  The factor graph (FG) based iterative detection is considered an effective
and practical method for multiple-input and multiple-out (MIMO), particularly
massive MIMO (m-MIMO) systems. However, the convergence analysis for the
FG-based iterative MIMO detection is insufficient, which is of great
significance to the performance evaluation and algorithm design of detection
methods. This paper investigates the mutual information update flow for the
FG-based iterative MIMO detection and proposes a precise mutual information
computation mechanism with the aid of Gaussian approximation and error
functions, i.e., the error functions-aided analysis (EF-AA) mechanism.
Numerical results indicate that the theoretical result calculated by the EF-AA
mechanism is completely consistent with the bit error rate performance of the
FG-based iterative MIMO detection. Furthermore, the proposed EF-AA mechanism
can reveal the exact convergent iteration number and convergent signal-to-ratio
value of the FG-based iterative MIMO detection, representing the performance
bound of the MIMO detection.
