Transient Analysis of the Block Least Mean Squares Algorithm

It is known that adaptive filtering algorithms may tackle relevant communication tasks. In order to reduce the adaptation rate, the least mean squares algorithm and its normalized version may be implemented in a block manner, so that the filter coefficients are adjusted once per each output block. This letter advances a stochastic model that is able to predict the learning capabilities of time-domain block extensions of these algorithms, and demonstrates that their behaviour is not governed by trivial generalizations of the rules presented by standard implementations. The devised model decouples the radial and angular distribution of input data for the sake of emphasizing the factors that drive the algorithms learning behaviour. Both algorithms are demonstrated to solve a local and deterministic optimization problem. This novel point of view is employed to derive new versions of these algorithms that are able to enhance asymptotic performance by the usage of coefficient reusing techniques. Theoretical results reveal good adherence to simulated learning curves and the proposed algorithms outperform the standard ones in steady-state.