Performance Analysis of Coded Massive MIMO-OFDM Systems Using Effective Matrix Inversion

In this paper, we derive the bit error rate and pairwise error probability (PEP) for massive multiple-input multiple-output orthogonal frequency-division multiplexing (MIMO-OFDM) systems for different $M$ -ary modulations based upon the approximate noise distribution after channel equalization. The PEP is used to obtain the upper-bounds for convolutionally coded and turbo coded massive MIMO-OFDM systems for different code generators and receive antennas. In addition, complexity analysis of the log-likelihood ratio (LLR) values is performed using the approximate noise probability density function. The derived LLR computations can be time-consuming when the number of receive antennas is very large in massive MIMO-OFDM systems. Thus, a reduced complexity approximation is introduced using Newton’s interpolation with different polynomial orders and the results are compared with the exact simulations. The Neumann large matrix approximation is used to design the receiver for a zero-forcing equalizer by reducing the number of operations required in calculating the channel matrix inverse. Simulations are used to demonstrate that the results obtained using the derived equations match closely the Monte Carlo simulations.