DOA Estimation Approaches Based On NYSTR(?)M Approximation

The rapid development of modem information technology,the research,and application of signal processing has attracted wide attention.Array signal processing,as an important branch of signal processing,is widely used in radar,sonar,communications,medicine,and other military and civilian fields.Array signal processing means that a series of antenna elements are arranged in a certain way to form an antenna array and the signals are received by the antenna array.In the last four decades,scholars have studied the problem theoretically in depth.Some high-resolution subspace-based algorithms for direction of arrival(DOA)estimation was proposed.However,these subspace-based algorithms involve calculating the whole covariance matrix,as well as eigenvalue decomposition(EVD)of the covariance matrix,which bear heavy computational complexity,especially for large-scale arrays.Therefore,this research studied the application of Nystrom approximation in DOA estimation and propose an efficient and reliable DOA estimation approach.The commercial software of MATLAB was used and the simulations were carried out to evaluate the performance of the different approaches such as Multiple Signal Classification(MUSIC),ROOT-MUSIC,Estimation of Signal Parameters via Rotational Invariance Technique(ESPRIT),the Nystrom-based ESPRIT approach,and the proposed Nystrom-based ROOT-MUSIC method.The simulation results show that the ROOT-MUSIC approach provides a better DOA estimating performance than ESPRIT approach.The Nystrom-based ESPRIT approach is more efficient and has low complexity than the traditional ESPRIT approach.The proposed Nystrom-based ROOT-MUSIC method uses Nystrom approximation to estimate the noise subspace,which only needs to calculate two sub-covariance matrices and avoid the EVD of the whole covariance matrix.Therefore,to obtain the noise subspace,the proposed Nystrom-based ROOT-MUSIC approach reduce the computational Complexity significantly.Accordingly,to get the estimated arriving angle,the proposed Nystrom-based ROOT-MUSIC approach costs O(MNK+MK2+M3)and the conventional ROOT-MUSIC approach costs O(M2N+2M3),which bear heavier computational cost as K<<min(M,N).Moreover,the Nystrom approximation method is verified to obtain the signal subspace and noise subspace in theory.The performance of the proposed Nystrom-based ROOT-MUSIC approach and the Nystrom-based ESPRIT approach with respect to SNR and the number of the snapshot respectively are studied.The proposed Nystrom-based ROOT-MUSIC approach provides a better estimating performance than the Nystrom-based ESPRIT approach by increasing the number of snapshot and signal to noise ration.To reduce the computational cost of DOA estimation,the application of the Nystrom approximation method on the field of DOA estimation is evaluated and the efficiency of the Nystrom approximation method are theoretically and experimentally verified.This thesis proposes a new DOA estimation approach called Nystrom-based ROOT-MUSIC approach and by comparing with other DOA estimation approach,it is more efficient and has low complexity.