Two-dimensional Sparse Array Signal Processing Based On Matrix Filling

Compared with the traditional uniform planar array,the aperture of antenna array is increased in the sparse array,thus the scanning beam is narrowed,and the effects of mutual coupling between array elements are weaken.Although the grating lobe is suppressed by random sparse array,the rise of average sidelobe is inevitable,to tackle those problem,this dissertation investigates on the two-dimensional(2D)array signal processing in sparse array,including the adaptive digital beamforming algorithm based on matrix completion,the spatial spectrum estimation algorithm based on matrix completion,and the 2D ESPRIT algorithm in sparse array,A more accurate estimation can be obtained and the performance of the array signal processing in sparse array is close to the performance of the whole array signal processing.The main work of this dissertation are accomplished as follows:(1)Research on 2D Adaptive digital beamforming based on the linearly constrained minimum variance criterionTo solve the problem that a large number of antennas and sampling equipment are required in uniform planar array,a singular value threshold based eigenvalues decomposition linearly constrained minimum variance criterion(SVT-ELCMV)algorithm and an Accelerated Proximal Gradient singular value thresholding based Linearly Constrained Singular Canceler(APG-LCSC)algorithm are proposed.The beamformer of the SVT-ELCMV algorithm was formed based on the modified LCMV algorithm taking use of the signal which has been recovered by SVT algorithm.And in the APG-LCSC algorithm,left and right singular value vector of the received signal matrix is achieved via matrix completion,and then a linearly constrained singular canceler is obtained by employing the singular value vector.These proposed algorithm decreases the required number of antennas,lowers the computational complexity.It keeps valid at the situation when some elements of the sparse array do not work.Compared with conventional 2D beamforming algorithms,the APG-LCSC algorithm avoids solving the auto-correlation matrix of received signal and functions properly even with few elements corrupted.(2)Research on 2D Direction of arriva estimation based on multiple signal classificationTo improve the performance of two dimensional Direction-of-Arrival(2-D DOA)estimation in sparse array,a singular value threshold based multiple signal classification(SVT-MUSIC)algorithm and a Fixed Point Continuation Polynomial-Roots(FPC-ROOT)algorithm are proposed.The sparse array is built to suit the requests of matrix completion in the SVT-MUSIC algorithm,and then the direction-of-arrival model based on matrix completion is sited up which satisfies the null space property(NSP).This algorithm could recovery the sparse signals to the complete signals by taking use of matrix completion,and then estimates 2D DOAs.On the basis of the above algorithm,this paper presents the FPC-ROOT algorithm,In which left and right singular vectors of received signals matrix are achieved using the matrix completion algorithm,and the 2D DOA estimation can be acquired through solving the polynomial roots.Using these algorithm,the estimation accuracy is increased,and the angle ambiguity problem is avoided.The FPC-ROOT algorithm can achieve high accuracy of 2D DOA estimation in sparse array,without solving auto-correlation matrix of received signals and scanning of two-dimensional spectral peak.(3)Research on 2D Direction of arriva estimation based on ESPRIT algorithmIn order to apply ESPRIT algorithm to two-dimensional sparse array,this dissertation presents a singular value threshold based estimation of signal parameters via rotational invariance technique(SVT-ESPRIT)algorithm and an Accelerated Proximal Gradient singular value thresholding based Subarray Reconstruct ESPRIT(APG-SRESPRIT)algorithm by introducing matrix completion.The sparse signals is recovered to the complete signals by taking use of matrix completion in SVT-ESPRIT algorithm,then the signal space is divided to two sub array,and 2D DOA estimation can be achieved through rotation invariance between subspaces.is proposed,the sparse signal model is recovered to the complete signal model via matrix completion,and the subarrays is reconstructed to build the merged matrix,and then the singular value decomposition(SVD)of the merged matrix is solved to acquire 2D DOA estimation.Compared with conventional algorithms,the ESPRIT algorithm can be used in sparse array in the these proposed algorithm,so the adaptability of the algorithm is improved.By dividing sub array and building the combined matrix suitably,the APG-SRESPRIT algorithm can obtain the target angles through only once SVD in sparse array,and the target angles would match automatically.