A modified μ-weighted normalised frequency-domain LMS algorithm

The transversal adaptive filter using the least mean square (LMS) algorithm of Widrow and Ropf (1976) has been widely used mainly due to its relative ease of implementation. The major drawback of this time-domain LMS (TDLMS) algorithm is that as the eigenvalue spread of the input autocorrelation matrix increases, the convergence speed of the algorithm decreases. This led to the transform domain adaptive filters where the input signals are orthogonalized. Normalized frequency domain LMS algorithms (NFDLMS) are known to be faster than the time domain implementations. However, in some implementations with low signal to return noise ratio, NFDLMS algorithms can have stability problems. The stability problem can be solved by weighting the normalization gain μ. We perform computer simulations for the telephone echo channel and show that the modified μ-weighted NFDLMS algorithm is 8 times faster than the time-domain LMS (TDLMS) algorithm and more stable than the NFDLMS algorithm over a wide range of signal to noise ratios