###### Abstract  
Both the long-term beam spreading caused by ocean turbulence and the pointing errors induced by the jitter of transmitters and receivers degrade the performance of underwater wireless optical communication (UWOC) links. To effectively alleviate their effects, an in-depth study was carried out over the Malaga turbulence channel with pointing errors and beam spreading in multiple-input and multiple-output (MIMO) UWOC. First, we analyzed the long-term beam spreading and the received light power for the finite receiving aperture in the presence of pointing error displacements. Based on this, the relationship between beam spreading, pointing errors, and signal power was established. Second, the approximate expressions of the average bit error rate (BER) and the communication outage probability were derived theoretically for this MIMO system using maximal-ratio combining (MRC) diversity. Third, the effects of the pointing errors on the coding and the diversity gains were explored for the MIMO links. Finally, using the observed ocean data from the Global Ocean Argo gridded dataset, we numerically verified the combined effects of ocean turbulence strength, beam spreading, and pointing errors on the average BER and outage probability of this system. These results also proved that adjusting the size of the receiving aperture or the order of the multiple quadrature amplitude modulation (mQAM) could effectively mitigate their effects. a _Article_  
Performance Analysis of MIMO-mQAM System with Pointing Errors and Beam Spreading in Underwater Malaga Turbulence  
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caused by temperature or pressure inhomogeneities in the atmosphere are very different from the refractive-index spectra for temperature or salinity in seawater. Thus, the UWOC physical channel is very different from the physical channel of FSO communication. Recently, numerous studies have been performed on misaligned UWOC links. Closed-form expressions for the average symbol error probability (SEP) and the average channel capacity in a system employing the M-ary pulse position modulation (PPM) over Malaga oceanic turbulence with pointing errors are proposed in [8]. The average BER in a system employing rectangular quadrature amplitude modulation (QAM) and aperture receiving technology for gamma-gamma strong oceanic turbulence fading with pointing errors was analyzed in [9], and it was proved that the contributions of four oceanic turbulence parameters must be considered in practical UWOC applications. The unified expression of the multi-layer UWOC system performance, considering generalized gamma (GG), exponential GG, exponentiated Weibull, and gamma-gamma oceanic turbulence channels with pointing errors, was analyzed in [10]. However, we found that the authors did not include the relevant assumptions for multiple-input multiple-output (MIMO) technology. As is known, the MIMO technology in UWOC can alleviate signal fading, reduce the system bit error rate (BER), and improve communication reliability by using the spatial diversity gain [11; 12; 13]. Previous studies have shown that multiple beams can effectively reduce turbulence effects [14; 15]. Pointing errors between the misaligned transceivers were analyzed in beam array systems for UWOC in [16], but long-term beam spreading was not involved. To the best of our knowledge, nobody has researched the performance of an MIMO system with pointing errors and long-term beam spreading suitable for the arbitrary intensity of ocean turbulence so far. Thus, further research is required on the combined effects of oceanic turbulence and pointing errors in the presence of long-term beam spreading in order to improve the achievable UWOC system performance. In our previous work [17], we assumed the salinity was 35 ppt and the temperature was 20 \({}^{\circ}\)C in the ocean water. Under these conditions, we analyzed the effects of the numbers of receivers and transmitters on the average BER and the outage probability in a turbulence channel with pointing errors based on its analytical solution.