Let us say that we have a estimated channel at the BS, denoted by H_e, and actual channel, denoted by H_a. How can we calculate spectral efficiency of a SU-mMIMO system using this information?
More specifically, I have a BS equipped with 64 transmit antennas and a UE equipped with 1 receive antenna.
Dear Muhammad Karem Shehzad,
Greetings!
I suggest you to refer the following links.
1) https://ieeexplore.ieee.org/document/7841817
2) Preprint Spectral Efficiency Analysis in Downlink Massive MIMO System...
You said mMIMO in the question (= MU-MIMO) and the mentioned SU-MIMO in the text. Which setup do you have in mind?
For MU-MIMO, I would recommend my book: massivemimobook.com
For SU-MIMO, I would recommend the paper "Capacity and power allocation for fading MIMO channels with channel estimation error" by You and Goldsmith.
Emil Björnson , thank you for the answer and corrections. I have updated my question.
The spectral efficiency of a SU-mMIMO system can be calculated based on the estimated and actual channels using the formula:
SE = log2(det(I + SNR * H_e * H_a^H))
where SE is the spectral efficiency, SNR is the signal-to-noise ratio, H_e is the estimated channel matrix, H_a is the actual channel matrix, and ^H denotes the conjugate transpose.
In your case, the actual channel H_a is a 1 x 64 vector, and the estimated channel H_e is also a 1 x 64 vector. To calculate the channel correlation between H_a and H_e, you can use the formula:
rho = abs(H_e * H_a') / (norm(H_e) * norm(H_a))
where rho is the correlation coefficient.
Once you have the channel correlation and the SNR, you can use the spectral efficiency formula to calculate the spectral efficiency of the SU-mMIMO system. Note that the spectral efficiency is a measure of how many bits per second can be transmitted over the channel, given a certain SNR and channel quality.
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