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最近,Buckley研究出了供宽带波源用的正交低维模型,并把此模型用于到达方向(direction of arrival)估算和波束形成。该低维模型的维数就是波源模型协方差阵的不相关特征向量的个数。当有两个或两个以上波源照射在阵列天线上时,合成信号子空间的维数就是各个波源表征空间的维数之和,以上情况是当波源之间互不相关时才成立的。本文研究一种两波源模型,首先指出,当来自这些源的信号相关时,如在有多路径情况下所发生的那样,合成信号子空间的维数衰减了(collapse)。这个维数减小的量值依赖于相关性程度。我们用直射和多路径信号的互相关矩阵的F-摸(Frobenius norm)作为两个波源之间相关程度的一种度量,借以说明F模是怎样随着延迟时间的增加而减小的;它表明随时延的增加相关性下降的程度。为了减小F-模,我们提出了空间平滑方法,并说明随着子阵列数目的增加这个F-模逐渐趋向于零。然后,推导出了F-摸的上界解析表达式;用这个上界表达式研究随着累进平滑这两个波源的间距和方向对去相关速率的影响。最后,为了说明累进平滑法对DOA估算和波束形成性能的影响,给出了计算机模拟结果。
Recently, Buckley developed an orthogonal low-dimensional model for broadband wave sources and used this model for direction of arrival estimation and beamforming. The dimension of the low-dimensional model is the number of uncorrelated eigenvectors of the covariance matrix of the wave source model. When two or more wave sources are irradiated on the array antenna, the dimension of the composite signal subspace is the sum of the dimensions of each wave source representation space, which is the case when the wave sources are not related to each other. This paper investigates a two-wave source model that first points out the collapse of the dimensions of the composite signal subspace when the signals from these sources are correlated, as occurs in the case of multipath. The magnitude of this reduction in dimension depends on the degree of relevance. We use the Frobenius norm of the cross-correlation matrix of direct and multipath signals as a measure of the degree of correlation between the two wave sources to show how the F-modulus decreases as the delay time increases; it It shows that with the increase of delay the degree of decrease of relevance. In order to reduce the F-mode, we propose a spatial smoothing method and show that as the number of subarrays increases, the F-mode gradually approaches zero. Then, the upper bound analytic expression of F-touch is deduced. Using this upper bound expression, we study the influence of spacing and direction on the decorrelation rate with progressive smoothing. Finally, to illustrate the effect of progressive smoothing on DOA estimation and beamforming performance, computer simulation results are given.