You can have a look at Corollary 1.3 in my book https://www.nowpublishers.com/article/DownloadSummary/SIG-093

and try to figure out what h, v, and n will be in your case. Then you need to verify that the necessary conditions stated in the corollary are satisfied so that it can be applied. If not, you need to revise what you call h, v, and n.

Alternatively, you can read Section 2.3 in Fundamentals of Massive MIMO and use one of the bounds that are listed there.

]]>However, I don’t see this as a problem. If a practical receiver cannot compute the optimal scaling factors that you refer to, then we have computed the mutual information in the wrong way; apparently, the received didn’t have access to all the information that we assumed it to have.

That said, I also think that the MSE or bit error rate can be good performance measures, but only for transmission of small packets, where one cannot operate at a rate close to the mutual information using a practical channel code. (See Fig. 3 in “Massive MIMO: Ten Myths and One Critical Question” for some details on that).

]]>The paper “MMSE transmit optimization for multi-user multi-antenna systems” explains how one can derive the MMSE transmit filters for the downlink channel for the perfect CSI.

This paper emphasizes the importance of the scaling factor that each user is using to estimate its symbols (beta_i). However, in the SINR analysis, this can not be taken into account (since it is only a scaling factor at the receiver, which is cancelled when you derive the SINR formula for that user). However, this is important for the user to correctly estimate its symbols.

So, I guess, when we are talking about SINR formulas, we implicitly assume that each receiver is using the correct scaling factor to estimate its symbol. Otherwise, in practice, the user can not achieve the data rate, guaranteed by the SINR value.

Thus, I think it’s better to use the normalized MSE or bit error rate for the downlink to avoid this ambiguity, rather than the data rates derived with the SINR values.