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Optical wireless communication is an energy-efficient and cost-effective solution for high-speed and highly-secure wireless connections. In this paper, we compare, discuss, and analyze three popular optical orthogonal frequency division multiplexing (OFDM) techniques, such as DC-biased optical OFDM (DCO-OFDM), asymmetrically-clipped optical OFDM (ACO-OFDM), and unipolar OFDM (U-OFDM), for underwater optical wireless communication systems. The peak power constraint, bandwidth limit of the light source, turbulence fading underwater channel, and the channel estimation error are taken into account. To maximize the achievable data propagation distance, we propose to optimize the modulation index that controls the signal magnitude, and a bitloading algorithm is applied. This optimization process trades off the clipping distortion caused by the peak power constraint and the signal to noise ratio (SNR). The SNR and clipping effects of the three compared OFDM techniques are modeled in this paper. From the numerical results, DCO-OFDM outperforms ACO- and U-OFDM when the transmitted bit rate is high compared to the channel bandwidth. Otherwise, U-OFDM can provide a longer propagation distance or requires less transmitted power. [ABSTRACT FROM AUTHOR]