宽带阵列信号波达方向估计算法研究
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摘要
阵列信号处理是信号处理中的一个重要研究分支,在雷达、声呐、无线通信和地震学等诸多领域得到了广泛的应用。随着现代科学技术的发展,宽带信号在阵列信号处理系统中的应用越来越普遍。迄今为止,已经有许多研究学者对宽带信号的波达方向(DOA: direction of arrival)估计进行了研究,并且取得了非常显著的研究成果。由于宽带信号具有较大的信号带宽和较复杂的信号波形,仍然有必要对宽带信号的DOA估计作进一步的研究。本论文的重点是利用均匀线性阵列研究宽带信号的DOA估计技术,本论文的基础是宽带阵列信号的数学模型和矩阵分析理论。本论文的主要研究工作可以概述如下:
首先,在非相干信号子空间算法的基础上,我们提出了一种扩展的投影子空间正交性测试(ETOPS: extended test of orthogonality of projected subspaces)算法。通过使用更多参考频率点的信息,ETOPS算法克服了TOPS算法中最佳参考频率点难以选择的问题,并且与任意选择参考频率点的TOPS算法相比,ETOPS算法具有更好的估计性能。
其次,在频域子空间正交性测试(TOFS: test of orthogonality of frequency subspaces)算法的基础上,利用空间差分技术和空间平滑技术,我们提出了一种宽带不相关信号和宽带相干信号DOA估计算法。该算法先利用TOFS算法对宽带不相关信号的DOA进行估计;然后对各个频率点的空间差分矩阵的特征值矩阵取绝对值操作来构造新矩阵,并通过空间平滑技术对相干信号进行解相干处理,最后利用TOFS算法估计出宽带相干信号的DOA。该算法对宽带不相关信号和宽带相干信号的DOA估计是分开进行的,因此该算法能够应用在阵元个数小于信号个数的场合。
再次,当阵列噪声是相关色噪声时,现有的大部分宽带信号DOA估计算法的估计性能会急剧恶化或者失效。基于矩阵变换技术和聚焦技术,我们提出了两种色噪声背景下的宽带相干信号DOA估计算法,其中色噪声的协方差矩阵具有Toeplitz结构。首先利用空间差分技术去除具有Toeplitz型协方差矩阵的相关噪声的影响,之后两种算法采用不同的方法来估计宽带相干信号的DOA。第一种算法先对各个频率点的空间差分矩阵的特征值矩阵取绝对值操作来构造新矩阵,然后利用旋转不变子空间算法中的聚焦准则进行聚焦操作,最后对聚焦平滑后的矩阵利用多重信号分类(MUSIC: multiple signal classification)算法估计出宽带相干信号的DOA;第二种算法先对各个频率点的空间差分矩阵取平方操作来构造新矩阵,然后进行聚焦操作,最后对聚焦平滑后的矩阵利用传播算法估计出宽带相干信号的DOA。虽然两种算法的估计性能大致相同,但是第二种算法的计算量要远小于第一种算法,因此第二种算法是一种更加高效的色噪声背景下的宽带相干信号DOA估计算法。
最后,基于一致聚焦的思想和双边相关变换的聚焦准则,我们提出了一种宽带信号DOA估计算法。通过一致聚焦矩阵的构造,该算法克服了双边相关变换算法中需要对方位角度进行预估计的缺点,并且是一种低复杂度的宽带信号DOA估计算法。
Array signal processing is an important research branch of the signal processing, and has been widely applied in many fields, such as radar, sonar, wireless communications and seismology. With the development of the modern science and technology, wideband signals have been used more and more commonly. To this day, there are many researchers have studied the direction-of-arrival (DOA) estimation for wideband signals, and have made many significant research results. Because broadband signals possess large signal bandwidth and more complex waveform, it is still necessary to further study the DOA estimation for wideband signals. The main objective of this thesis is to study the DOA estimation technology for wideband signals by using uniform linear array, and the mathematic model of wideband array signals and the theory of matrix analysis are the underlying basis. The main contributions of the thesis are listed as follows:
Firstly, we propose an extended test of orthogonality of projected subspaces algorithm (ETOPS) based on the incoherent signal subspace method (ISSM). By using more information from several reference frequencies, ETOPS overcomes the problem existed in TOPS that it is difficult to choose the optimal frequency, and its performance outperforms that of TOPS with arbitrarily chosen reference frequency.
Secondly, based on the test of orthogonality of frequency subspaces algorithm (TOFS), we propose a new DOA estimation method for wideband uncorrelated and coherent signals by using the spatial differencing technique and the spatial smoothing technique. The method obtains the DOA estimates of wideband uncorrelated signals by using TOFS directly. Then, at each frequency bin, a new matrix is constructed by performing the absolute operation on the eigen-value matrix of the spatial difference matrix. Afterwards, the coherency of coherent signals is removed with the help of the spatial smoothing technique and the DOAs of coherent signals are estimated by applying TOFS accordingly. Because the uncorrelated and coherent signals are resolved separately, the method is suitable to the scenario that the number of array elements is larger than that of signals.
Thirdly, the performance of most of the existing wideband DOA estimation methods degrades severely when the array noise is correlated. Based on the matrix transformation technology and focusing technology, two DOA estimation algorithms for wideband coherent signals are proposed in the presence of unknown correlated noise, whose covariance matrix is of Toeplitz structure. By using spatial differencing technique, the effect of correlated noise with Toeplitz-structure covariance matrix is removed. Afterwards, the two methods make use of different ways to estimate the DOAs of wideband coherent signals. In the first algorithm, by taking the absolute value of eigenvalue matrix of the spatial difference matrix at each frequency bin, a new matrix is constructed accordingly. Then, the focusing operation is performed with the exploitation of the focusing rule in rotation signal subspace method. Finally, the DOAs of wideband coherent signals can be estimated by applying MUSIC (multiple signal classification) on the newly coherently averaged covariance matrix. In the second algorithm, by performing the squaring operation on the spatial difference matrix at each frequency bin, a new matrix is construted. Then, the focusing operation is performed accordingly. Finally, the DOAs of wideband coherent signals can be obtained by exploiting the propagator method to the newly coherently averaged covariance matrix. Although the estimation performance of the two algorithms is almost same, the computational burden of the second one is far less than that of the first one. Therefore, the second one is a more effective DOA estimation method for wideband coherent signals in the presence of unknown correlated noise with Toeplitz -structure covariance matrix.
Finally, based on the idea of consistent focusing and the focusing rule of two sided transformation (TCT), we propose a wideband DOA estimation method. By constructing the consistent focusing matrix, the method overcomes the disadvantage that the initial DOAs should be pre-estimated in TCT and it is a low-complexity DOA estimation method for wideband signals.
首先,在非相干信号子空间算法的基础上,我们提出了一种扩展的投影子空间正交性测试(ETOPS: extended test of orthogonality of projected subspaces)算法。通过使用更多参考频率点的信息,ETOPS算法克服了TOPS算法中最佳参考频率点难以选择的问题,并且与任意选择参考频率点的TOPS算法相比,ETOPS算法具有更好的估计性能。
其次,在频域子空间正交性测试(TOFS: test of orthogonality of frequency subspaces)算法的基础上,利用空间差分技术和空间平滑技术,我们提出了一种宽带不相关信号和宽带相干信号DOA估计算法。该算法先利用TOFS算法对宽带不相关信号的DOA进行估计;然后对各个频率点的空间差分矩阵的特征值矩阵取绝对值操作来构造新矩阵,并通过空间平滑技术对相干信号进行解相干处理,最后利用TOFS算法估计出宽带相干信号的DOA。该算法对宽带不相关信号和宽带相干信号的DOA估计是分开进行的,因此该算法能够应用在阵元个数小于信号个数的场合。
再次,当阵列噪声是相关色噪声时,现有的大部分宽带信号DOA估计算法的估计性能会急剧恶化或者失效。基于矩阵变换技术和聚焦技术,我们提出了两种色噪声背景下的宽带相干信号DOA估计算法,其中色噪声的协方差矩阵具有Toeplitz结构。首先利用空间差分技术去除具有Toeplitz型协方差矩阵的相关噪声的影响,之后两种算法采用不同的方法来估计宽带相干信号的DOA。第一种算法先对各个频率点的空间差分矩阵的特征值矩阵取绝对值操作来构造新矩阵,然后利用旋转不变子空间算法中的聚焦准则进行聚焦操作,最后对聚焦平滑后的矩阵利用多重信号分类(MUSIC: multiple signal classification)算法估计出宽带相干信号的DOA;第二种算法先对各个频率点的空间差分矩阵取平方操作来构造新矩阵,然后进行聚焦操作,最后对聚焦平滑后的矩阵利用传播算法估计出宽带相干信号的DOA。虽然两种算法的估计性能大致相同,但是第二种算法的计算量要远小于第一种算法,因此第二种算法是一种更加高效的色噪声背景下的宽带相干信号DOA估计算法。
最后,基于一致聚焦的思想和双边相关变换的聚焦准则,我们提出了一种宽带信号DOA估计算法。通过一致聚焦矩阵的构造,该算法克服了双边相关变换算法中需要对方位角度进行预估计的缺点,并且是一种低复杂度的宽带信号DOA估计算法。
Array signal processing is an important research branch of the signal processing, and has been widely applied in many fields, such as radar, sonar, wireless communications and seismology. With the development of the modern science and technology, wideband signals have been used more and more commonly. To this day, there are many researchers have studied the direction-of-arrival (DOA) estimation for wideband signals, and have made many significant research results. Because broadband signals possess large signal bandwidth and more complex waveform, it is still necessary to further study the DOA estimation for wideband signals. The main objective of this thesis is to study the DOA estimation technology for wideband signals by using uniform linear array, and the mathematic model of wideband array signals and the theory of matrix analysis are the underlying basis. The main contributions of the thesis are listed as follows:
Firstly, we propose an extended test of orthogonality of projected subspaces algorithm (ETOPS) based on the incoherent signal subspace method (ISSM). By using more information from several reference frequencies, ETOPS overcomes the problem existed in TOPS that it is difficult to choose the optimal frequency, and its performance outperforms that of TOPS with arbitrarily chosen reference frequency.
Secondly, based on the test of orthogonality of frequency subspaces algorithm (TOFS), we propose a new DOA estimation method for wideband uncorrelated and coherent signals by using the spatial differencing technique and the spatial smoothing technique. The method obtains the DOA estimates of wideband uncorrelated signals by using TOFS directly. Then, at each frequency bin, a new matrix is constructed by performing the absolute operation on the eigen-value matrix of the spatial difference matrix. Afterwards, the coherency of coherent signals is removed with the help of the spatial smoothing technique and the DOAs of coherent signals are estimated by applying TOFS accordingly. Because the uncorrelated and coherent signals are resolved separately, the method is suitable to the scenario that the number of array elements is larger than that of signals.
Thirdly, the performance of most of the existing wideband DOA estimation methods degrades severely when the array noise is correlated. Based on the matrix transformation technology and focusing technology, two DOA estimation algorithms for wideband coherent signals are proposed in the presence of unknown correlated noise, whose covariance matrix is of Toeplitz structure. By using spatial differencing technique, the effect of correlated noise with Toeplitz-structure covariance matrix is removed. Afterwards, the two methods make use of different ways to estimate the DOAs of wideband coherent signals. In the first algorithm, by taking the absolute value of eigenvalue matrix of the spatial difference matrix at each frequency bin, a new matrix is constructed accordingly. Then, the focusing operation is performed with the exploitation of the focusing rule in rotation signal subspace method. Finally, the DOAs of wideband coherent signals can be estimated by applying MUSIC (multiple signal classification) on the newly coherently averaged covariance matrix. In the second algorithm, by performing the squaring operation on the spatial difference matrix at each frequency bin, a new matrix is construted. Then, the focusing operation is performed accordingly. Finally, the DOAs of wideband coherent signals can be obtained by exploiting the propagator method to the newly coherently averaged covariance matrix. Although the estimation performance of the two algorithms is almost same, the computational burden of the second one is far less than that of the first one. Therefore, the second one is a more effective DOA estimation method for wideband coherent signals in the presence of unknown correlated noise with Toeplitz -structure covariance matrix.
Finally, based on the idea of consistent focusing and the focusing rule of two sided transformation (TCT), we propose a wideband DOA estimation method. By constructing the consistent focusing matrix, the method overcomes the disadvantage that the initial DOAs should be pre-estimated in TCT and it is a low-complexity DOA estimation method for wideband signals.
引文
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