相干信源波达方向估计中的若干问题研究

发布时间：2018-03-12 16:08

本文选题：阵列信号处理　切入点：波达方向估计　出处：《哈尔滨工业大学》2016年博士论文　论文类型：学位论文

【摘要】：波达方向(DOA)估计在许多阵列系统中有着极为重要的意义。当信号源相干时,信号协方差矩阵不再满秩,使得信号或者噪声子空间的估计不准确。同时,相干源也会给信源数检测带来困难。在这种情况下,常规的信源数检测算法不能提供准确的信源数信息。此外,在低信噪比、小快拍的情况下,多数子空间算法不能提供正确的DOA估计值,造成它们的均方误差急剧地偏离克拉美罗界。这种现象被称为“门限效应”,在信号源相干时表现得尤为明显。以上种种问题都会造成许多现有的DOA估计算法失效,从而无法提供可靠的DOA估计值。尽管空间平滑可以有效地处理相干源的DOA估计问题,但是它依旧存在许多缺点,例如,该方法需要知道相干信源数的先验信息来确定平滑次数;它是以损失阵列自由度为代价的,即在空间平滑后,阵列孔径存在较大的损失,造成后续的DOA估计算法无法实现最优估计。本文主要针对上述相干信源的DOA估计问题进行深入研究,相应的成果包括以下几点:1)针对相干源DOA估计空间平滑算法存在的阵列孔径损失问题,提出了一种用于基于主特征矢量分析(PUMA)的相干DOA估计算法,并对它进行了理论性能分析。该方法利用线性预测理论将DOA估计问题转化为一个一元多项式求根问题。PUMA在求解多项式系数时只需要两三次迭代即可获得较好的估计性能;而且每步迭代具有闭式解,使得它的复杂度很低,远小于ML算法。但是,PUMA保留了ML算法在高信噪比时的统计有效性。相比空间平滑算法,PUMA的优点是无需相干信源数的先验信息以及不存在阵列孔径损失的问题。由于PUMA算法可以最大化利用阵列的自由度,它可以分辨的相干信源数远大于空间平滑算法。在单信源情况下,本文证明了PUMA算法的最优统计特性,并提出了一种工作在实数域的酉PUMA算法来进一步降低复杂度。仿真结果证明了PUMA及其改进方法的有效性,同时验证了理论分析的正确性。2)针对相干源情况下信源数难以准确估计的问题,提出了两种无需信源数信息的DOA估计算法,分别用于解决空间白高斯噪声和空间相关高斯噪声下的相干信源DOA估计问题。第一个算法是针对空间白高斯噪声设计的,它通过选择样本协方差矩阵的行来构造一组具有联合对角结构的Toeplitz矩阵以达到去相干的目的;然后利用这一联合对角结构来设计无需信源数信息的DOA估计器。第二个算法的设计思路与第一个类似。其中最主要的区别在于该方法预先利用高阶累积量来处理空间相关高斯噪声;其次,通过构造联合对角结构的伪协方差矩阵来设计无需信源数信息的DOA估计算法。一般的,在相同的物理条件下,第二个算法的性能会好于前一个,但是复杂度也更高。3)针对低信噪比、小快拍的情况下DOA估计算法估计性能低的问题,提出了两种具有较好门限性能的相干DOA估计算法。i)提出了一种改进的PUMA算法,该方法首先利用PUMA生成多余两倍信源数的DOA候选值,然后利用最大似然代价函数从中自适应地挑选出最终的DOA估计值。这种改进的PUMA算法能够有效地改善PUMA在低信噪比时的门限性能,同时保留了PUMA在高信噪比时的最优估计特性。ii)提出了一种基于伪噪声重采样的分布式检测算法来提升现有DOA估计方法的门限性能,该方法的原理是利用外加噪声来扰动原有样本中所携带的噪声,从而改变子空间特征,以增加估计出真实DOA的概率。该方法可以多次利用同一样本来生成多组DOA估计值;通过设计合理的选择策略,从中选出最准确的一组作为最终的DOA估计值,以此来降低门限效应。计算机仿真实验验证了本文算法的有效性。
[Abstract]:Direction of arrival (DOA) estimation in many array system has a very important significance. When the signal sources are coherent, the signal covariance matrix is no longer full rank, so that the signal or noise subspace estimation is not accurate. At the same time, coherent sources would bring difficulties to the source number detection. In this case, not the number of sources conventional methods provide accurate information of the source number. In addition, in low SNR, small sample case, most subspace algorithm can not provide the correct estimation of DOA, caused by their mean square error dramatically deviates from the CRLB. This phenomenon is called the "threshold effect" in the signal source coherent is particularly evident. These problems will cause many existing DOA estimation algorithm of failure, which can not provide reliable estimates of DOA. Although the spatial smoothing can effectively deal with the estimation of coherent sources of DOA, but it depends on The old there are many disadvantages, for example, the method needs to know the number of coherent signals prior information to determine the number of smooth; it is based on the degree of freedom at the cost of the loss of the array, namely the spatial smoothing, larger array aperture loss caused by subsequent DOA estimation algorithm can not achieve optimal estimation. This paper studies deeply the main problems above the DOA estimation of coherent sources, the corresponding results are as follows: 1) to solve the problem of the loss of the array aperture spatial smoothing algorithm for DOA estimation of coherent sources, for analysis of the main feature vector (PUMA) is proposed based on the coherent DOA estimation algorithm, and its theoretical performance analysis. The method of using linear the DOA estimation problem is transformed into a.PUMA polynomial root finding problem in solving polynomial coefficients requires only two or three iterations to obtain better estimates of prediction theory; and each Step iterative has closed solution, so its complexity is low, far less than the ML algorithm. However, PUMA retains the statistical validity of the ML algorithm in the high SNR. Compared with the spatial smoothing algorithm, the advantage of PUMA is the number of coherent signals without prior information and there is no loss of the array aperture. Because the PUMA algorithm can maximize the degree of freedom of the array, it is far greater than the number of coherent signals can be resolved. The spatial smoothing algorithm in the single source case, we prove that the optimal statistical properties of PUMA algorithm, and proposed a work in the unitary PUMA algorithm in real domain to further reduce the complexity. The simulation result shows that the the effectiveness of PUMA and the improved method, and proved the correctness of the theoretical analysis of the.2) for coherent source case is difficult to accurately estimate the number of sources, put forward two kinds of information without the source number estimation algorithm for DOA, respectively. To solve the problem of coherent sources DOA estimation space white Gauss noise and spatial correlation of Gauss noise. The first algorithm is designed for space white Gauss noise, it through the selection of the sample covariance matrix to construct a set of combined with diagonal structure Toeplitz matrix in order to achieve the purpose of decoherence; DOA estimator and then use the diagonal joint no need to design the source number information. The second algorithm design and similar to the first. The main distinction is that the advance method using high order cumulants to deal with space related Gauss noise; second, to design without the source number information through the pseudo covariance matrix is constructed with diagonal structure DOA estimation algorithm. In general, in the same physical conditions, performance of the second algorithms will be better than the previous one, but the complexity is higher.3) in low SNR, a small number of snapshots. Under the condition of the low performance of DOA estimation algorithm has better estimation, two threshold performance coherent DOA estimation algorithm for.I is proposed in this paper) puts forward a kind of improved PUMA algorithm, the DOA candidate firstly using PUMA to generate two times the number of sources of excess value, and then use the maximum likelihood cost function is adaptively selected from the final the estimated DOA. The improved PUMA algorithm can effectively improve the PUMA threshold performance when SNR is low, while retaining the characteristics of.Ii PUMA in optimal estimation at high SNR) proposed a distributed detection algorithm based on resampling pseudo noise to improve the performance of existing DOA estimation threshold method and the principle of this method is to use external noise to carry the original disturbance noise in the sample, thus changing the subspace feature, in order to increase the estimated probability of real DOA. This method can use many of the same sample life A set of DOA estimation values is set up. By designing a reasonable selection strategy, the most accurate group is selected as the final DOA estimation value to reduce the threshold effect. Computer simulation experiments verify the effectiveness of the algorithm.

【学位授予单位】：哈尔滨工业大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：TN911.7

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