# Research on Power Allocation in Multiple-Beam Space Division Access Based on NOMA for Underwater Optical Communication

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## Abstract

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## 1. Introduction

- This paper proposes a new multiple-beam access system model with a hemispherical LED antenna array. We propose an antenna selection strategy for each user node, which scans all beams on the hemispherical LED array of the access node and selects the access beam based on the channel gain maximization. Finally, multiple space division beams are determined according to the relative position of the access nodes;
- A power allocation algorithm that guarantees the quality of service (QoS) for single-beam and multiple-beam NOMA access systems, especially the QoS for edge users and fairness for fair users, is proposed. This paper studies a power allocation algorithm considering both QoS and max–min fairness in a single-beam underwater visible light communication (UVLC) system;
- Considering the intra-beam and inter-beam interference for the multiple-beam access system, a fairness-oriented power allocation algorithm under the constraint of the total power of all users is proposed. We establish a model to maximize the minimum rate of all access users. Additionally, the bisection method and the KKT condition are used to solve the non-convex model.

## 2. Related Work

#### 2.1. MB-SDMA and NOMA

#### 2.2. QoS Optimization of Multiple-Beam NOMA

## 3. System Model

#### 3.1. The Power Allocation Model for Single-Beam NOMA Access System

#### 3.2. The Power Allocation Model for Multiple-Beam Access System

## 4. Optimization of Power Distribution Algorithm

Algorithm 1 |

Input:${P}_{max}$,${h}_{max}$,${\sigma}_{n}^{2}$, ${R}_{{m}_{1}}$, $m$Output:${t}^{\ast}$, ${P}_{{m}_{2}}^{\ast}$1: Set initial interval ${t}_{min}=0$, ${t}_{max}={\mathrm{log}}_{2}\left(1+{P}_{max}{h}_{max}/{\sigma}_{n}^{2}\right)$ 2: Set ${P}_{max}-m\ast {P}_{{m}_{1}}^{\ast}$ obtained by ${R}_{{m}_{1}}$ and $m$ 3: while $\left|{t}_{max}-{t}_{min}\right|>\epsilon $do4: Set $t=\left({t}_{max}+{t}_{min}\right)/2$, bring the value of $t$ into Equation (15) to obtain the power distribution coefficient $\left\{{P}_{{m}_{1}}^{\u2019}\right\}$ 5: if $\sum}_{{m}_{2}=N+1}^{N}{P}_{{m}_{2}}\le {P}_{max}-m\ast {P}_{{m}_{1}}^{\ast$ then 6: Set ${t}_{min}=t$ 7: else8: Set ${t}_{max}=t$ 9: end if10: end while11: Set ${t}^{\ast}=\left({t}_{max}+{t}_{min}\right)$, $\left\{{P}_{{m}_{2}}^{\ast}\right\}=\left\{{P}_{{m}_{2}}\right\}$. |

Algorithm 2 |

Input: ${P}_{max}$, ${\widehat{h}}_{l,i}$, ${z}_{l,n}$, $v$, $l$, $n$Output:${t}^{\ast}$, ${P}_{l,n}^{\ast}$1: Set initial interval ${t}_{min}=0$, ${t}_{max}={\mathrm{log}}_{2}\left(1+{\gamma}_{i,n}^{l}\right)$ 2: Set ${P}_{max}-{P}_{l,n}$, obtained by $l,n$ 3: while$\left|{t}_{max}-{t}_{min}\right|>\epsilon $do4: Set $t=\left({t}_{max}+{t}_{min}\right)/2$, bring the value of $t$ into Equation (22) to obtain the power distribution coefficient $\left\{{P}_{l,n}\right\}$. 5: if $({P}_{\mathrm{max}}-{\displaystyle \sum _{l=1}^{{N}_{\mathrm{ODC}\text{}}}{\displaystyle \sum _{n=1}^{{\Omega}_{l}}{P}_{l,n}}}\text{})0$ then6: Set ${t}_{min}=t$. 7: else 8: Set ${t}_{max}=t$. 9: end if 10: end while11: Set ${t}^{\ast}=\left({t}_{max}+{t}_{min}\right)$, $\left\{{P}_{l,n}^{\ast}\right\}=\left\{{P}_{l,n}\right\}$. |

## 5. Experiment and Analysis

#### 5.1. Simulation Settings and Analysis for a Single Beam System

#### 5.2. Simulation Settings and Analysis for Multiple-Beam System

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 2.**Schematic diagram of the hemispherical multiple-beam space division multiple access transmission.

**Figure 4.**(

**a**) Sum rate of NOMA and OMA under the same QoS. (

**b**) Sum rate of NOMA and OMA under different QoS.

**Figure 5.**(

**a**) Rates of different users under the same QoS. (

**b**) Rates of different users under different QoS.

**Figure 7.**(

**a**) The minimum rate varies with SNR in the case of multiple beams. (

**b**) The minimum rate varies with SNR in a multi-user case.

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## Share and Cite

**MDPI and ACS Style**

Li, Y.; Mohsan, S.A.H.; Chen, X.; Tehseen, R.; Li, S.; Wang, J.
Research on Power Allocation in Multiple-Beam Space Division Access Based on NOMA for Underwater Optical Communication. *Sensors* **2023**, *23*, 1746.
https://doi.org/10.3390/s23031746

**AMA Style**

Li Y, Mohsan SAH, Chen X, Tehseen R, Li S, Wang J.
Research on Power Allocation in Multiple-Beam Space Division Access Based on NOMA for Underwater Optical Communication. *Sensors*. 2023; 23(3):1746.
https://doi.org/10.3390/s23031746

**Chicago/Turabian Style**

Li, Yanlong, Syed Agha Hassnain Mohsan, Xiao Chen, Riffat Tehseen, Shuaixing Li, and Jianzhao Wang.
2023. "Research on Power Allocation in Multiple-Beam Space Division Access Based on NOMA for Underwater Optical Communication" *Sensors* 23, no. 3: 1746.
https://doi.org/10.3390/s23031746