统计通信信号处理技术研究
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摘要
检测和滤波是统计信号处理的两个基本内容。噪声中的信号检测是通信、雷达、声纳等应用领域中的经典问题,寻找一个合适的检测统计量是问题的关键,利用高阶统计量有助于提高信号检测性能,CDMA系统已被广泛民用,在民为军用的情况下,针对通信侦察的需求,研究基于高阶统计量直扩码分多址(DS-CDMA)信号检测十分必要。自适应滤波算法是信道均衡、回波对消、系统辨识、参数估计等的重要技术,在实际应用中经常遇到大量的具有显著尖峰脉冲特性的信号和噪声,其服从α稳定分布,采用基于分数低阶统计量理论的自适应滤波算法,能够保证信号处理系统性能不出现退化。
本文对基于高阶统计量的DS-CDMA信号检测理论与方法、基于分数低阶统计量的自适应滤波算法做比较深入的研究,主要研究成果如下:
1)推导得到了DS-CDMA信号的四阶累积量及矩的表达式,为提出检测方法提供了理论依据。证明了同步DS-CDMA信号和异步DS-CDMA信号有相同的一至四阶累积量及矩,因此采用同一检测统计量,检测性能相同;指出了接收信号中的噪声分量对四阶矩切片起增强作用,而对四阶累积量切片没有贡献,因此,基于四阶矩切片的检测方法性能优于基于四阶累积量切片的检测方法性能;进一步指出了不同的四阶矩切片抑制高斯白噪声能力不同,(τ,τ,τ)切片与(0,0,τ)切片的四阶矩相同,且他们抑制高斯白噪声能力优于(0,0,0)切片和(0,τ,τ)切片的四阶矩,所以基于前二种四阶矩切片的DS-CDMA信号检测方法性能相同,且优于后二种四阶矩切片的检测方法性能。仿真结果与上述结论一致。
2)基于上述理论,利用假设检验,提出了基于四阶统计量的时域检测方法和频域检测方法。时域检测方法需要选择合适的延迟量τ,在盲侦察接收中,此方法难以保证检测性能。频域检测方法与τ无关,为了降低估计误差噪声的影响,频域检测方法采用了降噪处理,频域检测方法性能优于τ最佳选择的时域检测方法性能,优于自相关检测法,可用于DS-CDMA盲侦察。
3)研究了在α稳定分布背景下最小平均P范数类自适应滤波算法。为提高自适应滤波算法性能,提出了基于最小平均P范数准则的自适应数据块滤波算法,包括:定步长数据块最小平均P范数(DBLMP)及其归一化(DBNLMP)算法、变步长数据块归一化最小平均P范数(VDBNLMP)算法和广义数据块归一化最小平均P范数(GDBNLMP)算法。VDBNLMP算法既保持了DBNLMP算法收敛速度比NLMP算法快的优点,又具有稳态失调比NLMP算法小的优点;GDBNLMP算法的收敛速度比“动量”广义NLMP算法快。
4)研究了在α稳定分布背景下自适应格型滤波算法。提出了基于最小平均P范数准则的自适应广义伯格算法(GBurgAL)和基于最小P范数准则的自适应格型滤波算法(LPL)。GburgAL算法的稳定性和抗脉冲噪声能力比已有的基于最小平均P范数准则的格型算法(LMPL)和基于最小均方准则的格型算法(LMSL)都强;LPL算法比GburgAL算法和最小二乘格型滤波算法(LSL)具有更快的收敛速度和更强的抗脉冲噪声能力,LPL算法性能受参数影响比GburgAL算法小,参数选择简单。因此,LPL算法是目前性能最好的一种格型算法。
The detection and filtering are basic contexts of statistical signal processing. Signal detection in noise is a typical problem of communication, radar, sonar, and other applications areas. To find an appropriate detection statistic is the key problem. Higher-order statistics are helpful to improve detection performance. CDMA system is widely used in civil. When it is used in military, for communication reconnaissance, the detection of DS-CDMA signal based on higher-order statistics is very important. Adaptive filtering algorithms are important technologies in such diverse fields as channel equalization, echo cancellation, system identification, parameter estimation, among others. In practical applications, many signals and noises often accompany spikes and impulsiveness, andα-stable distribution can preferably describe these signals and noises. Adaptive filtering algorithms based on fractional lower-order statistics(FLOS) show better performance inα-stable distribution environment.
This dissertation deals with mainly concerned on the study of two aspects, which are DS-CDMA signal detection theory and methods based on higher-order statistics, and adaptive filtering algorithms based on fractional lower-order statistics, the main contributions are as follows.
1)The fourth-order cumulants and moments of DS-CDMA signal are derived, which are fundament of detection methods. It is shown that the first-order to fourth-order cumulants and moments for synchronization DS-CDMA signal and asynchronous DS-CDMA signal are the same. Thus the detection performance using the same statistics for the synchronization DS-CDMA signal and the asynchronous DS-CDMA signal is the same. And it is also shown that the noise is useful to fourth-order moment slices, but useless to fourth-order cumulant slices. Thus, the detection performance of methods based on fourth-order moment slices is better than that of methods based on fourth-order cumulant slices. Different fourth-order moment slices have different noise cancellation capability. The fourth-order moment with slice (τ,τ,τ) is the same as that with slice (0,0,τ), and their noise cancellation capability is superior to the fourth-order moment with slice (0,0,0) and slice (0,τ,τ). Thus, the detection performance of methods based on the former two fourth-order moment slices for DS-CDMA signal is the same, and is better than that of methods based on the latter two fourth-order moment slices.
2)Using above theories and hypothesis test theory detection methods based on fourth-order statistics in time domain and in frequency domain are proposed. It is shown that the performance of detection methods in time domain is dependent on the delayτ, and detection performance is difficult to ensure in communication blind reconnaissance. The performance of detection method in frequency domain is not dependent on the delayτ. To reduce the effect of estimation error of the fourth-order moment slice, de-noise processing is used. The performance of detection method in frequency domain is better than that of methods in time domain, and of the correlation method. The detection method in frequency domain can be used to blind reconnaissance for DS-CDMAsignals.
3)The least mean P-norm type algorithms inα-stable distribution environment are studied. To improve the performance of adaptive filtering algorithms, adaptive data block filtering algorithms based on the least mean P-norm criterion are proposed, which are fixed step-sized data block least mean P-norm (DBLMP) algorithm and its normalized version (DBNLMP algorithm), variable step-sized data block normalized least mean P-norm (VDBNLMP) and generalized data block normalized least mean P-norm (GDBNLMP) algorithm. And the VDBNLMP algorithm retains the advantage of faster convergence speed which is achieved by the DBNLMP algorithm as compared to the NLMP algorithm. Furthermore, it also has the advantage of smaller steady misadjustment as compared to the NLMP algorithm. The GDBNLMP algorithm converges faster than the“Momentum”-type generalized NLMP (Mom-GNLMP) algorithm.
4)Adaptive lattice filtering algorithms inα-stable distribution environment are studied. An adaptive generalized Burg algorithm (GBurgAL) based on the least mean p-norm criterion and an adaptive lattice filtering algorithm (LPL) based on the least p-norm criterion are proposed. GBurgAL has better steady misadjustment and stronger resisting impulse noise capability than least mean p-norm lattice(LMPL) algorithms and least mean square lattice(LMSL) algorithms. LPL has faster convergence rate and stronger resisting impulse noise capability than GBurgAL and least square lattice(LSL) algorithm. And the effect of parameters on the performance of LPL is less than that on the performance of GBurgAL, and parameters of LPL are easy to select. Therefore, LPL is the best lattice algorithm at present.
本文对基于高阶统计量的DS-CDMA信号检测理论与方法、基于分数低阶统计量的自适应滤波算法做比较深入的研究,主要研究成果如下:
1)推导得到了DS-CDMA信号的四阶累积量及矩的表达式,为提出检测方法提供了理论依据。证明了同步DS-CDMA信号和异步DS-CDMA信号有相同的一至四阶累积量及矩,因此采用同一检测统计量,检测性能相同;指出了接收信号中的噪声分量对四阶矩切片起增强作用,而对四阶累积量切片没有贡献,因此,基于四阶矩切片的检测方法性能优于基于四阶累积量切片的检测方法性能;进一步指出了不同的四阶矩切片抑制高斯白噪声能力不同,(τ,τ,τ)切片与(0,0,τ)切片的四阶矩相同,且他们抑制高斯白噪声能力优于(0,0,0)切片和(0,τ,τ)切片的四阶矩,所以基于前二种四阶矩切片的DS-CDMA信号检测方法性能相同,且优于后二种四阶矩切片的检测方法性能。仿真结果与上述结论一致。
2)基于上述理论,利用假设检验,提出了基于四阶统计量的时域检测方法和频域检测方法。时域检测方法需要选择合适的延迟量τ,在盲侦察接收中,此方法难以保证检测性能。频域检测方法与τ无关,为了降低估计误差噪声的影响,频域检测方法采用了降噪处理,频域检测方法性能优于τ最佳选择的时域检测方法性能,优于自相关检测法,可用于DS-CDMA盲侦察。
3)研究了在α稳定分布背景下最小平均P范数类自适应滤波算法。为提高自适应滤波算法性能,提出了基于最小平均P范数准则的自适应数据块滤波算法,包括:定步长数据块最小平均P范数(DBLMP)及其归一化(DBNLMP)算法、变步长数据块归一化最小平均P范数(VDBNLMP)算法和广义数据块归一化最小平均P范数(GDBNLMP)算法。VDBNLMP算法既保持了DBNLMP算法收敛速度比NLMP算法快的优点,又具有稳态失调比NLMP算法小的优点;GDBNLMP算法的收敛速度比“动量”广义NLMP算法快。
4)研究了在α稳定分布背景下自适应格型滤波算法。提出了基于最小平均P范数准则的自适应广义伯格算法(GBurgAL)和基于最小P范数准则的自适应格型滤波算法(LPL)。GburgAL算法的稳定性和抗脉冲噪声能力比已有的基于最小平均P范数准则的格型算法(LMPL)和基于最小均方准则的格型算法(LMSL)都强;LPL算法比GburgAL算法和最小二乘格型滤波算法(LSL)具有更快的收敛速度和更强的抗脉冲噪声能力,LPL算法性能受参数影响比GburgAL算法小,参数选择简单。因此,LPL算法是目前性能最好的一种格型算法。
The detection and filtering are basic contexts of statistical signal processing. Signal detection in noise is a typical problem of communication, radar, sonar, and other applications areas. To find an appropriate detection statistic is the key problem. Higher-order statistics are helpful to improve detection performance. CDMA system is widely used in civil. When it is used in military, for communication reconnaissance, the detection of DS-CDMA signal based on higher-order statistics is very important. Adaptive filtering algorithms are important technologies in such diverse fields as channel equalization, echo cancellation, system identification, parameter estimation, among others. In practical applications, many signals and noises often accompany spikes and impulsiveness, andα-stable distribution can preferably describe these signals and noises. Adaptive filtering algorithms based on fractional lower-order statistics(FLOS) show better performance inα-stable distribution environment.
This dissertation deals with mainly concerned on the study of two aspects, which are DS-CDMA signal detection theory and methods based on higher-order statistics, and adaptive filtering algorithms based on fractional lower-order statistics, the main contributions are as follows.
1)The fourth-order cumulants and moments of DS-CDMA signal are derived, which are fundament of detection methods. It is shown that the first-order to fourth-order cumulants and moments for synchronization DS-CDMA signal and asynchronous DS-CDMA signal are the same. Thus the detection performance using the same statistics for the synchronization DS-CDMA signal and the asynchronous DS-CDMA signal is the same. And it is also shown that the noise is useful to fourth-order moment slices, but useless to fourth-order cumulant slices. Thus, the detection performance of methods based on fourth-order moment slices is better than that of methods based on fourth-order cumulant slices. Different fourth-order moment slices have different noise cancellation capability. The fourth-order moment with slice (τ,τ,τ) is the same as that with slice (0,0,τ), and their noise cancellation capability is superior to the fourth-order moment with slice (0,0,0) and slice (0,τ,τ). Thus, the detection performance of methods based on the former two fourth-order moment slices for DS-CDMA signal is the same, and is better than that of methods based on the latter two fourth-order moment slices.
2)Using above theories and hypothesis test theory detection methods based on fourth-order statistics in time domain and in frequency domain are proposed. It is shown that the performance of detection methods in time domain is dependent on the delayτ, and detection performance is difficult to ensure in communication blind reconnaissance. The performance of detection method in frequency domain is not dependent on the delayτ. To reduce the effect of estimation error of the fourth-order moment slice, de-noise processing is used. The performance of detection method in frequency domain is better than that of methods in time domain, and of the correlation method. The detection method in frequency domain can be used to blind reconnaissance for DS-CDMAsignals.
3)The least mean P-norm type algorithms inα-stable distribution environment are studied. To improve the performance of adaptive filtering algorithms, adaptive data block filtering algorithms based on the least mean P-norm criterion are proposed, which are fixed step-sized data block least mean P-norm (DBLMP) algorithm and its normalized version (DBNLMP algorithm), variable step-sized data block normalized least mean P-norm (VDBNLMP) and generalized data block normalized least mean P-norm (GDBNLMP) algorithm. And the VDBNLMP algorithm retains the advantage of faster convergence speed which is achieved by the DBNLMP algorithm as compared to the NLMP algorithm. Furthermore, it also has the advantage of smaller steady misadjustment as compared to the NLMP algorithm. The GDBNLMP algorithm converges faster than the“Momentum”-type generalized NLMP (Mom-GNLMP) algorithm.
4)Adaptive lattice filtering algorithms inα-stable distribution environment are studied. An adaptive generalized Burg algorithm (GBurgAL) based on the least mean p-norm criterion and an adaptive lattice filtering algorithm (LPL) based on the least p-norm criterion are proposed. GBurgAL has better steady misadjustment and stronger resisting impulse noise capability than least mean p-norm lattice(LMPL) algorithms and least mean square lattice(LMSL) algorithms. LPL has faster convergence rate and stronger resisting impulse noise capability than GBurgAL and least square lattice(LSL) algorithm. And the effect of parameters on the performance of LPL is less than that on the performance of GBurgAL, and parameters of LPL are easy to select. Therefore, LPL is the best lattice algorithm at present.
引文
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