adaptive MISO in matlab

>
>I follow that H1 and H2 are the channel responses to the two input
>channels, and for a comm application X1 and X2 would both be recovered
>diversity inputs of the transmitted y (if that holds for what you're
>doing).   Since X1 and X2 have to be combined coherently in order to
>provide an improved estimate of y (rather than just taking X1 or X2
>independently), this suggests that synchronization is done
>independently on each channel prior to combining.
>
>I think my confusion is that since H1*X1 and H2*X2 have to be
>independently synchronized prior to combining, anyway, is there an
>advantage to making a single EQ work on both simultaneously (which
>seems to be what you're suggesting) or just run an independent EQ on
>each channel (to estimate H1 and H2 independently), and then combine
>the results?
>
>It sounds intriguing and if there's really an advantage to making one
>big MISO EQ rather than two SISO EQs that's something in which I'd be
>interested.
>
>Eric Jacobsen
>Minister of Algorithms
>Abineau Communications
>http://www.ericjacobsen.org
>
>Blog: http://www.dsprelated.com/blogs-1/hf/Eric_Jacobsen.php
>
I don't know what you mean by combining X1 and X2 coherently or what you
mean be synchronization prior to combining. What I am doing is taking y,
X1, and X2 and wiener filtering y with X1 and X2. MISO wiener filtering
involves calculation cross correlation coefficients between the inputs. So,
if X1 and X2 are correlated, it is taken into account. If you didn't take
into account the correlation between X1 and X2 and just SISO wiener
filtered y with X1 and SISO filtered y with X2 you would have a big
problem.
y~=H1*X1+H2*X2+residual
X1~=G*X2+residual (since X1 and X2 are correlated)
X2~=H*X1+residual
then
y~=(H1+H2*G)X1+residual
y~=(H2+H1*H)X2+residual
and then SISO wiener filtering y with X1 would give you an estimate of
(H1+H2*G) instead of an estimate of H1
and SISO wiener filtering y with X2 would give you an estimate of
(H2+H1*H)
instead of an estimate of H2.

I believe SISO adaptive filtering y with X1 and SISO adaptive filtering y
with X2 would suffer the same problem if X1 and X2 were correlated.
That is why I want a MISO adaptive filter