基于高阶非网格的压缩感知框架下非网格DOA估计算法研究

Direction-of-arrival (DOA) estimation is one of the crucial parts in the modern array signal processing field. This project keeps the focus on the situation in which the DOAs of the incident signals do not belong to the sampling set. The statistical analysis of grid error and the high-order Taylor expression are utilized to construct a novel high order off-grid DOA estimation model in the compressed sensing (CS) frame. By applying the unitary transformation, a real-valued sparse Bayesian inference is proposed, in which MA-ECM is presented for the solutions of DOA estimations. Moreover, an approximate expression is used for improving the computational efficiency of the proposed method. The Cramer Rao Bound (CRB) and the performance guarantee condition are derived to demonstrate the performance of the proposed method. Simulation results demonstrate that the proposed real-valued sparse Bayesian method ensures global convergence in the off-grid DOA estimaiton model and it not only estimates the grid error correctly, but also has a satisfactory performance such as high accuracy and high resolution.

波达角（Direction of Arrival, DOA）估计是现代阵列信号处理领域中的重要研究内容。本项目主要针对来波方向不属于空间采样网格集合这类问题，在压缩感知（Compressed Sensing, CS）框架下，通过分析网格误差的统计特性，利用高阶泰勒展开式建立高阶非网格DOA估计数学模型。基于酉变换将复数域运算转换到实数域处理；推导实值稀疏贝叶斯算法；提出Modified Aitken-Expectation Conditional Maximization（MA-ECM）方法，并采用近似表达式对算法进行优化，提高效率。对所提方法进行性能分析，数学推导克拉美罗界和性能保证条件。通过仿真分析可得，在高阶非网格DOA估计数学模型下探究实值稀疏贝叶斯方法具有全局收敛性，该方法不仅能够正确估计网格误差而且具有精度高，分辨率高等优点。