  In this paper, we evaluate the end-to-end bit error rate (BER) of
point-to-point underwater wireless optical communication (UWOC) systems with
multi-hop transmission. To do so, we analytically derive the BER expression of
a single-hop UWOC link as the building block for end-to-end BER evaluation. We
also apply photon-counting method to evaluate the system BER in the presence of
shot noise. Moreover, we use Gauss-Hermite quadrature formula to obtain the
closed-form solutions for the system BER in the case of log-normal underwater
fading channels. Our analytical treatment involves all the impairing effects of
the underwater optical channel, namely absorption, scattering and fading.
Numerical results demonstrate that multi-hop transmission by alleviating the
aforementioned impairing effects of the channel, can significantly improve the
system performance and extend the viable end-to-end communication distance. For
example, dual-hop transmission in $22.5$ m and $45$ m coastal water links can
provide $17.5$ dB and $39$ dB performance enhancement at the BER of $10^{-6}$,
respectively.
