Title :
When is the least-mean fourth algorithm mean-square stable?
Author :
Nascimento, Vítor H. ; Bermudez, José Carlos M
Author_Institution :
Dept. of Electron. Syst. Eng., Sao Paulo Univ., Brazil
Abstract :
We show that the least-mean fourth (LMF) and the least-mean mixed-norm (LMMN) algorithms are not mean-square stable when the input regressor is Gaussian-distributed. For the LMF algorithm, we propose an upper bound for the algorithm´s probability of divergence, given the input and noise statistics, the stepsize and the filter length. We show that the upper bound can also be used for the LMMN algorithm, which is a combination of LMS and LMF.
Keywords :
FIR filters; Gaussian distribution; adaptive filters; filtering theory; least mean squares methods; numerical stability; FIR adaptive filter; FIR filter; Gaussian distribution; LMS; divergence probability; filter length; input regressor; input statistics; least-mean fourth algorithm; least-mean mixed-norm algorithm; least-mean squares algorithm; mean-square stability; noise statistics; stepsize; Algorithm design and analysis; Finite impulse response filter; Gaussian noise; Gaussian processes; Least squares approximation; Noise measurement; Stability; Steady-state; Systems engineering and theory; Upper bound;
Conference_Titel :
Acoustics, Speech, and Signal Processing, 2005. Proceedings. (ICASSP '05). IEEE International Conference on
Print_ISBN :
0-7803-8874-7
DOI :
10.1109/ICASSP.2005.1416015
