It's common to know that performance of MMSE and ZF are pretty close over Massive MIMO, and i've been trying to prove it in my simulation.
Though there's a problem about MMSE equalization,
I've been using 10*100 (10 transmitting antennas over 100 receving antennas),
y = Hx + v
H'*y = H'Hx +Hv
xhat = M*H'y;
To simplify the notation, H = H'*H
For ZF: M_zf = H'inv(H*H') (pseudo inverse)
For MMSE: M_mmse = H'*inv(H*H'+ H*sigma_v2/sigma_x2)
If both algorithms' performance were close,
M_zf = M_mmse approximately.
However, when I implenmented MMSE equalization, I also need to consider the normalization, for ZF, on the other hand, it's unnecessary.
So the normalization was diag(gain*H)
Therefore, M_mmse_nor = M_mmse ./ diag(M_mmse * H)
Regardless the normalization, performance of MMSE and ZF should be simliar over 10*100 MIMO system theoratically due to the H and H'
Looking forward to a discussion.
Thanks,
Dear Zeyang,
You can find in the literature elaborate comparison between the the zero forcing equalization and the MMSE. The MMSE is more accurate and suits a wide range of channel sate conditions expressed in S/N ratio. The zero forcing method is an approximate method more suitable for high signal to noise ratio where one can consider that the noise is much smaller than the received signal.
The MMSE is working well for all signal to noise ratios but it needs nuch more computational effort.
Best wishes
Dear Zeyang,
You can find in the literature elaborate comparison between the the zero forcing equalization and the MMSE. The MMSE is more accurate and suits a wide range of channel sate conditions expressed in S/N ratio. The zero forcing method is an approximate method more suitable for high signal to noise ratio where one can consider that the noise is much smaller than the received signal.
The MMSE is working well for all signal to noise ratios but it needs nuch more computational effort.
Best wishes
Your expression for MMSE doesn't seem to be correct. There should be an identity matrix in the noise term, not H.
You can find implementations and formulas for many different equalization methods (also known as receive combining) in my book Massive MIMO networks: https://massivemimobook.com
Dear,
The MMSE is not correct , it needs much more computational effort.
The paper given in the following link will give you a comparison between the different MIMO detectors: Article FPGA Implementation of Sphere Detector for Spatial Multiplex...
Best wishes
For massive MIMO, with a good power scaling, MRC offers very good performance.... by minimizing SINR.....
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