Probability of Bit Error of MRC Detection in OFDM-MMIMO Systems Utilizing Gaussian Mixture Model

This paper derives probability distribution functions (PDFs) of the co-channel interference (CCI) and the effective noise (EN) of maximal-ratio combining (MRC) detection in orthogonal frequency-division multiplexing (OFDM) based massive multiple-input, multiple-output (MMIMO) systems. The effects of CCI and EN are expressed as a function of random variables and their PDFs for the OFDM-MMIMO system utilizing Gray-coded, binary and quadrature phase shift keying (BPSK, QPSK), and M-ary quadrature amplitude modulation (QAM) are derived. In addition, we firstly propose asymptotic closed-form expressions for the PDFs of the CCI and the EN in terms of Gaussian mixture model (GMM), i.e., a sum of multiple Gaussian distributions. Furthermore, the proposed PDFs are utilized to determine the probability of bit error (PBE) of the OFDM-MMIMO system. The derived equations are evaluated through Monte-Carlo simulations, and the results confirm that the derived equations produced accurate PDFs and PBE performances of OFDM-MMIMO systems. The PBE from the proposed equations for the 10 × 256 system with 16-QAM, operating at Eb/N0 = 5 dB, was 2.41 × 10−5, which was only 1.55 × 10−6 different from the simulation result. Therefore, the derived PDFs can be efficiently utilized to evaluate the performance of OFDM-MMIMO systems.