Proportional-type NLMS algorithm with gain allocation providing maximum one-step conditional PDF for true weights

In this paper, we present a proportionate-type normalized least mean square algorithm which operates by choosing adaptive gains at each time step in a manner designed to maximize the conditional probability that the next-step coefficient estimates reach their optimal values. We compare and show that the performance of the maximum conditional probability density one-step algorithm is superior to the normalized least mean square algorithm and the proportionate normalized least mean square algorithm. Additionally, we argue that the algorithm we present operates for any impulse response.