非对称非正交快速联合对角化算法

针对非对称联合对角化算法收敛速度慢以及有可能收敛到奇异解的问题, 首先提出一种基于最小二乘的非对称代价函数, 该代价函数在最小二乘标准的基础上增加了使对角化矩阵非奇异的约束项, 以保证算法不会收敛到奇异解. 然后利用一种循环最小化技术来优化提出的代价函数, 得到一种非对称非正交快速联合对角化算法. 算法的性能分析证明, 该算法不仅全局渐近收敛, 而且具有不变性. 左右对角化矩阵的关系也证明了非对称联合对角化的一般性. 实验仿真表明, 与原非对称联合对角化算法相比, 提出的算法收敛速度更快, 而且可以显著降低干扰信号比.

Non-symmetrical Non-orthogonal Fast Joint Diagonalization Algorithm

To overcome the drawbacks of slow convergence speed and possible singular solutions of existing non-symmetrical joint diagonalization algorithm, we first present a least-squares criteria based non-symmetrical cost function for joint diagonalization, in which a penalty term is added to the classical least-squares criteria to avoid singular solutions. Then a non-symmetrical non-orthogonal fast joint diagonalization algorithm is developed by using a cyclic minimizer technique. The performance analysis shows that the present algorithm globally asymptotically converges to the stable stationary point and has the invariance property. The relation between left and right diagonalization matrices is also investigated to show that the non-symmetrical joint diagonalization is a more general form for joint diagonalization problem. The simulation results show that the proposed algorithm converges faster than the original algorithm, and that the interference to signal ratio (ISR) is also significantly improved.