Optimal power allocation in serial relay-assisted underwater wireless optical communication systems

For a serial relaying underwater wireless optical communication (UWOC) system with ON-OFF keying modulation, we theoretically evaluate the optimal power allocation techniques in order to minimise the end-to-end bit error rate (BER), subject to transmission power constraints. At first, we evaluate the end-to-end BER with respect to all degrading effects of the UWOC channel, namely scattering, absorption, and turbulence-induced fading and then develop a closed-form BER expression as a function of transceiver parameters and water type. The optimal power allocation methods are obtained using the perfect channel state information available at the receiver (CSIR) and transmitter (CSIT) for both detect-and-forward (DF) and amplify-and-forward (AF) serial relaying systems. For each relaying method, we consider a dual-hop UWOC system and determine optimal power allocation to minimise the BER. Afterwards, the optimal power allocation in a multi-hop system is obtained to minimise the end-to-end BER. Compared to the equal power allocation, our results illustrate that UWOC relaying systems with optimal power allocation can significantly improve the end-to-end BER and expand the communication link. For instance, the proposed power allocation method for the DF and AF relay node in a 60 m single relay system improves the system performance at the BER of 10⁻⁵ by 2.5 and 1.8 dB compared to the equal power allocation, respectively.