Outage Probability Analysis of MRC Detection in OFDM-MMIMO System Utilizing Incomplete Gamma Function

This paper analyzes the outage probability of the maximal-ratio combining (MRC) detection in an uplink orthogonal frequency-division multiplexing (OFDM) based massive multiple-input, multiple-output (MMIMO) system over a frequency-selective Rayleigh fading channel. Binary and Quadrature Phase Shift Keying (BPSK and QPSK), and $M$-order Quadrature Amplitude Modulation (QAM) are chosen by this research work. We previously derived the probability distribution function (PDF) of the co-channel interference (CCI) and effective noise (EN) for the detection in a research work, and the PDF is utilized in this paper to derive the PDF of signal-to-interference-plus-noise ratio (SINR) and the outage probability of the output SINR. Furthermore, by employing the approximate PDF of CCI and EN, we prove that the outage probability of the OFDM-MMIMO system can be approximated as a combination of incomplete Gamma functions. Monte-Carlo simulations are utilized to evaluate the proposed equations, and the results reveal a good match between the analytical and the exact results. Moreover, the difference between the outcomes from the derived equations and the approximations were marginal. Thus, the proposed equations can be efficiently applied to analyze the performance of the OFDM-MMIMO system.