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This paper studies the distribution of the Signal-to-Interference-plus-Noise Ratios (SINR) of users in a Rayleigh multiuser channel, using large dimensional random matrix theory. It is shown that the empirical distribution of the SINRs of the users in a Rayleigh Multiple Access Channel (MAC) with Minimum Mean Square Error (MMSE) decoding behaves asymptotically as a Gaussian, with identified mean and variance. The result is applied to the estimation of the proportion of users in outage for a given target rate. The theoretical approach used is extended to broadcast channels in the full version of the paper.
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