  In practical mobile communication engineering applications, surfaces of
antenna array deployment regions are usually uneven. Therefore, massive
multi-input-multi-output (MIMO) communication systems usually transmit wireless
signals by irregular antenna arrays. To evaluate the performance of irregular
antenna arrays, the matrix correlation coefficient and ergodic received gain
are defined for massive MIMO communication systems with mutual coupling
effects. Furthermore, the lower bound of the ergodic achievable rate, symbol
error rate (SER) and average outage probability are firstly derived for
multi-user massive MIMO communication systems using irregular antenna arrays.
Asymptotic results are also derived when the number of antennas approaches
infinity. Numerical results indicate that there exists a maximum achievable
rate when the number of antennas keeps increasing in massive MIMO communication
systems using irregular antenna arrays. Moreover, the irregular antenna array
outperforms the regular antenna array in the achievable rate of massive MIMO
communication systems when the number of antennas is larger than or equal to a
given threshold.
