In this study, the performance of underwater optical wireless communication systems employing spatial diversity and multi-pulse position modulation techniques is assessed. The effects of inter-symbol interference, oceanic turbulence and receiver noise are taken into account. Oceanic turbulence is modelled by the log-normal distribution which is regarded as an appropriate model for weak turbulence conditions. For the system under consideration, approximate analytical expressions for the average bit error probability are deduced. The impact of the number of transmitting and receiving apertures, the achievable data rate and the water type on system performance is also investigated. Various numerical results are presented that demonstrate the proposed analysis.