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On the separability of signal and interference-plus-noise subspaces in blind pilot decontamination

Consider a multicell multiuser MIMO (multiple-input multiple-output) system with a very large number of antennas at each base station (BS). The number of users in each cell is assumed to be fixed as the number of BS antennas grows large. Under certain conditions on the powers of the transmitting users, the signal eigenvalue spectrum is asymptotically separated from the interference-plus-noise spectrum as the number of BS antennas grows large. As it was observed in [1], this phenomenon allows to mitigate the pilot contamination problem. We provide the power limits for each user in the cell of interest above which such a separation occurs asymptotically. Unlike the approximative methods used in [1], we obtain these power limits by making use of the exact asymptotic characterizations of the interference-plus-noise spectrum. The results are based on the theory of small rank perturbations of large dimensional random matrices.