This paper focuses on In-band Full-Duplex (IB-FD) based Underwater Acoustic Communication (UAC) systems using Coded Orthogonal Frequency Division Multiplexing (C-OFDM). Presently, most UAC systems utilize Half-Duplex (HD) operation implying that transmission and reception between underwater devices can occur in only one direction at a time. This doubles the latency and halves the effective bandwidth available, which is already severely limited for these systems. Latency can have a significant impact in system performance, especially in scenarios where real-time communication is crucial. In contrast to HD, IB-FD based systems utilize sophisticated Self-Interference Cancellation (SIC) signal processing methods to achieve simultaneous signal transmission and reception. In- band refers to the fact the UAC systems employs the same carrier frequency and acoustic bandwidth for operation in both directions. The paper presents modelling of the self-interference (SI) channel using experimental signal acquired during seatrials in the North Sea, off the coast of UK. The performance of a C-OFDM system using an adaptive SIC is investigated using simulation and experimental data, and numerical results such as convergence vs iterations, Bit-error Rate (BER) and SIC levels vs Signal-to-noise Ratio (SNR) are presented that take into account non-linear effects of the power amplifier.