摘要
阵列信号处理作为现代信号处理的一个重要分支,已经被广泛应用于雷达、声纳、通信、地震勘探等多个领域。由于现有的大多数阵列信号的处理方法都需要精确的知道关于阵列流形的信息,它们的性能会受到各种阵列误差(例如阵元间互耦等)的严重影响甚至失效。因此,一大批研究工作者致力于阵列误差校正这个领域的研究并提出了很多的校正方法。但是,目前在该领域仍然存在很多问题尚未解决。由于很多环境下我们不方便放置校正源进行校正,而且阵列的误差也可能会随着周围环境的改变而发生改变,因此在本文中,我们主要针对存在阵元间互耦条件下的无源自校正算法展开研究。本文通过对互耦模型的研究,提出了几种有效的自校正测向算法,主要工作可以概括如下:
首先,我们详细分析了阵元间的互耦对均匀线阵的影响,发现在极小概率的情况下会有盲角出现的可能。由于盲角带来的不利影响,我们在设计阵列的时候就应该尽量避免。在现有的均匀线阵的互耦模型的基础上,我们证明在阵列两端设置一定数量的辅助阵元后,MUSIC(multiple signal classification)和ESPRIT(estimation of signal parameters via rotation invariance techniques)等基于子空间理论的方法可以直接应用而基本不受到互耦的影响。在得到波达方向(DOA:direction of arrival)的初步估计值后,我们可以利用包括辅助阵元在内的全部阵元的输出信号来估计互耦系数。而后还可以利用这些互耦系数的估计值来对DOA进行精估计以进一步提高估计的精度。辅助阵元的方法还可以推广到波束形成方面。利用辅助阵元不但可以有效降低标准的Capon波束形成方法对互耦的敏感性,而且还可以与其他的稳健波束形成方法联合使用来进一步提高性能。色噪声背景下,同样可以利用辅助阵元和四阶累积量(FOC:fourth-ordercumulants)来消除互耦的影响并精确估计出信号DOA。
其次,我们研究了均匀矩形阵列下的互耦模型。由于均匀矩形阵列在各个方向上都具有和均匀线阵类似的几何结构,我们将辅助阵元的方法拓展到均匀矩形阵列和二维DOA估计的情况,并证明通过将均匀矩形阵列边缘上的那些阵元设置为辅助阵元,二维MUSIC算法可以不受互耦的影响,其估计性能会有明显的提升。同时,由于二维空间谱搜索的计算量太过庞大,为了减少其计算量,我们给出一种二次扫描的方法,该方法可以明显缩短二维空间谱搜索的计算时间。和均匀线阵的情况类似,在得到二维DOA的估计之后也可以用来对互耦系数进行估计。为了衡量算法的整体性能,我们还给出了一般的平面阵列在未知互耦的条件下二维DOA估计和互耦估计的均方误差理论下界的显式表达式。通过该下界,我们可以很好的衡量在这种情况下算法的统计性能。
最后,我们以六边形为例,介绍了两种平面阵列下的二维自校正测向算法。其中一种算法可以应用于任意的平面阵列,但是其计算量较大;而另一种算法计算量较小,估计精度也较高,但是只能应用于几何结构具有一定线性的阵列。尽管如此,即使互耦模型失配的情况下,它们仍然可以明显提高DOA的估计精度。在得到的信号DOA的估计值后。我们分别从矩阵的特征空间和约束最优化两个角度出发,给出了两种互耦系数的估计方法。而后利用互耦系数的估计值,可以对信号DOA进行再次精估计。文中的仿真实验也再次验证了算法良好的性能。结尾处对全文的工作进行总结,并指出了今后可能的研究方向。
As an important branch of the modern signal processing,array signal processing has been applied in many fields such as radar,sonar,communication,seismic prospecting and so on.Since most of existing array processing methods need the exact information of the array manifold,they will suffer from severe performance degradation in the presence of array perturbation such as mutual coupling with few exceptions.Therefore, a lot of researchers have made a good effort on this area,and have presented many calibration algorithms.However,there are still some problems need to be resolved.Since it is difficult to set calibration sources in some circumstances and the array perturbations may be changed with the environment,we focus on the autocalibration method of the mutual coupling between array elements without any iterative process or calibration sources.Several algorithms are presented to improved the performance against the mutual coupling in this paper,and the main contributions are illustrated as follows:
First,we give a detail analysis on the mutual coupling effect of uniform linear array (ULA),which indicate the existence of some blind angles in direction finding.Due to the severe effect of the blind angles,we should avoid this condition in array designing. Based on the mutual coupling model of ULA,we prove the non-sensitivity of the subspace based direction finding algorithm,such as MUSIC(multiple signal classification) and ESPRIT(estimation of signal parameters via rotation invariance techniques), against array sensor coupling by applying a group of auxiliary sensors on the side of the array.After getting the preliminary estimation of the DOAs(directions of arrival), we can estimate the mutual coupling coefficients by utilizing an extended sensor array including the auxiliary sensors.After that,a method for refining the DOA estimates can be carried out to further improve the estimation accuracy.Moreover,the auxiliary sensor technique can also be extend to beamforming area.It can not only greatly decrease the sensitivity of the standard Capon beamformer(SCB) against mutual coupling,but also be applied united with other robust beamforming method to further improve their performances.The unknown mutual coupling can also be blindly compensated by the inherent mechanism of the proposed method and the DOA of signals can be accurately estimated based on the fourth-order cumulants(FOC) in colored noise environment.
Second,we study the mutual coupling model of the uniform rectangular array (URA).Since it has a similar structure with the ULA,we also use the auxiliary technique to eliminate the mutual coupling effect during the 2-D DOA estimation.We prove that by setting the sensors on the boundary of the URA as auxiliary sensors,the MUSIC algorithm can still has a significant performance improvement.In order to reduce the computation of the 2-D spectrum search,we give a twice search technique, which can obviously shorten the computation time.Similar with the above,we can estimate the mutual coupling coefficients by using the 2-D DOA estimates.We also provide the Cramer-Rao lower bound(CRB) for the parameter estimations of a general planar array in the presence of unknown of mutual coupling as the benchmark.
At last,take the uniform hexagon array for example,two autocalibration methods are proposed for the 2-D DOA estimation with a planar array.One of them can be applied in any type of planar array with a little high computation.The other one can only be applied in the array with some linearity geometric configuration.However, both of them can achieve an obvious performance improvement even when there is a coupling model mismatch.After getting the DOA estimations,two methods are proposed to estimate the mutual coupling coefficients from the view of eigen-subspace and constrained optimization,respectively.Furthermore,these coefficient estimates can also be used to further improve the accuracy of DOA estimations.The superior performance of them have been validated in the numerical examples.Some significant conclusions and prospect is also included in the end.
引文
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