Adaptive Generalized Eigenvector Estimating Algorithm for Hermitian Matrix Pencil  

作　　者：Yingbin Gao 

机构地区：[1]the 54th Research Institute of China Electronics Technology Group Corporation(CETC54),Shijiazhuang 050050,China

出　　处：《IEEE/CAA Journal of Automatica Sinica》2022年第11期1967-1979,共13页自动化学报（英文版）

基　　金：supported by the National Natural Science Foundation of China(62106242,61903375);in part by the Natural Science Foundation of Shaanxi Province,China(2020JM-356)。

摘　　要：Generalized eigenvector plays an essential role in the signal processing field.In this paper,we present a novel neural network learning algorithm for estimating the generalized eigenvector of a Hermitian matrix pencil.Differently from some traditional algorithms,which need to select the proper values of learning rates before using,the proposed algorithm does not need a learning rate and is very suitable for real applications.Through analyzing all of the equilibrium points,it is proven that if and only if the weight vector of the neural network is equal to the generalized eigenvector corresponding to the largest generalized eigenvalue of a Hermitian matrix pencil,the proposed algorithm reaches to convergence status.By using the deterministic discretetime(DDT)method,some convergence conditions,which can be satisfied with probability 1,are also obtained to guarantee its convergence.Simulation results show that the proposed algorithm has a fast convergence speed and good numerical stability.The real application demonstrates its effectiveness in tracking the optimal vector of beamforming.

关 键 词：Deterministic discrete-time(DDT) generalized eigenvector learning rate online estimation 

分 类 号：TN911.7[电子电信—通信与信息系统] TP183[电子电信—信息与通信工程]