Any advice about how to implement this LMMSE technique ??
Your help is very appreciated.
Hany wrote:
> What you did is LS estimation technique, which is not my point of
> interest at the present time.
> many thanks for your reply...
>
> Regards
> Hany
>
>
> Arthur wrote:
> > Sorry, the equation should be
> >
> > H = 0.5 * (X1+X2) * conj(X) / abs(X)^2
> >
> > Regards,
> > Arthur.
> >
> > Arthur wrote:
> >
> > > I have also implemented IEEE802.11a channel estimation with preamble.
> > > it was pretty simple, which does not need LMMSE complex technique. The
> > > preamble is transmitted over 2 OFDM symbol, so
> > >
> > > H = (X1+X2) * conj(X) / abs(X)^2
> > >
> > > where H is the estimated channel information, X1 and X2 is the received
> > > preamble after FFT operation in OFDM receiver, and X is the original
> > > transmitted preamble before the IFFT operation in OFDM transmitter.
> > >
> > > cheers,
> > > Arthur.
> > >
> > > Hany wrote:
> > >
> > > > Thanks alot Arthur for your reply.
> > > > But actually I'm following & implementing HIPERLAN/2 standard and hence
> > > > I'm using a preamble to estimate the channel .. I didn't got through
> > > > the tracking using pilots yet.
> > > >
> > > > Thanks again
> > > >
> > > > Hany
> > > >
> > > >
> > > > Arthur wrote:
> > > > > You might want to try DFT based interpolation too, I have just
> > > > > implemented it, seems to work fine
> > > > >
> > > > > "DFT-based channel estimation in 2D-pilot-symbol-aided OFDM wireless
> > > > > systems"
> > > > > Fernandez-Getino Garcia, M.J. Paez-Borrallo, J.M. Zazo, S.
> > > > > Vehicular Technology Conference, 2001. VTC 2001 Spring. IEEE VTS 53rd
> > > > >
> > > > > Regards,
> > > > > Arthur,
> > > > >
> > > > > Hany wrote:
> > > > > > Hello ALL,
> > > > > >
> > > > > > I'm trying to simulate a LMMSE equalizer for OFDM signal.
> > > > > >
> > > > > > The general equation requires the calculation of (X.X^H) where X is
> > > > > > the transmitted signal OR >>-----> X is the diagonal matrix containing
> > > > > > the transmitted signal..!
> > > > > >
> > > > > > And X^H is the hermitian of X (hermitian is the conjugate transpose of
> > > > > > the matrix)
> > > > > >
> > > > > > I'm actually using the DL preamble to estimate the channel (as
> > > > > > HIPERLAN/2 says) so >>---> (X) would equal to this preamble vector..
> > > > > > Example : DL_Preamble = [1 -1 -1 1 -1 1 1 -1] "a vector of the
> > > > > > subcarriers"
> > > > > > then X = [1 -1 -1 1 -1 1 1 -1];
> > > > > > the diagonal matrix would be :
> > > > > > [1 0 0 0 0 0 0 0
> > > > > > 0 -1 0 0 0 0 0 0
> > > > > > 0 0 -1 0 0 0 0 0
> > > > > > 0 0 0 1 0 0 0 0
> > > > > > 0 0 0 0 -1 0 0 0
> > > > > > 0 0 0 0 0 1 0 0
> > > > > > 0 0 0 0 0 0 1 0
> > > > > > 0 0 0 0 0 0 0 -1];
> > > > > >
> > > > > > the matrix multiplication of this matrix and it's hermitian could not
> > > > > > be done on MATLAB .. it gives a matrix with "Inf" elements...!
> > > > > >
> > > > > > Could anybody try this simple operation and help please...
> > > > > >
> > > > > > How can I calculate this term in order to perform a LMMSE equalizer..
> > > > > >
> > > > > > Thanks a lot
> > > > > >
> > > > > > Hany
Reply by Hany●June 15, 20062006-06-15
What you did is LS estimation technique, which is not my point of
interest at the present time.
many thanks for your reply...
Regards
Hany
Arthur wrote:
> Sorry, the equation should be
>
> H = 0.5 * (X1+X2) * conj(X) / abs(X)^2
>
> Regards,
> Arthur.
>
> Arthur wrote:
>
> > I have also implemented IEEE802.11a channel estimation with preamble.
> > it was pretty simple, which does not need LMMSE complex technique. The
> > preamble is transmitted over 2 OFDM symbol, so
> >
> > H = (X1+X2) * conj(X) / abs(X)^2
> >
> > where H is the estimated channel information, X1 and X2 is the received
> > preamble after FFT operation in OFDM receiver, and X is the original
> > transmitted preamble before the IFFT operation in OFDM transmitter.
> >
> > cheers,
> > Arthur.
> >
> > Hany wrote:
> >
> > > Thanks alot Arthur for your reply.
> > > But actually I'm following & implementing HIPERLAN/2 standard and hence
> > > I'm using a preamble to estimate the channel .. I didn't got through
> > > the tracking using pilots yet.
> > >
> > > Thanks again
> > >
> > > Hany
> > >
> > >
> > > Arthur wrote:
> > > > You might want to try DFT based interpolation too, I have just
> > > > implemented it, seems to work fine
> > > >
> > > > "DFT-based channel estimation in 2D-pilot-symbol-aided OFDM wireless
> > > > systems"
> > > > Fernandez-Getino Garcia, M.J. Paez-Borrallo, J.M. Zazo, S.
> > > > Vehicular Technology Conference, 2001. VTC 2001 Spring. IEEE VTS 53rd
> > > >
> > > > Regards,
> > > > Arthur,
> > > >
> > > > Hany wrote:
> > > > > Hello ALL,
> > > > >
> > > > > I'm trying to simulate a LMMSE equalizer for OFDM signal.
> > > > >
> > > > > The general equation requires the calculation of (X.X^H) where X is
> > > > > the transmitted signal OR >>-----> X is the diagonal matrix containing
> > > > > the transmitted signal..!
> > > > >
> > > > > And X^H is the hermitian of X (hermitian is the conjugate transpose of
> > > > > the matrix)
> > > > >
> > > > > I'm actually using the DL preamble to estimate the channel (as
> > > > > HIPERLAN/2 says) so >>---> (X) would equal to this preamble vector..
> > > > > Example : DL_Preamble = [1 -1 -1 1 -1 1 1 -1] "a vector of the
> > > > > subcarriers"
> > > > > then X = [1 -1 -1 1 -1 1 1 -1];
> > > > > the diagonal matrix would be :
> > > > > [1 0 0 0 0 0 0 0
> > > > > 0 -1 0 0 0 0 0 0
> > > > > 0 0 -1 0 0 0 0 0
> > > > > 0 0 0 1 0 0 0 0
> > > > > 0 0 0 0 -1 0 0 0
> > > > > 0 0 0 0 0 1 0 0
> > > > > 0 0 0 0 0 0 1 0
> > > > > 0 0 0 0 0 0 0 -1];
> > > > >
> > > > > the matrix multiplication of this matrix and it's hermitian could not
> > > > > be done on MATLAB .. it gives a matrix with "Inf" elements...!
> > > > >
> > > > > Could anybody try this simple operation and help please...
> > > > >
> > > > > How can I calculate this term in order to perform a LMMSE equalizer..
> > > > >
> > > > > Thanks a lot
> > > > >
> > > > > Hany
Reply by Arthur●June 15, 20062006-06-15
Sorry, the equation should be
H = 0.5 * (X1+X2) * conj(X) / abs(X)^2
Regards,
Arthur.
Arthur wrote:
> I have also implemented IEEE802.11a channel estimation with preamble.
> it was pretty simple, which does not need LMMSE complex technique. The
> preamble is transmitted over 2 OFDM symbol, so
>
> H = (X1+X2) * conj(X) / abs(X)^2
>
> where H is the estimated channel information, X1 and X2 is the received
> preamble after FFT operation in OFDM receiver, and X is the original
> transmitted preamble before the IFFT operation in OFDM transmitter.
>
> cheers,
> Arthur.
>
> Hany wrote:
>
> > Thanks alot Arthur for your reply.
> > But actually I'm following & implementing HIPERLAN/2 standard and hence
> > I'm using a preamble to estimate the channel .. I didn't got through
> > the tracking using pilots yet.
> >
> > Thanks again
> >
> > Hany
> >
> >
> > Arthur wrote:
> > > You might want to try DFT based interpolation too, I have just
> > > implemented it, seems to work fine
> > >
> > > "DFT-based channel estimation in 2D-pilot-symbol-aided OFDM wireless
> > > systems"
> > > Fernandez-Getino Garcia, M.J. Paez-Borrallo, J.M. Zazo, S.
> > > Vehicular Technology Conference, 2001. VTC 2001 Spring. IEEE VTS 53rd
> > >
> > > Regards,
> > > Arthur,
> > >
> > > Hany wrote:
> > > > Hello ALL,
> > > >
> > > > I'm trying to simulate a LMMSE equalizer for OFDM signal.
> > > >
> > > > The general equation requires the calculation of (X.X^H) where X is
> > > > the transmitted signal OR >>-----> X is the diagonal matrix containing
> > > > the transmitted signal..!
> > > >
> > > > And X^H is the hermitian of X (hermitian is the conjugate transpose of
> > > > the matrix)
> > > >
> > > > I'm actually using the DL preamble to estimate the channel (as
> > > > HIPERLAN/2 says) so >>---> (X) would equal to this preamble vector..
> > > > Example : DL_Preamble = [1 -1 -1 1 -1 1 1 -1] "a vector of the
> > > > subcarriers"
> > > > then X = [1 -1 -1 1 -1 1 1 -1];
> > > > the diagonal matrix would be :
> > > > [1 0 0 0 0 0 0 0
> > > > 0 -1 0 0 0 0 0 0
> > > > 0 0 -1 0 0 0 0 0
> > > > 0 0 0 1 0 0 0 0
> > > > 0 0 0 0 -1 0 0 0
> > > > 0 0 0 0 0 1 0 0
> > > > 0 0 0 0 0 0 1 0
> > > > 0 0 0 0 0 0 0 -1];
> > > >
> > > > the matrix multiplication of this matrix and it's hermitian could not
> > > > be done on MATLAB .. it gives a matrix with "Inf" elements...!
> > > >
> > > > Could anybody try this simple operation and help please...
> > > >
> > > > How can I calculate this term in order to perform a LMMSE equalizer..
> > > >
> > > > Thanks a lot
> > > >
> > > > Hany
Reply by Arthur●June 15, 20062006-06-15
I have also implemented IEEE802.11a channel estimation with preamble.
it was pretty simple, which does not need LMMSE complex technique. The
preamble is transmitted over 2 OFDM symbol, so
H = (X1+X2) * conj(X) / abs(X)^2
where H is the estimated channel information, X1 and X2 is the received
preamble after FFT operation in OFDM receiver, and X is the original
transmitted preamble before the IFFT operation in OFDM transmitter.
cheers,
Arthur.
Hany wrote:
> Thanks alot Arthur for your reply.
> But actually I'm following & implementing HIPERLAN/2 standard and hence
> I'm using a preamble to estimate the channel .. I didn't got through
> the tracking using pilots yet.
>
> Thanks again
>
> Hany
>
>
> Arthur wrote:
> > You might want to try DFT based interpolation too, I have just
> > implemented it, seems to work fine
> >
> > "DFT-based channel estimation in 2D-pilot-symbol-aided OFDM wireless
> > systems"
> > Fernandez-Getino Garcia, M.J. Paez-Borrallo, J.M. Zazo, S.
> > Vehicular Technology Conference, 2001. VTC 2001 Spring. IEEE VTS 53rd
> >
> > Regards,
> > Arthur,
> >
> > Hany wrote:
> > > Hello ALL,
> > >
> > > I'm trying to simulate a LMMSE equalizer for OFDM signal.
> > >
> > > The general equation requires the calculation of (X.X^H) where X is
> > > the transmitted signal OR >>-----> X is the diagonal matrix containing
> > > the transmitted signal..!
> > >
> > > And X^H is the hermitian of X (hermitian is the conjugate transpose of
> > > the matrix)
> > >
> > > I'm actually using the DL preamble to estimate the channel (as
> > > HIPERLAN/2 says) so >>---> (X) would equal to this preamble vector..
> > > Example : DL_Preamble = [1 -1 -1 1 -1 1 1 -1] "a vector of the
> > > subcarriers"
> > > then X = [1 -1 -1 1 -1 1 1 -1];
> > > the diagonal matrix would be :
> > > [1 0 0 0 0 0 0 0
> > > 0 -1 0 0 0 0 0 0
> > > 0 0 -1 0 0 0 0 0
> > > 0 0 0 1 0 0 0 0
> > > 0 0 0 0 -1 0 0 0
> > > 0 0 0 0 0 1 0 0
> > > 0 0 0 0 0 0 1 0
> > > 0 0 0 0 0 0 0 -1];
> > >
> > > the matrix multiplication of this matrix and it's hermitian could not
> > > be done on MATLAB .. it gives a matrix with "Inf" elements...!
> > >
> > > Could anybody try this simple operation and help please...
> > >
> > > How can I calculate this term in order to perform a LMMSE equalizer..
> > >
> > > Thanks a lot
> > >
> > > Hany
Reply by Hany●June 15, 20062006-06-15
Thanks alot Arthur for your reply.
But actually I'm following & implementing HIPERLAN/2 standard and hence
I'm using a preamble to estimate the channel .. I didn't got through
the tracking using pilots yet.
Thanks again
Hany
Arthur wrote:
> You might want to try DFT based interpolation too, I have just
> implemented it, seems to work fine
>
> "DFT-based channel estimation in 2D-pilot-symbol-aided OFDM wireless
> systems"
> Fernandez-Getino Garcia, M.J. Paez-Borrallo, J.M. Zazo, S.
> Vehicular Technology Conference, 2001. VTC 2001 Spring. IEEE VTS 53rd
>
> Regards,
> Arthur,
>
> Hany wrote:
> > Hello ALL,
> >
> > I'm trying to simulate a LMMSE equalizer for OFDM signal.
> >
> > The general equation requires the calculation of (X.X^H) where X is
> > the transmitted signal OR >>-----> X is the diagonal matrix containing
> > the transmitted signal..!
> >
> > And X^H is the hermitian of X (hermitian is the conjugate transpose of
> > the matrix)
> >
> > I'm actually using the DL preamble to estimate the channel (as
> > HIPERLAN/2 says) so >>---> (X) would equal to this preamble vector..
> > Example : DL_Preamble = [1 -1 -1 1 -1 1 1 -1] "a vector of the
> > subcarriers"
> > then X = [1 -1 -1 1 -1 1 1 -1];
> > the diagonal matrix would be :
> > [1 0 0 0 0 0 0 0
> > 0 -1 0 0 0 0 0 0
> > 0 0 -1 0 0 0 0 0
> > 0 0 0 1 0 0 0 0
> > 0 0 0 0 -1 0 0 0
> > 0 0 0 0 0 1 0 0
> > 0 0 0 0 0 0 1 0
> > 0 0 0 0 0 0 0 -1];
> >
> > the matrix multiplication of this matrix and it's hermitian could not
> > be done on MATLAB .. it gives a matrix with "Inf" elements...!
> >
> > Could anybody try this simple operation and help please...
> >
> > How can I calculate this term in order to perform a LMMSE equalizer..
> >
> > Thanks a lot
> >
> > Hany
Reply by Arthur●June 15, 20062006-06-15
You might want to try DFT based interpolation too, I have just
implemented it, seems to work fine
"DFT-based channel estimation in 2D-pilot-symbol-aided OFDM wireless
systems"
Fernandez-Getino Garcia, M.J. Paez-Borrallo, J.M. Zazo, S.
Vehicular Technology Conference, 2001. VTC 2001 Spring. IEEE VTS 53rd
Regards,
Arthur,
Hany wrote:
> Hello ALL,
>
> I'm trying to simulate a LMMSE equalizer for OFDM signal.
>
> The general equation requires the calculation of (X.X^H) where X is
> the transmitted signal OR >>-----> X is the diagonal matrix containing
> the transmitted signal..!
>
> And X^H is the hermitian of X (hermitian is the conjugate transpose of
> the matrix)
>
> I'm actually using the DL preamble to estimate the channel (as
> HIPERLAN/2 says) so >>---> (X) would equal to this preamble vector..
> Example : DL_Preamble = [1 -1 -1 1 -1 1 1 -1] "a vector of the
> subcarriers"
> then X = [1 -1 -1 1 -1 1 1 -1];
> the diagonal matrix would be :
> [1 0 0 0 0 0 0 0
> 0 -1 0 0 0 0 0 0
> 0 0 -1 0 0 0 0 0
> 0 0 0 1 0 0 0 0
> 0 0 0 0 -1 0 0 0
> 0 0 0 0 0 1 0 0
> 0 0 0 0 0 0 1 0
> 0 0 0 0 0 0 0 -1];
>
> the matrix multiplication of this matrix and it's hermitian could not
> be done on MATLAB .. it gives a matrix with "Inf" elements...!
>
> Could anybody try this simple operation and help please...
>
> How can I calculate this term in order to perform a LMMSE equalizer..
>
> Thanks a lot
>
> Hany
Reply by Alan Tan●June 15, 20062006-06-15
If X is a diagonal matrix as you have given below then surely XX^H is
an identity matrix and its inverse is the same identity matrix. It
would probably be more helpful if you paste the segment of your Matlab
code here.
Alan T
Hany wrote:
> I'm sorry for this mistake but actually what I ment is that :
> the value of the inverse of (X.X^H) = (X.X^H)^ -1 gives a matrix with
> "Inf" elements...
>
> If anybody could help concerning that, it would be very appreciated.
>
> Thanks
>
>
>
> Hany wrote:
> > Hello ALL,
> >
> > I'm trying to simulate a LMMSE equalizer for OFDM signal.
> >
> > The general equation requires the calculation of (X.X^H) where X is
> > the transmitted signal OR >>-----> X is the diagonal matrix containing
> > the transmitted signal..!
> >
> > And X^H is the hermitian of X (hermitian is the conjugate transpose of
> > the matrix)
> >
> > I'm actually using the DL preamble to estimate the channel (as
> > HIPERLAN/2 says) so >>---> (X) would equal to this preamble vector..
> > Example : DL_Preamble = [1 -1 -1 1 -1 1 1 -1] "a vector of the
> > subcarriers"
> > then X = [1 -1 -1 1 -1 1 1 -1];
> > the diagonal matrix would be :
> > [1 0 0 0 0 0 0 0
> > 0 -1 0 0 0 0 0 0
> > 0 0 -1 0 0 0 0 0
> > 0 0 0 1 0 0 0 0
> > 0 0 0 0 -1 0 0 0
> > 0 0 0 0 0 1 0 0
> > 0 0 0 0 0 0 1 0
> > 0 0 0 0 0 0 0 -1];
> >
> > the matrix multiplication of this matrix and it's hermitian could not
> > be done on MATLAB .. it gives a matrix with "Inf" elements...!
> >
> > Could anybody try this simple operation and help please...
> >
> > How can I calculate this term in order to perform a LMMSE equalizer..
> >
> > Thanks a lot
> >
> > Hany
Reply by Hany●June 15, 20062006-06-15
I'm sorry for this mistake but actually what I ment is that :
the value of the inverse of (X.X^H) = (X.X^H)^ -1 gives a matrix with
"Inf" elements...
If anybody could help concerning that, it would be very appreciated.
Thanks
Hany wrote:
> Hello ALL,
>
> I'm trying to simulate a LMMSE equalizer for OFDM signal.
>
> The general equation requires the calculation of (X.X^H) where X is
> the transmitted signal OR >>-----> X is the diagonal matrix containing
> the transmitted signal..!
>
> And X^H is the hermitian of X (hermitian is the conjugate transpose of
> the matrix)
>
> I'm actually using the DL preamble to estimate the channel (as
> HIPERLAN/2 says) so >>---> (X) would equal to this preamble vector..
> Example : DL_Preamble = [1 -1 -1 1 -1 1 1 -1] "a vector of the
> subcarriers"
> then X = [1 -1 -1 1 -1 1 1 -1];
> the diagonal matrix would be :
> [1 0 0 0 0 0 0 0
> 0 -1 0 0 0 0 0 0
> 0 0 -1 0 0 0 0 0
> 0 0 0 1 0 0 0 0
> 0 0 0 0 -1 0 0 0
> 0 0 0 0 0 1 0 0
> 0 0 0 0 0 0 1 0
> 0 0 0 0 0 0 0 -1];
>
> the matrix multiplication of this matrix and it's hermitian could not
> be done on MATLAB .. it gives a matrix with "Inf" elements...!
>
> Could anybody try this simple operation and help please...
>
> How can I calculate this term in order to perform a LMMSE equalizer..
>
> Thanks a lot
>
> Hany
Reply by Hany●June 14, 20062006-06-14
Hello ALL,
I'm trying to simulate a LMMSE equalizer for OFDM signal.
The general equation requires the calculation of (X.X^H) where X is
the transmitted signal OR >>-----> X is the diagonal matrix containing
the transmitted signal..!
And X^H is the hermitian of X (hermitian is the conjugate transpose of
the matrix)
I'm actually using the DL preamble to estimate the channel (as
HIPERLAN/2 says) so >>---> (X) would equal to this preamble vector..
Example : DL_Preamble = [1 -1 -1 1 -1 1 1 -1] "a vector of the
subcarriers"
then X = [1 -1 -1 1 -1 1 1 -1];
the diagonal matrix would be :
[1 0 0 0 0 0 0 0
0 -1 0 0 0 0 0 0
0 0 -1 0 0 0 0 0
0 0 0 1 0 0 0 0
0 0 0 0 -1 0 0 0
0 0 0 0 0 1 0 0
0 0 0 0 0 0 1 0
0 0 0 0 0 0 0 -1];
the matrix multiplication of this matrix and it's hermitian could not
be done on MATLAB .. it gives a matrix with "Inf" elements...!
Could anybody try this simple operation and help please...
How can I calculate this term in order to perform a LMMSE equalizer..
Thanks a lot
Hany