multiuser MIMO can be implemented by using block diagonalization technqiue
Hi,
If you consider a multiuser (Nt,Nr) MIMO system with OFDM waveforms (as for LTE and 5G), generated using an IFFT of size nfft, the received signal vector of size (Nr * nfft) x 1 can be written as :
y = H A s + n
where H is the channel matrix of size (Nr*nfft) x (Nt*nfft) ; the square P = AxA of the diagonal matrix A is the transmitted power matrix of size (Nt*nfft) x (Nt *Nfft). The vector s of size (Nt*nfft) x 1 is the useful signal and b is a (Nr*Nfft) x 1 vector representing the additive noise.
Then, to counteract the channel H, the receiver needs to incorporate an equalizer, i.e. a rectangular matrix W of size (Nr*nfft) x (Nt*nfft) to produce the estimate :
s_hat = W' * y
with (.)' being the transconjugate.. Minimizing the MSE of e = y - y_hat, you get the Wiener Solution :
W_MMSE = inv(Ryy) x H x A
where Ryy is the (Nr * nfft) x (Nr * nfft) correlation matrix of the received signal : Ryy = E(y x y').
To respond to your question, this equalizer W_MMSE can be implemented as an adaptive filter using the LMS with teh fimlter taps being updated with the LMS algorithm that minimize the MSE E(|e|^2).
I hope that this will help,
Pascal.
Sorry,
there was 2 typos in my previous post :
1) y = H A s + n with n is a (Nr*Nfft) x 1 vector representing the additive noise.
2) Minimizing the power of the error e = (s - s_hat) so the MSE is :
J = E[ Trace(exe')]
produce the optimum MMSE equalizer :
W_MMSE = inv(Ryy) x H x A
when considering A = I ---> the power loading is P = A^2=I which means that each user is transmitting with the same power on the channel.
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