基于有限新息率的差分协阵欠定空间谱估计研究

In the military and civilian fields, with the increasing complexity of the electromagnetic environment, the underdetermined spatial spectrum estimation, where the number of sensors is less than the number of signals, is attracting more and more attention. Now, the difference co-array has become an important means to deal with the problem of underdetermined spatial spectrum estimation. However, the traditional algorithms have their shortcomings when applied on the difference co-array, e.g. only partly taking advantage of the degree of freedom of the difference co-array, the existence of grid effect and so on. In this project, the finite rate of innovation method which arises from the time domain sampling theory is introduced into the spatial domain and its application prospects on underdetermined spatial spectrum estimation with difference co-array are explored. Firstly, the model transformation from the difference co-array to the finite rate of innovation and the theoretical basis are analyzed. On this basis, the algorithm for the narrowband signals is proposed and then extended to the wideband scenario via frequency focusing without angle pre-estimation. Secondly, the finite rate of innovation is applied on the difference polarization diversity array to solve the problem of underdetermined spatial spectrum estimation under signals with multiple polarizations. Finally, the finite rate of innovation based on model fitting is adopted to study the self-calibration of sensor gain and phase error under underdetermined condition. The study of this project will hopefully break through the limitations of traditional methods and bring new theories, ideas and algorithms for the underdetermined spatial spectrum estimation with difference co-array.

在军用和民用领域，随着电磁环境的日益复杂，欠定空间谱估计（即传感器阵元数小于信号源数）受到越来越多的重视。目前，差分协阵已成为解决欠定空间谱估计问题的重要手段，但传统算法应用于差分协阵存在局限性，如无法充分利用差分协阵阵列自由度、存在网格效应等。本项目拟将时域采样理论中的有限新息率方法引入到空域，探索其在差分协阵欠定空间谱估计的应用前景。项目首先研究差分协阵数学模型向有限新息率模型的转化，分析其应用的理论基础，在此基础上提出针对窄带信号的算法，并通过无需角度预估的频域聚焦扩展到宽带场景。其次，研究有限新息率应用于差分极化分集阵，解决多极化信号场景下的欠定空间谱估计问题。最后采用基于模式拟合的有限新息率方法研究欠定条件下的阵元幅相误差自校正。通过本项目的研究将有望突破传统方法的局限，为差分协阵欠定空间谱估计带来新的理论、思路及算法。

可估计的信号源数不能超过阵元数的限制是空间谱估计的瓶颈问题之一。我们把信号源数大于阵元数的参数估计称为欠定估计。欠定空间谱估计的实现需要采用差分协阵的概念，但传统算法应用于差分协阵存在无法充分利用阵列自由度以及网格效应等问题。本项目将时域采样理论中的有限新息率理论引入到空域，探索其在差分协阵欠定空间谱估计的应用。项目分别研究了基于有限新息率理论的差分协阵窄带欠定空间谱估计、基于有限新息率理论的差分协阵宽带欠定空间谱估计研究、基于有限新息率理论的空间谱及信号极化参数欠定联合估计研究，以及基于有限新息率理论的阵列互耦自校正。研究结果显示，有限新息率理论中的零化滤波方法具有实现超分辨空间谱估计的能力，没有网格效应且计算复杂度低。应用在互质阵差分协阵时可借助于插值手段从而利用阵列的全部自由度。基于有限新息率理论实现的欠定空间谱估计算法需要设计对应的零化滤波器，而零化滤波器的设计可通过求解非线性最小二乘问题实现。本项目的科学意义在于，借助于有限新息率率理论，一方面可提高算法对差分协阵阵列自由度的利用率，另一方面提出了用零化滤波方法实现超分辨空间谱估计的新途径，可用来处理空间谱估计相关问题，提高算法性能。