  We investigate underwater optical communication system that is relayed by a
single decode-and-forward (DF) relay through an exponential-generalized Gamma
distribution (EGG) into a final destination. Specifically, a certain terminal
device sends data through underwater wireless optical link (UWO) that utilizes
the so-called blue laser technology into a nearby relay that in term sends a
decoded (and modulated) version of the received signal into a remote
destination. The RF link is assumed to follow the generalized $\alpha-\mu$
distribution; which include many distributions as a special cases, e.g.,
Rayleigh. In the other hand, the UWO link is presumed to follow the
state-of-art Exponential-Generalized Gamma distribution (EGG) which was
recently proposed to model the underwater optical turbulence. Closed-form
expressions of outage probability, average error rate and ergodic capacity are
derived assuming heterodyne detection technique (HD). Also, asymptotic outage
expression is obtained for more performance insights. Results show that high
achievable rate is obtained for high-speed underwater communication systems
when turbulence conditions underwater are relatively weak. In addition, the RF
link is dominating the outage performance in weak optical turbulence while UWO
link is dominating the outage performance in severe optical turbulence.
