Abstract
Multiple single antenna terminals transmit simultaneously to an array of hundreds of antennas in the uplink of a multi-user massive multiple- input-multiple-output (MIMO) system. Under Rayleigh fading and lognormal shadowing, the expression for the probability density function (PDF) for signal-to-interference-plus-noise-ratio (SINR) does not exist in a closed-form, which is required to calculate the outage probability of a user. This paper provides approximate closed-form expressions for the outage probability of a user when the base station (BS) uses a maximum-ratio- combining (MRC) receiver in the presence of above channel impairments. It has been shown that the PDF of SINR can be well-approximated by a lognormal random variable (RV). Moreover, the effects of shadowing on the performance of the system have been quantified and it has been shown that the shadowing does not average out by increasing the number of antennas.
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