Security enhancement for adaptive optics aided longitudinal orbital angular momentum multiplexed underwater wireless communications

The frozen-wave-based longitudinal orbital angular momentum multiplexing (LOAMM) system developed in [IEEE Photonics J. 10, 7900416 (2018)] has the potential to overcome the crosstalk effects induced by turbulence. In this paper, we propose a defocus measurement aided adaptive optics (DMA-AO) technique for turbulence compensation in a LOAMM underwater wireless optical communication (UWOC) system to investigate the enhancement of physical layer security. Relying on a phase retrieval algorithm and probe beam, three amplitude-only measurements obtained from different back focus planes can realize phase reconstruction of distorted OAM beams. Moreover, the so-called mixture generalized gamma-Johnson S_B(GJSB) distribution is proposed to characterize the probability density function (PDF) of reference-channel irradiance of OAM. The GJSB allows for obtaining closed-form and analytically tractable expression for the probability of strictly positive secrecy capacity (SPSC) in a single input single output (SISO) system. Furthermore, the average secrecy capacity (ASC) and probability of SPSC for a multiple input multiple output (MIMO) system are investigated. Compared to the traditional OAM multiplexing system based on Laguerre-Gaussian (LG) beams, the LOAMM system with a probe beam assisted DMA-AO technique has potential advantages for improving the security performance in UWOC.