16-07-2012, 02:29 PM
An Evolutionary Computation Embedded IIR LMS Algorithm
An Evolutionary Computation.pdf (Size: 46.44 KB / Downloads: 31)
INTRODUCTION
Adaptive filters are now commonly used in a
wide range of Digital Signal Processing (DSP)
systems. Commercial systems that rely on adaptive
filtering in one way or another include highspeed
modems, echo-cancellation in speakerphones,
interference removal in medical imaging,
active noise control applications, on-line
system identification in chemical plants, linear
prediction, and beamforming in radio astronomy.
ALGORITHM
The IIR LMS algorithm is an extension of
the FIR LMS algorithm. A direct-form implementation
of the recursive IIR filter is preferred
over the parallel and lattice forms in view of the
computational complexity associated with the
latter structures. The IIR direct-form filter can
be constructed as:
STABILITY MONITORING AND EVOLUTIONARY COMPUTATION
IIR filters become unstable if the poles move
outside the unit circle during the adaptation process.
As a result, the output can grow without
bounds and the filter breaks down. Stability
monitoring is essential when adapting IIR filters.
During each adaptation of the filter coefficients,
stability of the filter needs to be ascertained before
computing the output signal value.
CONVERGENCE RESULTS
The convergence behavior of the LMS algorithm
depends very much on the choices of step
size and the initial values of the filter coefficients.
Fig. 3 below shows the effect of different
initial values of the filter coefficients for three
parallel filters operating on the same input and
desired signals. A unit signal with white noise
was used as the input signal. The filter configuration
was M=3 and L=2 with the step size being
0.01. The results shown below are an average of
100 independent runs.
CONCLUDING REMARKS
In this paper, we extended the original IIR
LMS algorithm in two ways. First, we implemented
multiple parallel filters each initialized
with a different set of coefficients. Complexity
of different order filters with different number of
parallel filters was measured. Next, we embedded
an evolutionary computation into the IIR
LMS algorithm mainly for stability monitoring.
We used minimal computations to increase parallelism
in the algorithm. Results show that even
if one filter goes unstable, evolutionary computation
can redirect the search in correct directions
while parallel filters that are not unstable
contribute to the output.