# Research on Adaptive Transmit Diversity Strategy for Reducing Interference in Underwater Optical Multi-Beam Non-Orthogonal Multiple Access Systems

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## Abstract

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## 1. Introduction

- In order to solve the serious inter-beam and intra-beam interference issues caused by multiple space-division beams and multiple access users, we propose an adaptive transmit diversity strategy. We design an adaptive selection merge algorithm to combine different LED beams according to the degree of interference. Diversity techniques are used at the transmitter to reduce inter-beam interference.
- Based on the adaptive transmit diversity strategy for underwater optical multi-beam NOMA systems, a model and method for evaluating beam interference are proposed. The method can find the optimal merging scheme.
- Further, we propose an OFDM-NOMA scheme with an adaptive transmit diversity strategy, where users are grouped according to their channel gains and different user groups are assigned to transmit on different subcarriers. This will resist the influence of interference within the beam.

## 2. Multi-Beam NOMA System Model

_{k}denotes the power allocation coefficient of user k, and P

_{m}is the transmit power of the LED m.

_{k}denotes additive white Gaussian noise (AWGN) of zero mean and variance ${\sigma}^{2}$.

**H**of the underwater wireless optical multi-beam system is expressed as:

## 3. Adaptive Transmit Diversity Strategy

#### 3.1. Adaptive Selection Merge Algorithm

Algorithm 1: Adaptive Selection Merge Algorithm |

Input: Channel gain matrix H.Output: LED combine index set L.Initialization: Inter-beam interference tolerance threshold ε = 0.27, beam interference ratio ${\rho}_{k,m}=0$, LED combine index set ${L}_{0}=\varnothing $, index ${C}_{0}=\varnothing $, $m=1$, $k=1$, $i=1$, $j=1$.Steps 1: Find the element ${h}_{k,m}$ with ${\rho}_{k,m}=1$ in each user in the channel gain matrix H. The strongest light signal comes from the corresponding LED, which is labeled as ${C}_{m},m\in [1,M]$.Steps 2: Find the LED corresponding to the element ${h}_{k,m}$ in the channel gain matrix H where each user satisfies ${\rho}_{k,m}\ge \epsilon $. If the LED belongs to the index set C, it is labeled as ${l}_{m},m\in [1,M]{l}_{m},m\in [1,M]$, ${L}_{k}=\left\{{l}_{m}\right\}$.Steps 3: Updating the index set $\mathbf{L}=\left\{{L}_{k}\right\}$, $k=k+1$.Steps 4: If k > K, the iteration stops. Otherwise go to Step 2 to continue.Steps 5: Compare each subset of the index set L and merge the intersecting subsets until each subset of the index set L no longer intersects. |

**L**is obtained, and each subset in

**L**is the set of LEDs with higher inter-beam interference, and the LED combinations are merged, while the served users are merged into a cluster accordingly. The transmit diversity is used within the LED groups to send the same data, and the space-split beams with low inter-beam interference are used between different LED groups, which balances the frequency efficiency and BER performance of the optical multi-beam NOMA system.

#### 3.2. OFDM-NOMA Scheme

## 4. Simulation Results Analysis

_{1}is around 0.8, the BER of the strong user is minimized. Therefore, in this section using the OFDM-NOMA scheme for superposition coding of two users, consider setting ${a}_{1}=0.8$.

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Qiu, T.; Zhao, Z.; Zhang, T.; Chen, C.; Chen, C.L.P. Underwater Internet of Things in Smart Ocean: System Architecture and Open Issues. IEEE Trans. Ind. Inform.
**2020**, 16, 4297–4307. [Google Scholar] [CrossRef] - Tsonev, D.; Chun, H.; Rajbhandari, S.; McKendry, J.; Videv, S.; Gu, E.; Haji, M.; Watson, S.; Kelly, A.; Faulkner, G.; et al. A 3-Gb/s Single-LED OFDM-Based Wireless VLC Link Using a Gallium Nitride μLED. IEEE Photon. Technol. Lett.
**2014**, 26, 637–640. [Google Scholar] [CrossRef] - Hong, W.; Jiang, Z.H.; Yu, C.; Zhou, J.Y.; Chen, P.; Yu, Z.Q.; Zhang, H.; Yang, B.Q.; Pang, X.D.; Jiang, M.; et al. Multibeam Antenna Technologies for 5G Wireless Communications. IEEE Trans. Antennas Propag.
**2017**, 65, 6231–6249. [Google Scholar] [CrossRef] - Zhu, L.P.; Xiao, Z.Y.; Xia, X.G.; Wu, D.O. Millimeter-Wave Communications with Non-Orthogonal Multiple Access for B5G/6G. IEEE Access
**2019**, 7, 116123–116132. [Google Scholar] [CrossRef] - Higuchi, K.; Benjebbour, A. Non-orthogonal multiple access (NOMA) with successive interference cancellation for future radio access. IEICE Trans. Commun.
**2015**, 98, 403–414. [Google Scholar] [CrossRef] - Dai, L.L.; Wang, B.C.; Peng, M.G.; Chen, S.Z. Hybrid Precoding-Based Millimeter-Wave Massive MIMO-NOMA With Simultaneous Wireless Information and Power Transfer. IEEE J. Sel. Areas Commun.
**2019**, 37, 131–141. [Google Scholar] [CrossRef] - Marshoud, H.; Sofotasios, P.C.; Muhaidat, S.; Karagiannidis, G.K.; Sharif, B.S. On the Performance of Visible Light Communication Systems with Non-Orthogonal Multiple Access. IEEE Trans. Wirel. Commun.
**2017**, 16, 6350–6364. [Google Scholar] [CrossRef] - Li, Y.L.; Mohsan, S.A.H.; Chen, X.; Tehseen, R.; Li, S.X.; Wang, J.Z. Research on Power Allocation in Multiple-Beam Space Division Access Based on NOMA for Underwater Optical Communication. Sensors
**2023**, 23, 1746. [Google Scholar] [CrossRef] - Jiao, R.C.; Dai, L.L.; Wang, W.; Lyu, F.; Cheng, N.; Shen, X.M. Max-Min Fairness for Beamspace MIMO-NOMA: From Single-Beam to Multi-Beam. IEEE Trans. Wirel. Commun.
**2022**, 21, 739–752. [Google Scholar] [CrossRef] - Wang, A.; Lei, L.; Lagunas, E.; Pérez-Neira, A.I.; Chatzinotas, S.; Ottersten, B. NOMA-Enabled Multi-Beam Satellite Systems: Joint Optimization to Overcome Offered-Requested Data Mismatches. IEEE Trans. Veh. Technol.
**2021**, 70, 900–913. [Google Scholar] [CrossRef] - Almasi, M.A.; Amiri, R.; Vaezi, M.; Mehrpouyan, H. Lens-Based Millimeter Wave Reconfigurable Antenna NOMA. In Proceedings of the 2019 IEEE International Conference on Communications Workshops (ICC Workshops), Shanghai, China, 20–24 May 2019; pp. 1–5. [Google Scholar]
- Mesleh, R.; Mehmood, R.; Elgala, H.; Haas, H. Indoor MIMO Optical Wireless Communication Using Spatial Modulation. In Proceedings of the 2010 IEEE International Conference on Communications, Cape Town, South Africa, 23–27 May 2010; pp. 1–5. [Google Scholar] [CrossRef]
- Renzo, M.D.; Haas, H. Improving the performance of space shift keying (SSK) modulation via opportunistic power allocation. IEEE Commun. Lett.
**2010**, 14, 500–502. [Google Scholar] [CrossRef] - Xu, K.; Yu, H.; Zhu, Y.-J. Channel-Adapted Spatial Modulation for Massive MIMO Visible Light Communications. IEEE Photonics Technol. Lett.
**2016**, 28, 2693–2696. [Google Scholar] [CrossRef] - Ijeh, I.C.; Khalighi, M.A.; Elamassie, M.; Hranilovic, S.; Uysal, M. Outage probability analysis of a vertical underwater wireless optical link subject to oceanic turbulence and pointing errors. J. Opt. Commun. Netw.
**2022**, 14, 439–453. [Google Scholar] [CrossRef] - Cox, W.; Muth, J. Simulating channel losses in an underwater optical communication system. JOSA A
**2014**, 31, 920–934. [Google Scholar] [CrossRef] [PubMed] - Wang, P.L.; Li, C.; Xu, Z.Y. A Cost-Efficient Real-Time 25 Mb/s System for LED-UOWC: Design, Channel Coding, FPGA Implementation, and Characterization. J. Light. Technol.
**2018**, 36, 2627–2637. [Google Scholar] [CrossRef] - Zedini, E.; Oubei, H.M.; Kammoun, A.; Hamdi, M.; Ooi, B.-S.; Alouini, M.S. Unified Statistical Channel Model for Turbulence-Induced Fading in Underwater Wireless Optical Communication Systems. IEEE Trans. Commun.
**2019**, 67, 2893–2907. [Google Scholar] [CrossRef] - Jamali, M.V.; Nabavi, P.; Salehi, J.A. MIMO Underwater Visible Light Communications: Comprehensive Channel Study, Performance Analysis, and Multiple-Symbol Detection. IEEE Trans. Veh. Technol.
**2018**, 67, 8223–8237. [Google Scholar] [CrossRef] - Li, Y.L.; Zhu, K.L.; Jiang, Y.T.; Mohsan, S.A.H.; Chen, X.; Li, S.X. Adaptive Diversity Algorithm Based on Block STBC for Massive MIMO Link Misalignment in UWOC Systems. J. Mar. Sci. Eng.
**2023**, 11, 772. [Google Scholar] [CrossRef] - Chen, W.W.; Wang, P.; Wang, W.; Pang, W.N.; Li, A.; Guo, L.X. Impact of temperature gradients on average bit error rate performance of low-density parity-check-coded multihop underwater wireless optical communication systems over the generalized gamma distribution. Opt. Eng.
**2020**, 59, 016114. [Google Scholar] [CrossRef] - Wang, G.Y.; Shao, Y.J.; Chen, L.-K.; Zhao, J. Subcarrier and Power Allocation in OFDM-NOMA VLC Systems. IEEE Photonics Technol. Lett.
**2021**, 33, 189–192. [Google Scholar] [CrossRef] - Kim, K.; Lee, K.; Lee, K. An inter-lighting interference cancellation scheme for MISO-VLC systems. Int. J. Electron.
**2017**, 104, 1377–1387. [Google Scholar] [CrossRef] - Lin, B.J.; Tang, X.; Yang, H.; Ghassemlooy, Z.; Zhang, S.H.; Lin, Y.W.; Lin, C. Experimental Demonstration of IFDMA for Uplink Visible Light Communication. IEEE Photonics Technol. Lett.
**2016**, 28, 2218–2220. [Google Scholar] [CrossRef] - Islam, S.M.R.; Zeng, M.; Dobre, O.A.; Kwak, K.-S. Resource Allocation for Downlink NOMA Systems: Key Techniques and Open Issues. IEEE Wirel. Commun.
**2018**, 25, 40–47. [Google Scholar] [CrossRef] - Almohimmah, E.M.; Alresheedi, M.T. Error Analysis of NOMA-Based VLC Systems with Higher Order Modulation Schemes. IEEE Access
**2020**, 8, 2792–2803. [Google Scholar] [CrossRef]

**Figure 1.**Illustration of a typical buoy-AUV underwater multi-beam NOMA system communication scenario. (

**a**) Multi-user clusters communication, (

**b**) LEDs communicate with the cluster, (

**c**) communications link misalignment, change LEDs to maintain communication.

**Figure 3.**ZEMAX software simulation (

**a**) Semi-spherical multi-beam array, (

**b**) Spot distribution at 3 m, (

**c**) Spot distribution at 10 m, (

**d**) Spot distribution at 20 m.

**Figure 8.**The BER comparison of both the conventional and proposed strategy at different interference scenarios.

**Figure 9.**Constellation of (a) user 1 symbols at the transmitting end, (b) user 2 symbols at the transmitting end, (c) two users superimpose symbols, (d) four users superimpose symbols, (e) user 1 symbols using conventional scheme under high interference, (f) user 2 symbols using conventional scheme under high interference, (g) user 1 symbols using conventional scheme under low interference, (h) user 2 symbols using conventional scheme under low interference, (i) user 1 symbols using the proposed strategy under high interference, and (j) user 2 symbols using the proposed strategy under high interference.

Parameter | Value |
---|---|

Number of LEDs | 17 |

LED half power angle | 18° |

LED transmitting power | 1 W |

Number of traced rays | 106 |

Semi-spherical array radius | 0.5 m |

Parameter | Value |
---|---|

Modulation order | 4-QAM |

Number of subcarriers | 256 |

Number of OFDM symbol | 1000 |

Imaging lens diameter | 50 mm |

Total attenuation factor for seawater | 0.15 |

Communication distance | 5 m |

Emission LED conversion efficiency | 0.1289 |

Detector conversion efficiency | 0.95 |

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**MDPI and ACS Style**

Li, Y.; Jiang, Y.; Chen, X.; Jiang, P.; Li, S.; Hu, Y.
Research on Adaptive Transmit Diversity Strategy for Reducing Interference in Underwater Optical Multi-Beam Non-Orthogonal Multiple Access Systems. *Photonics* **2023**, *10*, 1152.
https://doi.org/10.3390/photonics10101152

**AMA Style**

Li Y, Jiang Y, Chen X, Jiang P, Li S, Hu Y.
Research on Adaptive Transmit Diversity Strategy for Reducing Interference in Underwater Optical Multi-Beam Non-Orthogonal Multiple Access Systems. *Photonics*. 2023; 10(10):1152.
https://doi.org/10.3390/photonics10101152

**Chicago/Turabian Style**

Li, Yanlong, Yutong Jiang, Xiao Chen, Pengcheng Jiang, Shuaixing Li, and Yu Hu.
2023. "Research on Adaptive Transmit Diversity Strategy for Reducing Interference in Underwater Optical Multi-Beam Non-Orthogonal Multiple Access Systems" *Photonics* 10, no. 10: 1152.
https://doi.org/10.3390/photonics10101152