  In this paper, novel expressions are derived to evaluate the ergodic mutual
information (EMI) under BPSK modulation of single-input single-output (SISO)
systems operating in generalized fading channels, including $\eta$-$\mu$ fading
and $\kappa$-$\mu$ fading. To verify our derivation, we first investigate the
specific fading types, namely Rayleigh, Nakagami-$m$ and Rician, and then turn
to generalized fading scenarios. It is shown that all the expressions concluded
from the generalized cases can be specialized into those derived from the
specific ones. Different from the conventional results of the EMI, our
developed expressions contain only the simplest numerical calculations, without
any Meijer's G-functions which must be implemented in the particular computing
software. Additionally, it should be noted that our work provides a complete
analysis of the EMI in wireless channel under discrete inputs.
