Global convergence of variable step size LMS adaptive filtering algorithm based on variable region

A new variable step size LMS adaptive filtering algorithm is proposed based on variable region. The step size mu(k) in the algorithm varies with variation of the deviation e(k) region to ensure the optimization of the three performance objectives, which are initial convergent speed, tracking ability of the time-varying system and stable state convergence precision. The convergence of the algorithm is respectively proved by Lyapunov function and ODE with random noise and non-random noise.