# The BER Performance of the LDPC-Coded MPPM over Turbulence UWOC Channels
## 1 Introduction  
The fifth-generation (5G) wireless communication network is widely deployed, which has significantly increased capacity and supported larger-scale connections, but is limited primarily to terrestrial communication. The upcoming sixth-generation (6G) network is expected to provide wider coverage with a seamless connection from space to underwater [1]. Though an important part of heterogeneous and massive-scale networks, underwater wireless communication has many challenges, due to the complex nature of the underwater channel. Underwater wireless optical communication (UWOC) is considered an effective solution, due to its high energy-efficiency, high-speed communication and security [2]. To make the UWOC robust and reliable in all conditions, the effects of absorption, scattering and turbulence, resulting in attenuation, delay spread and fading must be comprehensively understood. Many studies have experimentally and theoretically characterized the underwater optical absorption and scattering caused by suspended matter, ions, plankton and other factors [3, 4, 5]. Random fluctuations of water density, temperature and salinity, resulting from surf, tide geothermal and so on, generate random variations on the refractive index of water, which causes turbulence. When a light beam passes through water, turbulence effects, such as beam wandering, spreading, jitter, and intensity fluctuation (i.e., fading), degrade the received optical signal [6, 7]. It is of great significance to investigate the fading characteristics of underwater turbulence and to find corresponding mitigation techniques. Various studies have investigated the scintillation index, describing turbulence strength, which is affected by the eddy diffusivity ratio, aperture diameter, wave model and soon [8; 9; 10]. Experimental studies also characterized underwater turbulence caused by different phenomena and proposed statistical distributions to fit the optical intensity fluctuations [7; 11; 12; 13; 14; 15; 16]. A combination of exponential and log-normal distributions was proposed in [11] to describe the fluctuations of the probability density function (PDF) in the presence of air bubbles. Furthermore, to obtain closed-form and analytically tractable expressions for crucial system performance metrics, the mixture exponential-gamma distribution is adopted to characterize channel irradiance fluctuations resulting from air bubbles [12]. In [13; 14], a generalized-gamma (GG) distribution was used to model the fading of coherent and non-coherent light induced by temperature inhomogeneity. For salinity variation induced turbulence, Weibull distribution can efficiently fit the acquired scintillation data [15]. Moreover, the mixture exponential-GG (EGG) distribution can describe the statistics of underwater optical beam irradiance fluctuations due to air bubbles and temperature gradient [16]. Experimental study under different underwater scenarios, incorporating the effects of temperature gradients, salinity variation and air bubbles, demonstrate that using beam expander-and-collimator (BEC) at the transmitter side, and/or aperture averaging lens (AAL) at the receiver side, GG and exponentiated Weibull (EW) distributions can excellently match the PDF of measured data in weak to strong turbulence [7]. Several turbulence mitigation techniques, such as channel coding [17], multi-hop relaying transmission [18], aperture averaging [19], and spatial diversity [20], were studied. Spatial diversity with linear combining at the receiver, such as equal gain combining (EGC) and maximum ratio combining (MRC), can effectively alleviate fading impairments. Though the MRC has optimal linear diversity reception, it is complicated due to the requirements of both phase and fading amplitude estimation of all branches. However, EGC, with low complexity and implementation simplicity, performs close to MRC in most scenarios [21]. Aperture averaging can reduce the scintillation by enlarging the receiver aperture area.