Research of Adaptive Beamforming Algorithm Based on Matrix Decomposition

In this paper, in order to avoid the sample autocorrelation matrix inversion of antenna array in the adaptive beamforming, first of all, a QR decomposition algorithm is investigated. In the algorithm, the problem of solving weight vector is transformed into the problem of solving triangular linear equations by QR decomposition of direct sample data matrix, and the estimation and the inversion of the autocorrelation matrix is avoided, which improves the numerical robustness. Then, a new algorithm is proposed, which uses the singular value and singular value vector for the calculation of weight vector by singular value decomposition (SVD) of the sample data matrix. The proposed algorithm also avoids the estimation and the inversion of the autocorrelation matrix, and the estimation computation and the estimation error is reduced. Furthermore, the complexity and performance can be compromised by changing the number of zero assigned of the smaller singular value. Simulation result shows that the proposed method possesses almost the same performance as the QR decomposition method, and both the methods can achieve the correct beamforming.