Widrow-Hoff least-mean-squares algorithm

Widrow-Hoff least-mean-squares algorithm

(communications)
An algorithm that is widely used in adaptive signal processing; for time-discrete analysis with a finite-response filter, it is represented by the first-order difference equationWk +1=Wk + 2μ ek Xk , where k is a time index that takes on integral values;Wis a vector whose components are the coefficients of the filter; μ is the convergence coefficient; ek is the residual signal or error, equal to yk -ŷk , where yk and ŷk are the outputs of the plant (where the unprocessed signal is generated) and the filter, respectively; andXis a vector whose components are the present value of the input and L- 1 past values of the input, where L is the number of filter coefficients.