Abstract
In orthogonal multiple access (OMA) communication systems, resources are allocated to numerous users based on time, frequency, or code domains. The low bandwidth of the underwater acoustic network limits the number of nodes that can be supported by the OMA system, due to limited resources. The innovative concept of nonorthogonal multiple access (NOMA) provides a solution that offers more nodes and increases spectral efficiency. As a promising technique, it optimizes power allocation through channel characteristics and adopts serial interference cancellation algorithms to decode the signal at the receiver. This paper introduces an underwater communication system based on the node pairing algorithm of maximum and minimum weight (MMWNOMA). First, we build the system model in a UAN scenario. Second, we present the node pairing strategy. Third, we design a node replacement mechanism. Furthermore, we offer a power allocation algorithm. Finally, we compare the performance of MMWNOMA with randomly paired NOMA (RPNOMA) and orthogonal frequency division multiplexing (OFDM). Numerical results show that MMWNOMA outperforms RPNOMA and OFDM in throughput, mean square error, and energy efficiency. However, the complexity of MMWNOMA is slightly higher than that of RPNOMA but significantly lower than OFDM. These results show that MMWNOMA achieves a reasonable tradeoff between performance and complexity.
1. Introduction
An underwater acoustic network (UAN) is a monitoring system composed of sensor nodes with acoustic communication and computing capabilities [1]. They are widely used to discover marine resources, detect underwater life, monitor environmental conditions, predict tsunamis and underwater earthquakes, navigation, tracking, antitracking, torpedoes [2], etc. As common technologies of the OMA type, frequency division multiple access (FDMA), time division multiple access (TDMA), code division multiple access (CDMA), and orthogonal frequency division multiple access (OFDMA) allocate resources in the time, frequency, or code domains. According to OMAbased UANs, each data stream corresponds to a single node in the code, time, or frequency resource block [3]. Hence, it cannot access multiple nodes simultaneously within a limited spectrum.
As an emerging technology, NOMA consists of a power domain (PDNOMA) [4] and a code domain (CDNOMA) [5]. For PDNOMA, the number of nodes is superimposed on the power domain to achieve multiplexing gain [6]. In NOMAbased UANs, signals are multiplexed in frequency and differentiated by the transmit power of the sender. Serial interference cancellation (SIC) resolves the signal with different channel gains at the receiver [7]. Therefore, many nodes share the same resource block to ensure maximum transmission rate and fairness [8].
This paper proposes MMWNOMA, an underwater uplink NOMA communication system. To the best of our knowledge, it is the first work to design a NOMA model based on maximum and minimum weight for underwater acoustic networks. The main contributions of the work are as follows.
First, we establish the MMWNOMA model in a UAN scenario. Second, we design a node pairing algorithm based on maximum and minimum weight. Third, we design a node replacement mechanism by computing the channel correlation coefficient to learn more about the system. Furthermore, we suggest a power allocation method through distribution factors. Finally, we compare the performance of MMWNOMA with that of randomly paired NOMA (RPNOMA) and OFDM.
The rest of the paper is organized as follows. Section 2 introduces related work. Section 3 describes the implementation of the system. Section 4 shows the numerical results. Finally, Section 5 concludes this paper.
2. Related Work
2.1. Progress of NOMABased UANs
Recently, underwater NOMA technology has progressed considerably. Makled et al. [9] advice on a UAN with NOMAbased timing and frequency sharing mechanism for uplink and downlink information transmission. The results show that under the actual SIC algorithm, the sum rate of the network is higher than that of the OFDMdriven system. Wang and Qin [10] examine the spectral efficiency of underwater networks by modeling multiuser interference as a noncooperative game. Goutham and Harigovindan [11] present NOMACRS, a cooperative relay strategybased NOMA for underwater acoustic networks. Experiments show that it significantly improves traversal and rate and energy efficiency.
Bocus et al. [12] study the performance of underwater NOMA systems using OFDM (NOMAOFDM) and filter bank multicarrier (NOMAFBMC). The results show that NOMAFBMC has a higher bit rate. Jiang et al. [13] consider a partially overlapping NOMA algorithm (PONOMA) for the uplink UANs, which solves the optimal power allocation and determines the closed power spectral density (PSD). Esmaiel et al. [14] apply the timereversed NOMA to mitigate the timefrequency dispersion of the underwater acoustic channel. Experiments show a higher bit error rate (BER) and outage probability than traditional methods. Goutham and Harigovindan [15] develop a fullduplex cooperative relay solution for a NOMA system (FDCRNOMA). The simulation results show that it significantly improves the ergodic rate, the probability of outage, and the energy efficiency of the UAN. Cheon and Cho [16] introduce a NOMAbased power allocation strategy for underwater acoustic networks. As a result of the numerical results, the proposed system improves performance over the sumrate maximization (SRM) method. Liu et al. [17] design a NOMA scheme for large underwater systems. The experimental results show that the outage probability is low, and the spectral efficiency is high.
2.2. Advances in NOMA Node Pairing Strategies
Nodes share the same time or frequency resources in a NOMA uplink system and transfer data to base stations (BSs) with different transmit power. With the aid of SIC, the BS separates and decodes the multiplexed signal [18]. Therefore, node pairing and power distribution are fundamental components of the NOMA system.
Chen et al. [19] provide a pairing algorithm for massive MIMONOMA systems. It maintains the maximum sum rate by choosing one primary and one secondary for each pair. Theoretical analysis and simulation show that the algorithm has a lower interruption probability and higher sum rate. Mounchili and Hamouda [20] recommend a user pairing algorithm to ensure an optimal sum rate between NOMA clusters and improve performance with minimal gain differences. Salehi et al. [21] establish a collaborative NOMA (CNOMA) system that allocates resources to maximize efficiency by using a user pairing scheme. Nearend users act as relays for maximum and minimum throughput. Numerical analysis shows that the average throughput of the CNOMA system is better than that of the hybrid NOMA/OMA approach, while the fairness index decreases slightly. Wang et al. [22] present a positioningbased pairing scheme for MIMONOMA systems. The results show that the system reduces resource requirements and improves both time and frequency utilization.
2.3. NOMABased Power Allocation Technologies
Azam et al. [23] analyze the impact of power allocation in NOMA uplink systems. Experiments show that it maximizes the capacity of the uplink NOMA system while satisfying the individual rates for each user pair. Nguyen and Le [24] study a NOMAbased wireless network power allocation algorithm. Numerical results show that the performance is close to the optimal solution. Pischella and Ruyet [25] recommend a resource block allocation schema for PDNOMA, which constructs resource blocks using the maximum weight matching strategy. Zuo and Tao [26] formulate the problem of maximizing throughput within the transmit power constraints of NOMA uplink systems. According to numerical results, it provides better throughput than its OMA counterpart.
Li et al. [27] present a power allocation algorithm in a MIMONOMA system using the Stackelberg game model, where the throughput of a single user is the optimization object. The optimal solutions for users and base stations are determined based on the Lagrangian multiplier scheme. The results show that energy consumption is reduced, and capacity is increased. Hao et al. [28] suggest a power allocation strategy for a multicarrier NOMA system based on an improved particle swarm optimization algorithm. The results show that the algorithm significantly improves energy efficiency. Zeng et al. [29] integrate NOMA into the OMA system to create an efficient allocation mechanism that treats users and resource blocks as bipartite graphs. By exchanging resources, they achieved a joint userresource block. The numerical results show that the algorithm is more efficient than the OMAbased scheme. Jing et al. [30] propose a power allocation algorithm for the uplink Internet of Things (IoT) to maximize the traversal rate. Each node determines the transmitting power through feedback from the base station and a selfmaintaining virtual queue. An experiment shows that the optimal power is obtained by comparing the queue length with traversal rate and using a low complexity dichotomy. Zeng et al. [31] introduce a dynamic power allocation algorithm to ensure the quality of service (QoS) in uplink NOMA systems. The simulation shows that it significantly improves energy efficiency and capacity.
3. The MMWNOMA Communication System
3.1. The Uplink MMWNOMA Model in a UAN Scenario
There are three main components in a UAN, namely, underwater nodes, surface buoys, and offshore buoy stations. All nodes are connected to an underwater buoy. Various sensors seal underwater buoy, and an anchor chain connects it to the anchor. When the node is deployed, the anchor chain sinks to the bottom, and the anchor chain expands to a fixed length depending on the application and location. All buoys are suspended in the water, forming a 3D structure. Surface buoys are located on autonomous underwater vehicles (AUVs), unmanned underwater vehicles (UUVs), remotely controlled vehicles (ROVs), and other devices that communicate between underwater nodes and offshore buoys.
For the MMWNOMA uplink system, clusters are formed according to the region managed by the surface buoys. Each underwater node is considered a user. A nearend node (NEN) and a farend node (FEN) are allocated in a cluster. We assume that NENs and surface buoys have relatively short Euclidean distances and good channel conditions. And the distance between the surface buoy and the FEN is longer, and the channel condition is poor. All resources, such as time, frequency, and code, are shared between the twonode cluster. Users are divided into orthogonal frequency clusters to simplify serial interference cancellation. The NOMA mechanism is running in intracluster communication, and the OMA technology is used in intercluster communication. Figure 1 shows the MMWNOMA model in the UAN scenario.
In the MMWNOMA system, the channels have different characteristics, and the node with good channel gain has the optimal power. The signals are sent simultaneously by some nodes whose strength is not correlated. The surface buoy receives all superimposed signals. Intracluster interference measured at underwater nodes is a function of channel gain. Therefore, nodes with low channel gain are more susceptible to strong intracluster interference. A SIC receiver mounted on a surface buoy decodes the signal, subtracts the interfering signal from the superimposed information, and resolves with a suboptimal gain. Subsequently, the signal is decoded.
For convenience, we designed an uplink MMWNOMA scenario for a smallscale UAN. The underwater nodes are transmitters in the system, and the surface buoy is the receiver. Each buoy has multiple antennas for sending and receiving. Supposing the number of underwater nodes is (). As a result, the received signal of the th cluster is shown as follows: where represents the channel vectors of the th cluster. means the white Gaussian noise. is the th beamforming vector. is the transmitting signal of the th set, which is expressed as follows:
and are signals of a NEN and a FEN in the th cluster. and are the power factors of the two nodes, namely, . The channel matrix is shown in the following equation: where is the transpose matrix, and is the channel vector of the NEN. The coding matrix is shown in the following equation: where represents the zeroforce beamforming (ZFBF) vector, is the pseudoinverse matrix, and is the conjugate complex number. Therefore, the signal which received by the NEN is shown in the following equation: where is the signal interference. Since the NEN generates the beam forming vector, it can be eliminated by ZFBF. Thus, we get that . is the interference of a FEN, which can be eliminated by a SIC receiver, so the received signal of the NEN is simplified, as shown in the following equation:
Since SIC and ZFBF cannot be used to cancel interference of the FEN, the received signal of a FEN is shown in the following equation:
3.2. The Node Pairing Algorithm
After the UAN is deployed, the surface buoy broadcasts a registerrequest message. The underwater node responds to the buoy with a registerresponse message. After decoding the registerresponse message containing the node ID, location, energy, and signal strength, the surface buoy resolves the pairing weight and creates a weight table. Then, the underwater node sends a pairrequest message. The buoy checks the weight table and responds with a pairresponse message. Figure 2 shows the pairing procedure.
This paper suggests a maximum and minimum weight algorithm to construct the node pairing procedure. Two nodes with considerable differences in gain are paired into a cluster and share the same channel resources. The NEN is the closest node to the surface buoy and has optimal channel conditions. The FEN is relatively far from the surface buoy, and the channel conditions may be poor. The pairing weight may be the same when considering position and residual energy. In this case, the node with the smallest ID will be selected first.
An objective of the pairing algorithm is to establish a hierarchical weight difference between a FEN and a NEN. As shown in (8), the nodes must meet the maximum pairing weight. where and mean the FEN and the NEN. and are sets of NENs and FEN, respectively. The pairing weight is shown in the following equation: where is the factor of the residual energy for node , is the signal strength, is the distance factor, and is the Euler distance between node and the surface buoy. Algorithm 1 shows the node pairing algorithm.
Algorithm 1 description: this program implements the node pairing process of MMWNOMA. Pair generation is established based on node state values in the traversal system. The remaining energy and distance factor are inputs to the program. The pairing weights for nodes are calculated based on their Euclidean distance from the buoy. Then, implement the mapping between nodes and their pairing factors and construct a max weight queue and min weight queue. It constructs the minmax node pair by selecting each queue object.

3.3. The Node Replacement Schema
The nodes move due to ocean currents. Thus, the distance between the NEN, FEN, and the surface buoy can vary. Furthermore, the energy of each node must be consumed. Therefore, a node replacement mechanism must be designed. We define a relevant threshold based on business requirements during initialization. After a period of operation, the node sends its channel status message (CSI) to the surface buoy. The buoy uses CSI to calculate the channel correlation coefficient between two nodes, as shown in the following equation:
If , the buoy will count for the gain difference between the NEN and the FEN and then store it in , which is the set of gain difference, as shown in the following equation: where is the gain difference between a NEN and a FEN.
After that, the surface buoy traverses unpaired nodes in the UAN and calculates their peak signaltonoise ratio (PSNR) in turns. The buoy selects a node with the largest PSNR and compares it with node . If , it will use node to replace node , as shown in the following equation:
If , it maintains the pairing of and , as shown in the following equation:
Algorithm 2 shows the node replacement mechanism.
Algorithm 2 description: this program implements the node replacement mechanism. The channel correlation threshold is an input to the program. The channel correlation coefficient and channel gain difference are counted by traverse nodes of the MMWNOMA system. The buoy selects the node with the peak signaltonoise ratio (PSNR) in turns and compares it with node . If it is greater than , replace with , and modify the channel gain, otherwise, maintain the original node pair.

3.4. The Power Allocation Mechanism
Once the pairing procedure is complete, MMWNOMA communication will be implemented in each cluster. Therefore, a power distribution mechanism for the FEN and the NEN should be devised. The achievable data rate reflects the capacity of each node. The mean square error (MSE) of NOMA is shown in the following equation: where , , and indicate the transmission coefficients, and denotes the transmission rate. Unlike the OMA mode, which needs two slots to support nodes, the MMWNOMA system requires only a slot to supply them. Consequently, the data transmission rate is half that of the NOMA model, as shown in the following equation:
The optimization of power allocation in MMWNOMA is shown in the following equation:
As the optimal solution, is derived by the KarushKuhnTucker (KKT) condition, as shown in the following equation:
The objective function and the restrictive condition are derived by KKT, as shown in the following equations, respectively. where represents the MSE in the quadrature modulation mode.
Consider a cluster with a FEN and an NEN, and suppose that the channel condition of the NEN is better than the FEN, i.e., . Consequently, the transmission rates are shown in the following equation: where and are the transmit power of the NEN and FEN, and is the Gaussian white noise.
Due to the decoding order, NEN first performs signal parsing on the buoy using the SIC mechanism. However, NENs interfere with FENs. When a NEN signal decodes, it subtracts from FEN signal, and then, the FEN signal is decoded. The power allocation factors are shown in the following equation: where , means the transmitting power of the cluster, that is, .
Let , the transmission rates of a NEN and a FEN are shown in the following equation:
The throughput of the nodes pair may be counted by adding the transmission rates, as shown in the following equation:
For an MMWNOMA system, there is a limit to the power allocated to the node with optimal channel gain. When the surface buoy demodulates the received signal, there is a power interval between a NEN and FEN, which can ultimately be used to determine the maximum transmission power of the NEN and the FEN. The constraints of are shown in the following equation:
Based on (24), the power allocation factors and can be rewritten as the following equation: where , so the upper limit of the power allocation factor is shown in the following equation:
Let be the communication threshold of FEN, and be a condition to maintain the normal communication. Then, we obtain the lower limit of the power allocation factor, as shown in the following equation:
Algorithm 3 shows the power allocation algorithm.
Algorithm 3 description: this program is used to implement the power distribution of the MMWNOMA system. The maximum transmit power and communication threshold are inputs to the program. First, traverse whole nodes to count the MSE of the NOMA system and then compute the MSE in the OMA type. Followed by, solving the objective function and constraint value of the NOMA system, and calculate the power distribution factor of the FEN node and NEN node.

4. Numerical Results
4.1. Experimental Settings
We set up an experiment with a surface buoy and 20 underwater nodes in an underwater MMWNOMA scenario. The buoy is fixed with 48 hydrophones, and each underwater node has two hydrophones. The Poisson distribution is considered to be the system deployment model. Typically, nodes are 3 to 10 meters deep. Various tools are used in this experiment, including MATLAB 2019, WOSS, and BELLHOP Acoustic Toolbox [32]. The following main parameters are listed in Table 1.
Suppose that the acoustic channel is perfectly known and that the underwater nodes are divided into ten clusters based on the pairing algorithm. The OFDM technology is used for intracluster communication, and NOMA is used for intercluster communication. We compare MMWNOMA with RPNOMA and OFDM techniques in exact scenarios. For a RPNOMA communication system, clusters are formed via the random pairing mechanism. In OFDM, all nodes are considered a management cluster. Specifically, throughput, MSE, energy efficiency, and complexity of the three systems are compared. We design an MMWNOMA simulation program. Figure 3 shows the distribution plots for 20, 40, 80, and 160 node pairs.
(a) Pairing of 20 nodes
(b) Pairing of 40 nodes
(c) Pairing of 80 nodes
(d) Pairing of 160 nodes
4.2. Comparison of Throughput
In general, throughput refers to the amount of data successfully transmitted per cycle and is an essential indicator of a communication system. This work evaluates the achievable throughput of MMWNOMA, RPNOMA, and OFDM. The performance of the three methods at different nodes is shown in Figure 4. The cumulative distribution function (CDF) of throughput is shown in Figure 5.
Under low SNR conditions, MMWNOMA shows roughly the same throughput as RPNOMA. As SNR increases, MMWNOMA outperforms RPNOMA, while OFDM has relatively low throughput. Simulation results show that MMWNOMA has specific advantages in terms of high throughput with multiple nodes.
A pair of nodes is scheduled simultaneously for each subband in MMWNOMA. In addition to the near and farreaching effect, the SIC receiver is also used to decode and demodulate the signal. Therefore, we choose more levels of modulation and coding strategy (MCS) for the allocation of power to underwater nodes. However, the possibility of selecting the MCS level in the OFDM scheme is low, which undoubtedly leads to low throughput. MMWNOMA uses maximum and minimum weight to reduce correlation and interference and maintain optimal throughput. As for RPNOMA, it uses the random pairing algorithm between nodes, and the channel difference between a FEN and a NEN cannot be kept optimally unchanged. Therefore, throughput of RPNOMA is lower than that of MMWNOMA. Overall, it achieves the minimum transfer rate and SIC constraints in MMWNOMA and improves signal and throughput.
4.3. Performance of the MSE
Measurement of MSE is critical to determining the reliability of a communication system. The MSE of a UAN refers to both the propagation characteristics of the underwater channel and the access technology. This paper compares the MSEs of MMWNOMA, RPNOMA, and OFDM without channel coding. The MSEs with different numbers of nodes are shown in Figure 6. As the number of nodes increases, the MSE of all three systems increases. In contrast, the rise of OFDM is enormous. Furthermore, the MSEs of RPNOMA and MMWNOMA are approximately the same.
Figure 7 illustrates the MSE at different SNRs. It is clear that as the SNR increases, the MSE of the three systems decreases. In contrast, the MSE of OFDM is relatively high, while the MSE of MMWNOMA is slightly lower. MMWNOMA shows the most significant reduction in MSE.
Due to the fixed modulation strategies in OFDM, the MSE is determined by the subcarrier that performs the most poorly. However, the multiplexed signal is less sensitive to the delay of channeldependent feedback in MMWNOMA, or CSI no longer strongly affects the multiplexed signal. A significant difference between MMWNOMA and RPNOMA is that the optimal gain difference of a NEN and FEN is not fully guaranteed. If the gain difference is slight, the throughput will be reduced. Therefore, the MSE of RPNOMA is higher than that of MMWNOMA.
4.4. Comparison of Energy Efficiency
In general, batteries power underwater nodes with limited energy. It is difficult to replace the battery or charge it after deploying a node. Since the UAN is an energyconstrained system, energy efficiency is a crucial factor to consider. Figure 8 shows the energy efficiency for MMWNOMA, RPNOMA, and OFDM with different transmitting power. As the transmission power increases, the energy efficiency of the three systems increases. In contrast, the energy efficiency of MMWNOMA is approximately 13.33% higher than that of OFDM and 4.31% higher than that of RPNOMA.
Figure 9 illustrates the EE of three systems with different transmission rates. For MMWNOMA, it uses the maximum and minimum weight algorithm to achieve the optimal fair distribution of FENs and NENs and then constructs a power control strategy based on the allocation factor to optimize energy efficiency. Although RPNOMA adopts the power control schema based on NOMA, there is no suitable node replacement mechanism. FENs and NENs cannot be allocated fairly and optimally using a random pairing algorithm. Therefore, the energy efficiency of RPNOMA could not be significantly improved.
All three systems show a decreasing trend in energy efficiency as the transmission rate increases. Experiments show that the energy efficiency of NOMA is higher than that of OMA technology. NOMA allocates spectrum resources to multiple nodes and selects SIC at the receiver to maximize system capacity. On the contrary, OMA only grants resources to a single node and cannot be used at the receiving end, thus failing to reach maximum capacity.
4.5. Comparison of Complexity
Complexity is a crucial metric for evaluating the realtime performance of a communication system. When the number of nodes is less than 8, the complexity of the three methods is close to the same level, as shown in Figure 10. However, the complexity of OFDM increases significantly with the number of nodes, while that of MMWNOMA is slightly higher than that of RPNOMA.
The acoustic channel resources of underwater OFDM systems are limited, and subcarrier allocation is required to minimize the transmission power and maximum the transmission rate. For an OFDM system, surface buoys allocate resources to each node based on CSI and associated subcarrier allocation criteria. When CSI changes, the buoy reassigns subcarriers. Therefore, the complexity of multiplication for subcarrier allocation and update reallocation is , and that of addition is in an OFDM system with nodes. For MMWNOMA, the multiplicative complexity of node pairing, node selection, replacement, and power allocation is , and that of addition is . For RPNOMA, the node pairing scheme is realized based on the random elimination mechanism. The complexity of multiplication is , and that of addition is . Multiple clusters are constructed in MMWNOMA and RPNOMA, and OFDM communication is still used between clusters. Thus, the complexity of multiplication and addition is increased relative by and , respectively, for MMWNOMA and RPNOMA.
5. Conclusions
This paper proposes MMWNOMA, a NOMA communication system that allocates power to underwater nodes based on the quality of the channel. We build the MMWNOMA model in the UAN scene. SIC receivers placed on surface buoys allow the superimposed signals to be separated from each other. These superimposed signals share the same time or frequency resource block. We design a node pairing algorithm based on maximum and minimum weight. To verify performance, we review the throughput, MSE, EE, and complexity of MMWNOMA, RPNOMA, and OFDM, respectively. The simulation shows that it achieves the highest throughput in MMWNOMA, keeps the smallest MSE, and guarantees the highest EE. Nonetheless, under the same experimental scenario, the complexity is slightly higher than RPNOMA, but significantly lower than that of OFDM. It has been shown that MMWNOMA achieves a reasonable balance between performance and complexity.
As an interesting research direction, we are designing a prototype for a NOMAenabled underwater node. Based on this work, we intend to verify the performance of MMWNOMA in various scenarios thoroughly. Currently, we have designed a UAN [33–36] built on a softwaredefined networking (SDN) architecture. It is worth mentioning that the development process of UAN can be significantly shortened, and experimental construction can be easily realized based on SDN. Then, field deployment and smallscale experiments will be the main work.
Abbreviations
AUVs:  Autonomous underwater vehicles 
BS:  Base station 
BER:  Bit error rate 
CSI:  Channel status message 
CDMA:  Code division multiple access 
CDNOMA:  Code domain NOMA 
CNOMA:  Collaborative NOMA 
CDF:  Cumulative distribution function 
FEN:  Farend node 
FDMA:  Frequency division multiple access 
FDCRNOMA:  Fullduplex cooperative relay for NOMA 
IoT:  Internet of Things 
KKT:  KarushKuhnTucker 
MMWNOMA:  Maximum and minimum weightsbased NOMA 
MSE:  Mean squared error 
MIMONOMA:  Multiple in multiple out based NOMA 
MCS:  Modulation and coding strategy 
NEN:  Nearend node 
NOMAFBMC:  NOMA using filter bank multicarrier 
NOMAOFDM:  NOMA using OFDM 
NOMACRS:  Cooperative relaybased NOMA 
NOMA:  Nonorthogonal multiple access 
OFDMA:  Orthogonal frequency division multiple access 
OFDM:  Orthogonal frequency division multiplexing 
OMA:  Orthogonal multiple access 
PONOMA:  Partially overlapping NOMA 
PDNOMA:  Power domain NOMA 
PSD:  Power spectral density 
QoS:  Quality of service 
RPNOMA:  Randomly paired NOMA 
ROVs:  Remotely controlled vehicles 
RB:  Resource block 
SIC:  Serial interference cancellation 
SRM:  Sumrate maximization 
TDMA:  Time division multiple access 
UAN:  Underwater acoustic network 
UUVs:  Unmanned underwater vehicles 
ZFBF:  Zeroforce beamforming. 
Data Availability
The data used to support this study are available from the corresponding author upon request.
Conflicts of Interest
The authors declare that they have no conflicts of interest.
Acknowledgments
This work was supported in part by the Science and Technology Major Project of Xinxiang City under Grant 21ZD003, in part by the Key Scientific and Technological Project of Henan Province under Grant nos. 222102320181, 222102110011, 212102210422, 212102310087, and 202102210388, in part by the Young Scholar Training Program of Higher Education in Henan Province under Grant 2019GGJS172, and in part by the Key Scientific Research Project of Colleges and Universities in Henan Province under grant 20A520002 and 21A520001.