Interdependent Coefficients and LMS

Hi ,
    Can LMS algorithm deal with an adaptive filter with coefficients that
depend on each other such as :
   y= x(n)+(W1+W2)*x(n-1)+(W1.W2)x(n-2);
In my experiments it does not converge. Can anyone point me in the correct
direction to solve such problems?
   Thanks much

       

taken wrote:

> Hi ,
>     Can LMS algorithm deal with an adaptive filter with coefficients that
> depend on each other such as :
>    y= x(n)+(W1+W2)*x(n-1)+(W1.W2)x(n-2);
> In my experiments it does not converge. Can anyone point me in the correct
> direction to solve such problems?

You created a non-linear problem. LMS will fall into a local minima.

Your question is not very clear.
If you're considering a 'standard' LMS algorithm and you don't see any
convergence it may be that you need to tune your step-size.
If you're considering a modified or extended LMS algorithm where
you're trying to embed a priori information you have about the
coefficients in the adaptive filter you need to work out the math.

If this is your filter
y= x(n)+a1(w1,w2)*x(n-1)+a2(w1,w2)*x(n-2);
where
a1(w1,w2) = w1+w2
a2(w1,w2) = w1*w2
you may run into some problems in doing the math because the
coefficients are now coupled. Is this what you mean?

On Jun 20, 6:45=A0am, "taken" <shafqat_alikhan@n_o_s_p_a_m.yahoo.com>
wrote:
> Hi ,
> =A0 =A0 Can LMS algorithm deal with an adaptive filter with coefficients =
that
> depend on each other such as :
> =A0 =A0y=3D x(n)+(W1+W2)*x(n-1)+(W1.W2)x(n-2);
> In my experiments it does not converge. Can anyone point me in the correc=
t
> direction to solve such problems?
> =A0 =A0Thanks much

BTW, to answer your question more directly: yes.

Maurice Givens

On Jun 20, 6:45=A0am, "taken" <shafqat_alikhan@n_o_s_p_a_m.yahoo.com>
wrote:
> Hi ,
> =A0 =A0 Can LMS algorithm deal with an adaptive filter with coefficients =
that
> depend on each other such as :
> =A0 =A0y=3D x(n)+(W1+W2)*x(n-1)+(W1.W2)x(n-2);
> In my experiments it does not converge. Can anyone point me in the correc=
t
> direction to solve such problems?
> =A0 =A0Thanks much

You need to think about several things.

1. Your system model is y=3D x(n)+(W1+W2)*x(n-1)+(W1.W2)x(n-2).

2. Does your system model relate to your actual system?
     For example, y =3D a*x + b is not a very good model for y =3D a*x^1 +
b*x(n-1)^2 + c*x +d.

3. What is your cost function?
    LMS assumes an error signal e =3D y - y_model. y is the signal from
the actual system, y_model from your model system. Will your error
ever be small?

4. Second to the most important, what does the LMS attempt to do?

5. Probably most important, what does convergence mean for LMS? Think
about this for the example in #2.

Maurice Givens