# Interdependent Coefficients and LMS

Started by June 20, 2011
```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.

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

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).

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