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Accurate log‐normal approximation to the signal‐to‐interference ratio in massive multiple‐input multiple‐output systems

In this paper, a very tight approximation is derived for the signal‐to‐interference ratio of a multicell massive multiple‐input multiple‐output system with a finite number of base station (BS) antennas. The approximation is derived considering that each term in the SIR is log‐normal distributed. To this end, the first and second moments of the logarithm of each variable are used. In addition, an exact expression is derived for the cumulative distribution function for the net capacity. In order to corroborate our derivations, simulations using the Monte Carlo method were carried out, and it was observed that the proposed analytical results tightly match the numerical simulations. The asymptotic result is also obtained for the case in which the number of BS antennas tends to infinity (M → ∞), considering both uniform and nonuniform spatial user distributions.