Matrix Pen Decomposition Algorithm Research And Application In Communication Signal Processing

Matrix pen triangle and diagonal decomposition,such as generalized Schur decomposition (GSD), generalized eigenvalue decomposition (GEVD) and generalized singular values decomposition (GSVD), is a important subject on matrix computing and Matrix pen decomposition has important application to wireless communication and signal processing.The problem on wireless and space-time receptive signal processing often can be come down to matrix pen decomposition. This kind of matrix pen often incudes senser shift corrlection matrix and time delay correlation matrix, they are not Hermitian and positive. Strong correlation or Coherent signal often cause correlative matrix is close to singular, means has a bad condition. It is difficult that investigates approximative singular and unsymmetry positive matrix pen decomposition, but it is important to wireless commiunication signal processing.By investigating matrix decomposition algorithm and its application in wireless communication, the following innovating results are achieved:â‘ The cross-iterative algorithm of matrix generalized Schur decomposition was built up. And it is applied to improve the ESPRIT subspace method on direction of arrival of array signal strong correlating. The estimating precision and probability of recognition is improved.By exchanging the unitary matrix factor from QR and RQ factorization between A, B , and multipling triangle factor inhere, the author derive out the circulative iterative program of pen( A, B ) that converges at triangle matrix pen at last, called cross-iterative algorithm. And it is proved that the convergence of algorithm is equivalent to the one of QR iterative of Schur decomposition of AB ?1. Of course, it is unpractical that straight computing AB ?1. Due to product and inverse calculate, the matrix condition number is bad and iterative computing accuracy can not be promised in limited words length condition. Cross-iterative algorithm avoids computing inverse and product of A &B and the result has approximately same condition number with A, B . The speed is free from the deficient rank of B .In Cross-iterative algorithm, The QR&RQ factorization is independent each other, so do the product of Q and R. So the algorithm is parallel annular structurally.The computing of one step iterative of cross-iterative algorithm fastens on QRF (RQF) and product of Q&R, the inverse program of former. So, it is fit to carry out modularly.â‘¡Recursive cross-iterative algorithm on adaptive GSD and GEVD is set up and is applied to blind identify to unknown CDMA system in fast time varing environment.In actual application, the input data is updated real time. Contrast with batch method, such as QZ algorithm, cross-iterative algorithm is easy to carry out adaptively. Its one step need ( )O n 2 flops to compute GSD of rank one update matrix pen. The author gives a recursive cross-iterative algorithm to achieves adaptive GSD and GEVD,namely generalized subspace tracking. This method with Low-complexity provides an effective way to rapidly calculate the decomposition of matrix pencil update eigenvalue. Distinguish from subspace tracking, the generalized subspace tracking need not the correlation matrix is Hermitian and the orthonormal restriction to generalized eigenvector, so it is fit to identify the ordinary matrix without rows orthogonal each other, such as multiusers'extend sequence matrix of CDMA system.With the help of antenna array, you can realize the detection of blind identification and receiving signal of effective spreading spectrum waveform of user on the unknown of spread spectrum waveform (such as interception, disaster, etc.) of multipath CDMA system desire user. Taking into account the fast time-varying characteristic of multipath channel and the requirements on low complexity of calculation, the author puts forward generalied subspace tracking method on unknown CDMA system blinds identification with antenna array. Based on the recursion cross-iterative algorithm or recursion Lanzocs iterative, we achieves self-adaptive generalied eigenvalue decomposition of correlation matrix pen, and identifies the unknown user'available extend sequence and achieve blind multiuser detection. Computer simulation shows the validity of GSST, and makes a comparison of the two adaptive subspace tracking methods between Lanzocs iterative algorithm and recursive cross-iterative algorithm proposed by the author. The results show that cross-iterative algorithm is superior to lanzocs method for signal processing in the convergence rate and numerical accuracy of steady output.â‘¢Tangent CCD algorithm on accurate calculating canonical correlation decompoction is built up. It is applied to blind multiuser detection of multipath CDMA with correlation noise, and the output permance of detector of recepted signal is improved.Canonical Correlation Analysis (CCA) is a statistical analysis method to examine the correlation between two random variables, by analyzing the correlation between two linear transformations of data, then searching for the public model. It considers the correlation between two sets of input data and the inter-relation of data from each group. Canonical correlation decomposition (CCD) is the singular value decomposition of typical correlation coefficient matrix, can achieve maximize relevance between the two linear transformation of data, and thereby obtain the optimal estimation of the relevant parts of the data (i.e., signal). CCD is the singular value decomposition of the product of three matrixes, so it is vulnerable in the impact of bad matrix condition number and element error. The Gram-Schmidt orthogonal preprocessing of data matrix will also be affected by the accumulated error, particularly evident when the matrix is large-scale.Based on the tangent algorithm combines the accurate calculation of the generalized singular value decomposition and the product of singular value decomposition, the author puts forward a tangent algorithm to achieve precise calculation of canonical correlation decomposition. The CCD tangent algorithm need not Gram-schmidt orthogonal preprocessin and exist not accumulated error impact.The CCD tangent algorithm is applied to improve subspace method on multipath CDMA blind multi-user detection with unknown related ambient noise and it estimates accurately of effective characteristic waveform in multipath channel. Simulation shows that the blind multi-user detector has been significant improvement in performance. Compared to existing algorithms, the results of signal detection are not sensitive to the scale of the matrix and condition number.