Convergence of the DLMS algorithm with decreasing step size

Convergence analyses for the least mean square algorithm with update delay (DLMS) exist, but most of them are based on the unrealistic independence assumption between successive input vectors. We consider the DLMS algorithm with decreasing step size /spl mu/(n)=a/n,a>0 and prove the almost-sure convergence of the algorithm under the mixing input, satisfying of the law of large numbers, and uniformly bounded input assumptions.