  This paper answers a fundamental question about the exact distribution of the
signal-to-interference-plus-noise ratio (SINR) under matched-filter (MF)
precoding. Specifically, we derive the exact expressions for the cumulative
distribution function (CDF) and the probability density function (PDF) of SINR
under MF precoding over Rayleigh fading channels. Based on the exact analysis,
we then rigorously prove that the SINR converges to some specific distributions
separately in high SNR and in massive MIMO. To simplify the exact result in
general cases, we develop a good approximation by modelling the interference as
a Beta distribution. We then shift to the exact analysis of the transmit rate,
and answer the fundamental question: How does the exact rate converge to the
well-known asymptotic rate in massive MIMO? After that, we propose a novel
approximation for the ergodic rate, which performs better than various existing
approximations. Finally, we present some numerical results to demonstrate the
accuracy of the derived analytical models.
