Is it implied in your paper that the difference between the SINR simulations (when we know the fast-fading channel and pathloss) and SINR approximation (only pathloss known) is small and close to zero?

Do you have any condition how small your difference until it is considered “small” enough?

Does the deterministic equivalent hold for small number of antenna, i.e less than 50 antennas?

]]>*You tell me how the many users and cells that you have and how many bit/s/Hz/user you need, and I tell you how many antennas do we need*

(to paraphrase Hoydis’ seminal paper).

This fixed-L assumption is one of the reservations that I have against the conclusions in your recent paper. I do not contest the correctness of the main theorem per se, but it is obtained under the assumption that L is fixed while M->infinity. The more interesting case would be when the limits are interchanged, L->infinity before M->infinity. I conjecture that pilot contamination cannot be overcome in that case, but I do not really know, and I think it is an important open problem.

]]>If one allows for time-sharing between cells, i.e., only users in one cell are active at any given time, pilot contamination is non-existent and one gets unbounded capacity for every user as the number of antennas goes to infinity (for any finite number of cells). This holds even for independent Rayleigh fading with MR combining/precoding. However, this is a highly inefficient scheme which one would never use in practice.

If we assume simultaneous transmissions in the cells, pilot contamination necessarily arises and I am not aware of any existing information-theoretic upper bounds. Maybe some area for future research…

]]>Do we know for sure, whether pilot contamination ultimately limits performance in independent Rayleigh fading? Granted, available lower bounds on capacity suggest so, and I conjecture that it does… But are any rigorous upper bounds on capacity available?

]]>However, as soon as one deviates from this assumption, the exact analysis becomes in general intractable and one needs to resort to either Monte Carlo simulations or large system approximations. Simulations are fine if one is only interested in spectral efficiency estimates, but they fail to provide any insight. Large system approximations on the other hand often provide some insight about the most relevant system parameters.

What is very important though is that the asymptotic analyses of the uncorrelated and correlated fading models lead to different conclusions. The former reveals that pilot contamination ultimately limits the performance and MR combining/precoding is asymptotically optimal. The latter indicates that there is no ultimate performance limitation and that M-MMSE combining/precoding is optimal.

]]>Regarding multi-cell processing, I too concede that it does appear that the out-of-cell channel responses can be sufficiently well estimated for M-MMSE interference suppression to give real gains. And here, the random-matrix approximations do seem to be the only way forward.

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