Fast Direction Of Arrival Estimation Based On Krylov Subspace

Direction of arrival(DOA)estimation is one of the core technologies in the field of array signal processing.Most super-resolution DOA estimation algorithms of subspace classes need to accurately estimate the signal-subspace or noise-subspace,the main method which they used is to calculate the Array Covariance Matrix(ACM)and carry out Eigenvalue Decomposition(EVD)on it.However,ACM and its EVD usually involve excessively high computational complexity,especially in large arrays.In order to solve the problem of high computation complexity in subspace estimation,a new fast DOA estimation based on real-value transformation and polynomial order reduction is deeply studied under the framework of Krylov subspace concept in this paper.The main research contents are as follows:Firstly,the basic knowledge of eigenvalue subspace and Krylov subspace are thoroughly analyzed and compared.Besides,the theoretical derivation and experimental simulation of the traditional DOA estimation algorithms in the two subspace classes are carried out,including Multiple Signal Classification(MUSIC)algorithm,Conjugate Gradient(CG)algorithm and Multiple Wiener Filtering(MWF)algorithm.Secondly,aiming at the high complexity problem of calculating ACM and the complex-value iteration process under CG algorithm,a modified conjugate gradient(WCC-CG)algorithm based on Krylov subspace without constructing the covariance matrix is proposed.This method uses real-value changes to transform the iterative process into real-value operations,which effectively reduces the complexity.At the same time,the Wiener-hoff equation is simplified by the least square method,avoiding the calculation of the array covariance matrix.Further,a new construction method of reference signal is proposed in the WCC-CG algorithm,which makes it completely get rid of the dependence on ACM and realizes the fast DOA estimation.Finally,in the multiple Wiener filtering algorithm,for the high complexity of the complex-value forward recursion process and high-order root polynomial,the real-valued reduced-order multilevel Wiener filter root finding(RVRO-MWF-Root)algorithm based on Krylov subspace and the improved reduced-order Wiener filter root finding(IRO-MWF-Root)algorithm are proposed.RVRO-MWF-Root algorithm converts array received data matrix into a real matrix by using real-value transformation,and reduces the order of polynomial to half by using minimum norm method.IRO-MWF-Root algorithm uses the classical root finding method to construct a symmetrical polynomial with coefficients,and the greatest common factor is obtained by using matrix variation method and derivative transformation method,further reducing the order of the polynomial to the number of sources,which not only reduces the computational complexity significantly,but also maintains a good estimation accuracy.