Estimating signal fading while ignoring envelope variation?

I'm playing around with estimating the signal fading on a signal while
ignoring amplitude variations due to a non-constant amplitude. 

Let's say I've got an antenna with a clear line of sight to a signal, it
collects something like:

x(t) = s(t) + v(t)  where v is AWGN 

Then I have another antenna that's sees the signal, but with fading on it,
so it receives something like:

y(t) = A(t)*s(t) + u(t) where u is AWGN

I'm not an estimation guy so I was wondering if someone could get me
started on a reasonable way to estimate A(t) given x(t) and y(t).  How
about if I want to integrate to pull s(t) out of the noise?

On Mon, 15 Aug 2011 10:32:09 -0500, "gct"
<smcallis@n_o_s_p_a_m.gmail.com> wrote:

>I'm playing around with estimating the signal fading on a signal while
>ignoring amplitude variations due to a non-constant amplitude. 
>
>Let's say I've got an antenna with a clear line of sight to a signal, it
>collects something like:
>
>x(t) = s(t) + v(t)  where v is AWGN 
>
>Then I have another antenna that's sees the signal, but with fading on it,
>so it receives something like:
>
>y(t) = A(t)*s(t) + u(t) where u is AWGN
>
>I'm not an estimation guy so I was wondering if someone could get me
>started on a reasonable way to estimate A(t) given x(t) and y(t).  How
>about if I want to integrate to pull s(t) out of the noise?

If the system has a single AGC then A(t) will be estimated by the AGC
signal. You probably don't even need x(t).


Eric Jacobsen
http://www.ericjacobsen.org
http://www.dsprelated.com/blogs-1//Eric_Jacobsen.php

gct wrote:

> I'm playing around with estimating the signal fading on a signal while
> ignoring amplitude variations due to a non-constant amplitude. 
> 
> Let's say I've got an antenna with a clear line of sight to a signal, it
> collects something like:
> 
> x(t) = s(t) + v(t)  where v is AWGN 
> 
> Then I have another antenna that's sees the signal, but with fading on it,
> so it receives something like:
> 
> y(t) = A(t)*s(t) + u(t) where u is AWGN
> 
> I'm not an estimation guy so I was wondering if someone could get me
> started on a reasonable way to estimate A(t) given x(t) and y(t).  How
> about if I want to integrate to pull s(t) out of the noise?

If the fading is slow compared to the baud rate (which is the usual 
case) you can estimate the fading pattern from decision error vector at 
every received symbol using the Kalman-like algorithm. It is even 
possible to predict the fading pattern into the future so to avoid the 
expected deep fades by maneuvering the signal in time or frequency in 
advance.

Vladimir Vassilevsky
DSP and Mixed Signal Design Consultant
http://www.abvolt.com

>If the system has a single AGC then A(t) will be estimated by the AGC
>signal. You probably don't even need x(t).
>
>

The problem comes when the signal itself isn't steady.  An AGC can't
distinguish fading from things like the signal not being constant-modulus.

Eric Jacobsen wrote:

> On Mon, 15 Aug 2011 10:32:09 -0500, "gct"
> <smcallis@n_o_s_p_a_m.gmail.com> wrote:
> 
> 
>>I'm playing around with estimating the signal fading on a signal while
>>ignoring amplitude variations due to a non-constant amplitude. 
>>
>>Let's say I've got an antenna with a clear line of sight to a signal, it
>>collects something like:
>>
>>x(t) = s(t) + v(t)  where v is AWGN 
>>
>>Then I have another antenna that's sees the signal, but with fading on it,
>>so it receives something like:
>>
>>y(t) = A(t)*s(t) + u(t) where u is AWGN
>>
>>I'm not an estimation guy so I was wondering if someone could get me
>>started on a reasonable way to estimate A(t) given x(t) and y(t).  How
>>about if I want to integrate to pull s(t) out of the noise?
> 
> 
> If the system has a single AGC then A(t) will be estimated by the AGC
> signal.

Dear doctor Jacobsen,
A(t) is complex.

VLV

>If the fading is slow compared to the baud rate (which is the usual 
>case) you can estimate the fading pattern from decision error vector at 
>every received symbol using the Kalman-like algorithm. It is even 
>possible to predict the fading pattern into the future so to avoid the 
>expected deep fades by maneuvering the signal in time or frequency in 
>advance.
>
>Vladimir Vassilevsky
>DSP and Mixed Signal Design Consultant
>http://www.abvolt.com
>

I'd actually like to be able to estimate the fading in a
modulation-agnostic way.  

gct wrote:

>>If the fading is slow compared to the baud rate (which is the usual 
>>case) you can estimate the fading pattern from decision error vector at 
>>every received symbol using the Kalman-like algorithm. It is even 
>>possible to predict the fading pattern into the future so to avoid the 
>>expected deep fades by maneuvering the signal in time or frequency in 
>>advance.
>>
> 
> I'd actually like to be able to estimate the fading in a
> modulation-agnostic way.  

I think you are actually a stupident. Right?

> Let's say I've got an antenna with a clear line of sight to a signal, it
> collects something like:
> 
> x(t) = s(t) + v(t)  where v is AWGN 
> 
> Then I have another antenna that's sees the signal, but with fading on it,
> so it receives something like:
> 
> y(t) = A(t)*s(t) + u(t) where u is AWGN
> 
> I'm not an estimation guy so I was wondering if someone could get me
> started on a reasonable way to estimate A(t) given x(t) and y(t).

Make an LMS algorithm using x(t) as a reference. Track the coefficients 
of the resulting filter.

VLV

>Make an LMS algorithm using x(t) as a reference. Track the coefficients 
>of the resulting filter.
>
>VLV

Can you elaborate on this?

gct wrote:

>>Make an LMS algorithm using x(t) as a reference. Track the coefficients 
>>of the resulting filter.
>>
> Can you elaborate on this?

Sure. And I'll send you the bill also. The contact is at the web site in 
the signature.


Vladimir Vassilevsky
DSP and Mixed Signal Design Consultant
http://www.abvolt.com

>Sure. And I'll send you the bill also. The contact is at the web site in 
>the signature.
>

Ah sorry I thought you were trying to be helpful.  You're welcome to not
post if you don't want to help think through my problem.