Research And Performance Analysis On KR-Subspace-Based DOA Estimation Algorithms

Direction of Arrival(DOA) estimation is an important research topic in array signal processing and has attracted wide concerns in speech, communications, radar, sonar and many other fields. How to estimate more sources with less number of sensors is one of the important issues in DOA estimation. This is called underdetermined DOA estimation. Using Khatri-Rao(KR) subspace to construct a virtual array is an effective way to solve this problem. Starting with the basic KR subspace method, this thesis has investigated a few methods using the virtual array, and has proposed several algorithms to increase the degree of freedoms(DOF) and improve the performance of existing KR-subspace-based methods. The thesis are organized as follows:Firstly, we study the theoretical foundation of the spatial spectrum estimation. The mathematical model of array signal and the antenna array model have been derived and analyzed. We also describe the basic principle of the spatial spectrum estimation.Secondly, we investigate the KR subspace method based on the uniform linear array(ULA), from the perspectives of narrowband and wideband array signals. The definition of KR product and the basic KR subspace algorithm are introduced. The methods about estimating the noise covariance and reducing the operational dimension are studied. The KR-subspace method of the wideband array signals based on Incoherent Signal-Subspace Method(ISM) and Coherent Signal-Subspace Method(CSM) are deeply investigated.Thirdly, we also focus on nonuniform linear array for KR-subspace DOA estimation problems. From the perspective of difference co-array, we studied the method for calculating the DOF. As an example of nonuniform linear array, the method of DOA estimation using spatial smoothing technique based on the two-level nested array are studied deeply. Through simulation experiments, the KR-subspace DOA estimation method based on the nested array and several nonuniform linear array are compared and analyzed.In this thesis, real-valued KR approaches are developed on the ULA and the nested array. The complexities of subspace decomposition and spectral search are reduced compared with the complex-valued KR approach. By designing a special transformation matrix, the influence of the noise is removed in the meantime while the data is transformed from the complex domain to the real domain. Deploying the sensors with nonuniform spacing can raise the degree of freedom(DOF) and hence help detect more sources in the underdetermined situation. To increase the DOF further, a new nested array geometry is designed. The real-valued denoising KR approach developed on the new nested array can resolve more sources with reduced complexities. Based on the local stationarity of quasi-stationary signals, this thesis proposed a new method, in which the whole MUSIC spatial spectrum and the covariance matching spectrum of each local covariance are combined together when searching spectral peaks. The new method is able to overcome the defect of requiring large number of snapshots in the original KR subspace method. The performance improvement is demonstrated by simulation experiments.