# Trouble regarding correlation matrix in LMMSE channel estimation

Started by November 30, 2010
Hi,
I’m currently making a simulation of LMMSE channel estimation for OFDM system using Matlab. To find the LMMSE coefficient we’d use this equation :
http://img545.imageshack.us/img545/7605/20080423599a788991f3f8b.png
The main problem is I can’t find the correlation matrix (Rhh). What confused me are :
1. Some papers said t Rhh is E(H*H), with H is the channel measurement. But it’s so strange. If we’ve known the channel already, why we should bother to find the Rhh, since H is actually what we’re looking for
2. The other paper said that Rhh is the Fourier transform of Power Delay Profile. But how to find this Power Delay Profile? Can we find it using the pilots?

I found this sample program to calculate the Rhh matrix in internet :

Rhh=zeros(N,N);
for k=1:N
for l=1:N
Rhh(k,l)=(1-exp((-1)*t_max*((1/trms)+j*2*pi*(k-l)/N)))./(trms*(1-exp((-1)*t_max/trms))*((1/trms)+j*2*pi*(k-l)/N));
end
end

with N represents the number of subcarriers (fft length).
But I can’t understand the mathematical origin of this code. I mean, I can’t get how to derive the equation of Rhh to get this code. If we write the above code into mathematical expression, it’s clear that it’s not a code to find an expected value.

Any kind of advice or Matlab code would help me a lot.

Best regards,