A time-domain adaptive algorithm for rapid convergence

A time-domain adaptive LMS algorithm is presented which has, theoretically, the fastest convergence rates. The algorithm requires o(N²) operations where N is the length of the adaptive filter. It is shown that this algorithm is equivalent to the transform-domain adaptive algorithm with the optimum convergence rates proposed by Narayan et al. However the present algorithm does not require Karhunen-Loeve transforms for its implementation. It is also shown that the algorithm can be implemented with a complexity of o(mN) operations if the input process to the adaptive filter can be modeled as an autoregressive process of order m.