Optimized Zero Cross-Correlation Code for Free Space and Underwater Optical Communication Using a Modular Rotational Matrix

This paper introduces a novel code construction method called the modular rotation matrix zero cross-correlation code (MRM ZCCC), designed to enhance multi-user optical communication systems such as free space optics (FSO) and underwater wireless optical communication (UWOC). The proposed method generates zero cross-correlation codes through a modular and rotational strategy, ensuring scalability, minimal multi-user interference, and reduced computational complexity. Two variants—constant weight (CW) and variable weight (VW) MRM ZCCC—are developed to accommodate users with different data rate requirements. Simulation results demonstrate that the VW MRM-ZCCC reduces code length by up to 50% compared to Basic ZCCC and by 25% compared to Pascal ZCCC, thereby improving spectral efficiency. Moreover, under the most demanding underwater conditions, the VW MRM-ZCCC demonstrates up to a 60-dB enhancement in Log of BER compared to the Basic ZCCC. It also delivers an overall system performance boost of approximately 35–65% in both FSO and UWOC scenarios relative to conventional methods. In addition, its modular design supports up to 33% more simultaneous users within the same code length, making it a scalable, adaptable, and interference-tolerant solution for future optical wireless communication systems.