A Simplified Form of Beam Spread Function in Underwater Wireless Optical Communication and its Applications

Underwater wireless optical communication (UWOC) refers to the transmission of data in unguided water medium through optical carriers. Beam spread function (BSF) characterizes the amount of light irradiance received at the receiver as a function of receiver's distance from main beam axis for a particular link length. The existing form of BSF includes multiple integrals which are burdensome to use for mathematical analysis. Because of this, it gets very difficult to employ the existing form of BSF to derive non-integral expressions for bit error rate (BER), capacity, and outage probability of UWOC systems. Moreover, it is very difficult to find any insight into the UWOC systems based on this integral form of BSF. In this paper, we derive a simplified power series expression of BSF by solving the existing integral form. Closed-form expressions of BSF with some approximations, which simplify the derived power series expression, are also provided as special cases. Important insights regarding the behavior of BSF are also obtained from the derived simplified forms. Furthermore, closed-form expressions of BER, capacity, and outage probability of the UWOC system, taking the effect of scattering, absorption, and misalignment in consideration, are also derived.