LEAST MEAN SQUARES AS A CONTROL-SYSTEM

The least mean squares (LMS) algorithm is analysed as a control system rather than the conventional statistical approach. This approach greatly simplifies the understanding of the problem and presents a more convenient way of performing stability and convergence analysis. It is shown that the gain required for stability, i.e. the step size, derived using control theory is exactly the same as the result obtained by Widrow et al. (1979). It is also shown that the above gain value does not have to be constant but can vary at each iteration by the use of a sliding rectangular window whose length is equal to the number of parameters of the model. Furthermore, the gain of the system can be increased by the addition of integrators. The classical control approach was used to stablize the system, i.e. by considerations of phase advance, span ratios and system bandwidth.