Mean-square performance of the filtered-reference/ filtered-error LMS algorithm

This paper describes two properties of the filtered-reference/filtered-error least-mean-square (LMS) algorithm proposed by Sujbert. First, by using the averaging method, the stability condition of the algorithm is investigated, which is affected by the compensating filter being inserted into both the input signal path and the error signal path. Second, the formula to express the mean-square error of the algorithm is theoretically derived by the ordinary differential equation method. Based on the derived formula, the convergence speed of the algorithm is compared to other types of LMS algorithms.