Low-Complexity Look-Up Table-Based Frequency-Domain Trigonometric Nonlinear Equalizer for Underwater Wireless Optical Communications

A low-complexity frequency-domain trigonometric nonlinear equalizer (FD-TNLE) is proposed and experimentally validated for underwater wireless optical communication (UWOC) systems. The proposed FD-TNLE replaces 2<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">nd</sup>-order nonlinear operations in conventional time-domain Volterra nonlinear equalizers (TD-VNLE) with cosine operations and fast Fourier transform (FFT)-based multiplications. The cosine operation is not computed directly; instead, a look-up table (LUT) is pre-generated, from which values are retrieved. This reduces the required number of real-valued multiplications (RNRM) per symbol by 79.8% and 66.1% compared to TD-VNLE and time-domain trigonometric nonlinear equalizers (TD-TNLE), respectively, for memory lengths exceeding 10. Experimental results in an orthogonal frequency-division multiplexing (OFDM) based UWOC system with bit-power loading demonstrate that FD-TNLE achieves a data rate comparable to FD-VNLE, TD-VNLE and TD-TNLE under a 7% hard-decision forward error correction (HD-FEC) limit of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$3.8 \times {{10}^{ - 3}}$</tex-math></inline-formula>, and with 4.3% and 13.4% capacity improvements over frequency-domain absolute-term nonlinear equalizer (FD-ATNLE) and FD linear equalizers (FD-LE), respectively. Meanwhile, the proposed FD-TNLE achieves 18.1% lower computational complexity than the FD-VNLE while matching the complexity of the FD-ATNLE, making it a promising solution for balancing performance and complexity.