Soft dB Zen-Ten User guide - Manual (Page 15)

User manual for the ZEN 3-channel X-LMS controller Soft dB inc.
3.1.4 Adaptative step size normalization technique
Normalization of the adaptative step size allows an optimal convergence rate of the LMS
algorithm. For a single channel system, normalization of the adaptative step size can be
computed using the following equation (Mu is divided by the energy of the reference
signal):
∑
=
n
n f
norm
filtrered
Mu
Mu
0
2
) ( Re
Mu is provided by the user and can vary between 0 and 1 (the maximum convergence rate
is achieved when Mu=1). The n of the normalization equation is the size of the control
filter. For a multi-channel system, normalization must be done for each optimization. For
a non-coupled three–channel system, this means three normalizations. For coupled
systems, nine normalizations. However, the ZEN controller computes only one
normalization per channel even for the coupled version. Before each LMS function, the
output of the CxEx filter is used to normalize Mu. So, with the coupled version,
optimizations using the CxEy (x≠y) filter output use the same Mu as the optimization that
uses the CxEx filter output. On the DSP, the equation used to normalize Mu is:
outCxEx
normx
Energy
Mu
Mu =
The energy of the signal at the output of the CxEx filter is estimated with the help of a
first order IIR filter. The time constant of this IIR filter is set to match the control filter
length. This approach is more efficient and easier to implement on a fixed-point DSP
than the traditional technique used to evaluate the signal energy.
ZEN User Manual p. 15