On the Steady State Performance of Frequency Domain LMS Algorithms

The use of the fast Fourier transform (FFT) in the implementation of the least mean square (LMS) algorithm in the frequency Manuscript received May 24, 1990; revised May 4, 1992. A. Feuer is with the Department of Electrical Engineering, TechnionIsrael Institute of Technology, Haifa 32000, Israel. R. Cristi is with the Department of Electrical and Computer Engineering, Naval Postgraduate School, Monterey, CA 93943. IEEE Log Number 9203376. 1053-587X/93$03.00 © 1993 IEEE 420 IEEE TRANSACTIONS ON SIGNAL PROCESSING. VOL. 41. NO. I. JANUARY 1993 domain results in several types of algorithms, two of which can be classified as constrained and unconstrained. In this correspondence, we point out that, in general, especially with correlated data, the unconstrained algorithm may have a significant performance advantage in steady state if block mean square error is the criterion. Furthermore, we point out here that, in the constrained algorithms, the choice of different step sizes in different frequency bins (as is commonly done) will very likely result in a deterioration of steady state performance. This does not happen in the unconstrained algorithm.