被研究过;长码DSSS信号的极大似然估计问题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,得到的主要研究成果包括以下几个方面:
1.在确定与随机信号模型条件下,首次由理论上分别推导了DSSS信号扩频波形估计的CRB,可同时适用于长码与短码情况,为衡量各种扩频波形估计方法的性能提供了理论下界。
2.针对单用户短码DSSS信号的盲同步问题,提出了一种具有低计算复杂度的基于协方差矩阵m1范数改进算法,并推广至多用户且截获信号含有未知频偏的情况;针对短码QPSK-DSSS信号,提出了一种基于恒模特性的扩频序列估计改进算法;通过理论推导证明了扩频波形估计可达到CRB的传统特征分析方法,本质上为高斯极大似然估计器;针对异步短码CDMA信号的盲解扩,通过降维和去噪处理,提出了一种具有低计算复杂度且估计性能更优的改进算法。
3.针对单用户长码DSSS信号,对扩频波形的极大似然估计进行了理论推导,注意到该极大似然估计问题为组合优化问题,提出了一种基于半定规划的盲解扩算法并推广至截获信号含有未知频偏的情况,在低信噪比和短数据条件下相对传统方法具有优良的估计性能且可达到CRB。同时,提出算法可适用于短码DSSS信号。
4.针对多用户长码DSSS信号,确定信号模型和用户个数已知条件下,提出了一种基于缺失数据模型低秩近似的盲解扩算法,并在单用户情况下扩频波形估计可达到CRB;随机信号模型条件下提出了一种基于多元高斯缺失模型极大似然估计的盲解扩算法,可实现用户个数的估计。针对单用户长码DSSS信号,提出了一种基于单调缺失数据模型的非优化迭代盲解扩算法,可避免优化估计方法中的初始值和步长的选取、局部收敛性等问题。
5.针对多用户长码DSSS信号,利用多通道接收技术,通过将二维缺失数据模型向三维空间推广,提出了一种基于缺失张量模型的盲解扩算法。由于充分利用了空、时、码的分集结构,提出算法相对单通道盲解扩算法具有更优估计性能。
Direct sequence spread spectrum (DSSS) signals have been widely used for military and civil communications due to their anti-multipath, anti-jamming, low probability of intercept and multiple access properties. In non-cooperative applications such as communication reconnaissance, wireless spectrum surveillance and localization tracking of illegal communication transmitters, the transmitted information should be recovered without prior knowledge of the spreading sequence at the receiver. Therefore, blind despreading of DSSS signals plays an important role in non-cooperative scenarios.
Although in the past years the study on blind despreading of DSSS signals has witnessed many developments, not so much in problem solving means and with new measures due to lack of profound theoretic investigation. However, some important problems have not been solved satisfactorily. For an example, the theoretical lower bound of spreading waveform estimation has not been studied. Another example is that the Maximum Likelihood Estimate (MLE) of long-code DSSS signals has seldom been evaluated comprehensively under the non-cooperative context.
These problems are comprehensively studied from theoretical viewpoint. The main contributions of this dissertation include some aspects as follows:
1. For the first time, under the stochastical and the deterministic models for the DSSS signals, we derive the Cramér–Rao bound (CRB) for the spreading waveform estimation problem. The derived CRB holds for both long-code and short-code DSSS signals, and gives a performance lower bound for all spreading waveform estimators.
2. For the problem of blind synchronization for single-user short-code DSSS signals, an improved algorithm based on m1 -norm of the covariance matrix is proposed. The proposed algorithm has low computational complexity and can be used for the multi-user signals with unknown carrier offset. For the spreading sequence estimation problem of short-code QPSK-DSSS signals, an improved algorithm based on constant modulus property is proposed. Through theoretical analysis, we prove that the existing eigenanalysis-based spreading waveform estimator, which can approach the CRB, is essentially the Gaussian MLE. Using de-noising and reduced-dimension techniques, an improved blind despreading algorithm for asynchronous CDMA signals is presented, which has low computational complexity and shows good performance.
3. For single-user long-code DSSS signals, we derive the MLE of spreading waveform. Note that the MLE problem belongs to the field of combinatorial optimization. We propose a blind despreading algorithm based on semidefinite programming and extend it to the case when unknown carrier offset exists. The proposed algorithm provides significant performance improvements compared to existing methods in the case of low numbers of data samples and low SNR, and can be applied to the short-code DSSS signals.
4. For multi-user long-code DSSS signals, under the deterministic model and the assumption that the user number is known apriori, we propose a blind despreading algorithm based on low-rank approximation of missing-data model, and the proposed algorithm can approach the CRB in the single-user case. Under the stochastical model, based on the MLE for incomplete multivariate Gaussian data, we propose a blind despreading algorithm which can estimate the user number. For the single-user DSSS signals, to overcome the drawbacks concerning convergence towards local minima and the difficulty to choose the initial value and iterative step precisely in optimization methods, a non-iterative blind despreading algorithm based on monotone missing-data model is proposed.
5. Using multi-channel receiver, we propose a blind despreading algorithm based on missing-tensor model for multi-user long-code DSSS signals through the three-dimensional extension of the two-dimensional missing-data model. Due to fully exploiting the structure of spatial-temporal-spreading diversity, the proposed algorithm provides better performance compared to the ones using single-channel receiver.
尽管过去在DSSS信号盲解扩方面已经取得了很多进展,但由于缺乏深入的理论分析,使得问题的解决手段比较单一,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,对于扩频波形估计的理论下界一直没有被研究过;长码DSSS信号的极大似然估计问题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,得到的主要研究成果包括以下几个方面:
1.在确定与随机信号模型条件下,首次由理论上分别推导了DSSS信号扩频波形估计的CRB,可同时适用于长码与短码情况,为衡量各种扩频波形估计方法的性能提供了理论下界。
2.针对单用户短码DSSS信号的盲同步问题,提出了一种具有低计算复杂度的基于协方差矩阵m1范数改进算法,并推广至多用户且截获信号含有未知频偏的情况;针对短码QPSK-DSSS信号,提出了一种基于恒模特性的扩频序列估计改进算法;通过理论推导证明了扩频波形估计可达到CRB的传统特征分析方法,本质上为高斯极大似然估计器;针对异步短码CDMA信号的盲解扩,通过降维和去噪处理,提出了一种具有低计算复杂度且估计性能更优的改进算法。
3.针对单用户长码DSSS信号,对扩频波形的极大似然估计进行了理论推导,注意到该极大似然估计问题为组合优化问题,提出了一种基于半定规划的盲解扩算法并推广至截获信号含有未知频偏的情况,在低信噪比和短数据条件下相对传统方法具有优良的估计性能且可达到CRB。同时,提出算法可适用于短码DSSS信号。
4.针对多用户长码DSSS信号,确定信号模型和用户个数已知条件下,提出了一种基于缺失数据模型低秩近似的盲解扩算法,并在单用户情况下扩频波形估计可达到CRB;随机信号模型条件下提出了一种基于多元高斯缺失模型极大似然估计的盲解扩算法,可实现用户个数的估计。针对单用户长码DSSS信号,提出了一种基于单调缺失数据模型的非优化迭代盲解扩算法,可避免优化估计方法中的初始值和步长的选取、局部收敛性等问题。
5.针对多用户长码DSSS信号,利用多通道接收技术,通过将二维缺失数据模型向三维空间推广,提出了一种基于缺失张量模型的盲解扩算法。由于充分利用了空、时、码的分集结构,提出算法相对单通道盲解扩算法具有更优估计性能。
Direct sequence spread spectrum (DSSS) signals have been widely used for military and civil communications due to their anti-multipath, anti-jamming, low probability of intercept and multiple access properties. In non-cooperative applications such as communication reconnaissance, wireless spectrum surveillance and localization tracking of illegal communication transmitters, the transmitted information should be recovered without prior knowledge of the spreading sequence at the receiver. Therefore, blind despreading of DSSS signals plays an important role in non-cooperative scenarios.
Although in the past years the study on blind despreading of DSSS signals has witnessed many developments, not so much in problem solving means and with new measures due to lack of profound theoretic investigation. However, some important problems have not been solved satisfactorily. For an example, the theoretical lower bound of spreading waveform estimation has not been studied. Another example is that the Maximum Likelihood Estimate (MLE) of long-code DSSS signals has seldom been evaluated comprehensively under the non-cooperative context.
These problems are comprehensively studied from theoretical viewpoint. The main contributions of this dissertation include some aspects as follows:
1. For the first time, under the stochastical and the deterministic models for the DSSS signals, we derive the Cramér–Rao bound (CRB) for the spreading waveform estimation problem. The derived CRB holds for both long-code and short-code DSSS signals, and gives a performance lower bound for all spreading waveform estimators.
2. For the problem of blind synchronization for single-user short-code DSSS signals, an improved algorithm based on m1 -norm of the covariance matrix is proposed. The proposed algorithm has low computational complexity and can be used for the multi-user signals with unknown carrier offset. For the spreading sequence estimation problem of short-code QPSK-DSSS signals, an improved algorithm based on constant modulus property is proposed. Through theoretical analysis, we prove that the existing eigenanalysis-based spreading waveform estimator, which can approach the CRB, is essentially the Gaussian MLE. Using de-noising and reduced-dimension techniques, an improved blind despreading algorithm for asynchronous CDMA signals is presented, which has low computational complexity and shows good performance.
3. For single-user long-code DSSS signals, we derive the MLE of spreading waveform. Note that the MLE problem belongs to the field of combinatorial optimization. We propose a blind despreading algorithm based on semidefinite programming and extend it to the case when unknown carrier offset exists. The proposed algorithm provides significant performance improvements compared to existing methods in the case of low numbers of data samples and low SNR, and can be applied to the short-code DSSS signals.
4. For multi-user long-code DSSS signals, under the deterministic model and the assumption that the user number is known apriori, we propose a blind despreading algorithm based on low-rank approximation of missing-data model, and the proposed algorithm can approach the CRB in the single-user case. Under the stochastical model, based on the MLE for incomplete multivariate Gaussian data, we propose a blind despreading algorithm which can estimate the user number. For the single-user DSSS signals, to overcome the drawbacks concerning convergence towards local minima and the difficulty to choose the initial value and iterative step precisely in optimization methods, a non-iterative blind despreading algorithm based on monotone missing-data model is proposed.
5. Using multi-channel receiver, we propose a blind despreading algorithm based on missing-tensor model for multi-user long-code DSSS signals through the three-dimensional extension of the two-dimensional missing-data model. Due to fully exploiting the structure of spatial-temporal-spreading diversity, the proposed algorithm provides better performance compared to the ones using single-channel receiver.
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