Soft decision feedback equalizer for OFDM systems in underwater wireless optical communications with signal-dependent noise and channel estimation error

To improve the performance of orthogonal frequency division multiplexing (OFDM) systems in underwater wireless optical communication, a soft decision feedback equalizer (SDFE), which considers the impacts of signal non-negativity, channel estimation error, and signal-dependent noise (SDN), is proposed to suppress inter-carrier interference, thus being more suitable for the actual communication environment. Different from the conventional SDFE, the introduction of SDN makes the relationship between the received signal and the noise become complicated, and renders the turbo equalization framework inapplicable for OFDM systems. To solve this problem, we incorporate a Fourier transform and an inverse Fourier transform into the noise term and derive a series of specific expressions, leading to a modified approach compatible with the turbo equalization framework. Furthermore, both the a posteriori moments of estimated symbols and the a priori moments of unestimated symbols are used in our proposed SDFE, and a general expression for turbo equalization has been derived. To further reduce the computational complexity while obtaining the frequency reversal diversity and mitigating the error propagation, a bidirectional threshold-SDFE (BiT-SDFE) with a controllable inverse matrix update and a serially connected bidirectional structure is developed. Simulation results demonstrate that the bit error rate of the proposed equalizer significantly outperforms existing counterparts, especially in the case of high noise intensity and severe channel estimation error.