As you mentioned, the point that I missed was that MSE curve measures the performance of channel estimation phase only, while what we truly need is the performance of MRC scheme during data transmission period which is measured by BER curve.

The MSE floor I observed tells us that channel estimation error (MSE) caused by the pilot contamination during pilot transmission phase could be no longer improved by increasing the SINR, but this does not tell us how badly this estimation error impacts the performance of the MRC signal processing block in the receiver during the data transmission period. We may expect that in the many-antennas regime, the MRC processing scheme keep on eliminating the interfering data symbols even in presence of even weakly estimated channel gains giving excellent BER curve while the opposite case might also be the case. Hence both MSE and BER curves are required for deciding on the performance of overall system.

Thanks a lot.

]]>So, yes, what you observe is pilot contamination, but we cannot say how serious this pilot contamination will be without also studying the data phase. And it is not the high SNR regime that is of main interest in massive MIMO but the many-antennas regime.

]]>I plotted the MSE curve as a function of the transmit SNR for M=1000 antenna (massive MIMO case) and different number of cells. For L=1 cell, no floor appears in MSE curve while for L>1 cells, the curves encounter floors and the level of these floors grows with increase in number of cells. In case of L=1 cell, there exists no pilot contamination and the corresponding curve does not suffer from floor therefore noise itself could not produce floor in MSE curve while for the mult-icell case, there exists pilot contamination and the curves suffer from floor which increases with in crease in the number of cells.

If my simulation is bug free and the results are valid, then would it be true to claim that MSE curve vs TxSNR could somehow measure pilot contamination level?

Thanks a lot ]]>

2. Pilot contamination has always existed in cellular networks, but it is first when start doing coherent beamforming from arrays with many antennas that the coherent interference problem becomes clearly visible. It is not the MMSE estimation itself that is the problem; in fact, MMSE estimation scheme is what can solve the pilot contamination problem by exploiting the spatial correlation that always exists in practice: https://arxiv.org/pdf/1705.00538.pdf

]]>Since the coherent interference is something that scales with M and the error floor (or lack thereof) is something that appear when the signal power (or SNR) grows, I don’t think there are any simple conclusions to be made.

]]>1. What are other relevant metrics other than SINR that can satisfy “(or some other performance indicator in the data phase)”?

2. I did not see the same argument in papers considering general transceiver design in single-cell scenarios or multi-cell scenarios employing pilot reuse plan to design pilot allocation. I mean is this an inherent property in MMSE estimation, that it does not distinguish between noise and interference, or is it a property of the pilot contamination problem?

]]>Thanks for the important point.

According to my observation, pilot contamination causes floor in MSE curves in i.i.d Rayleigh fading channels while noise does not. If my observation is valid, then would it be true to say that if an algorithm mitigated this floor then it has mitigated pilot contamination for sure ?

Thanks ]]>