ZHENG Yu, LIU Yingjie, REN Yuanhong, FEI Chen, ZHANG Shijiang, and LI Hongzhi

Orthogonal Frequency Division Multiplexing Adaptive Technology for Multinode Users of Seawater Channel Based on Inductively Coupled Mooring Chain

ZHENG Yu1), *, LIU Yingjie1), REN Yuanhong1), FEI Chen2), ZHANG Shijiang2), and LI Hongzhi3)

1),,300387,2),,300387,3),300112,

As an important part of buoy-type ocean monitoring systems, the inductively coupled mooring chain solves the problem of data cotransmission through the multinode sensors that it carries, which is significant for the rapid acquisition of fish, hydrology, and other information. This paper is based on a seawater channel transmission model with a depth of 300 m and a bandwidth of 2 MHz. An orthogonal frequency division multiplexing (OFDM) technology is used to overcome the multipath effect of signal transmission on a seawater medium. The adaptive technology is integrated into the OFDM, and an improved joint subcarrier and bit power allocation algorithm is proposed. This algorithm solves the problem of dynamic subcarrier allocation during the cotransmission of underwater multinode user data in seawater channels. The results show that the algorithm complexity can be reduced by 0.18126 × 10?2s during one complete OFDM system data transmission by the improved greedy algorithm, and a total of 216 bits are transmitted by the OFDM. The normalized channel capacity can be improved by 0.012 bit s?1Hz?1. At the bit error ratio (BER) of 10?3, the BER performance can be improved by approximately 6 dB. When the numbers of users are 4 and 8, the improved algorithm increases the channel capacity, and the higher the number of users, the more evident the channel capacity improvement effect is. The results of this paper have an important reference value for enhancing the transmission performance of inductively coupled mooring chain underwater multinode data.

inductively coupled mooring chain; seawater channel; multinode users; OFDM; adaptive technology

1 Introduction

The ocean contains abundant biological, mineral, and va- rious energy sources, and its research and exploration are becoming increasingly important (Vasilescu., 2005). With the development and progress of marine science and technology, countries around the world have established three-dimensional marine environment monitoring systems and biological information collection, transmission, and real- time feedback systems based on global strategies (Ku., 2008; Wang., 2012; Cai., 2015). Marine life mo- nitoring is based on the study of the ocean and its uses. The marine biological environment fixed-point observation plat- form, which is represented by sea-air interface observation buoys and submersibles, offers the advantage of continuous monitoring and can automatically obtain parameters, such as temperature and water quality, of marine or- ganisms (Yang, 2002). As a modern marine biological monitoring new technology, marine buoys are an important part of marine biological three-dimensional monitoring networks and have application and research signifi-cance (Luo, 2022). The inductive coupling mooring chain is an important part of marine buoy biological mo- nitoring systems. The data sensor node is mounted on the chain’s transmission cable (Zheng., 2022) and realizes the noncontact transmission of underwater biological infor- mation collection data based on the principle of inductive coupling. Marine buoy platforms that use noncontact data transmission technology show good scalability and con- venient structure and can form a long-term, real-time, and autonomous working observation network (Wu., 2016). Fig.1 shows a schematic of underwater current data trans- mission based on an inductively coupled mooring chain. During the transmission, the magnetic ring is excited on the water to generate an excitation current, and the signal is transmitted in the form of underwater current. The data col- lected by the underwater sensor node fixed on the transmission cable are coupled to the loop through the coil based on the principle of inductive coupling to realize noncontact transmission of the underwater sensor node data. Underwater sensors can collect underwater ocean information, such as temperature, salinity, and depth, at different depths. Finally, the coupling and transmission of the collected in- formation to the water magnetic loop ease further analysis and processing. However, with the densification of under- water sensors, higher requirements for underwater communication performance must be met.

Fig.1 Schematic of the underwater data transmission process.

Current communication has its own advantages in sea- water: it is not easily affected by suspended particles and marine plankton, and it easily adapts to various external en- vironments. In the absence of displacement current, the carrier frequency of current communication can reach the order of several megahertz (Kim., 2010). The pro- pagation velocity of the current field approximates 3.3 × 107m s?1, which is close to the speed of light (Goh., 2009). This speed allows the underwater current communication system to attain a strong real-time performance.

The research on underwater current communication is relatively mature. Kim. (2010) realized underwater short-range wireless current communication by establishing a path loss channel model and proposed the potential use of adaptive modulation technology in allocating different bits and power to various subcarriers to improve data rate and reliability. Based on the principle of inductive coupling, a voltage conversion model of the two-stage electromagnetic coupler was established, and the data and energy transmission of the noncontact underwater sensor node was realized (Huang, 2013). A simplified electric dipole model was used to explain the working principle of current communication, and an amplitude-shift keying modulation and demodulation technology was applied to realize data transmission based on underwater current com- munication (Wang, 2015). Marine environment si- mulation was conducted, a mathematical transmission mo- del of seawater channels was established, and noncontact data acquisition from single or multiple nodes was realized. The prospect of designing orthogonal frequency division multiplexing (OFDM) systems with unequal bit loading has also been presented (Zoksimovski., 2012). Underwater noncontact data transmission was realized based on the two-stage electromagnetic coupler transmission mo- del and the adopted differential phase-shift keying method (Wu., 2016). High data rates can be obtained by the application of the OFDM to multinode inductive communication systems, which use quadrature phase-shift keying as the modulation method (Thanh and Agbinya, 2016). Based on the principle of inductive coupling, a physical mo- del of current transmission was established (Zheng., 2019a, 2021a), and the channel impedance characteristics of different sensing node users were explored (Jin., 2017). Elamassie. (2019) proposed a joint subcarrier allocation algorithm suitable for OFDM technology and used it in the transmission network of underwater optical sensor nodes; the simulation results showed that the adaptive allocation algorithm based on the rate maximization criterion can allocate dynamically subchannels, bits, and power for each sensor node in accordance with the subchannel channel state information (CSI) under a satisfying preset bit error rate. Yu (2019) established an underwater acoustic channel model and proposed a system model for multiuser dynamic adaptive bit allocation adapted to underwater acoustic channels; they also used multiple algorithms to allocate resources, such as subcarriers, bits, and power and analyzed their transmission performance. Yuan. (2019) proposed an artificial bee colony algorithm, which can maximize the system capacity while ensuring user fairness, to realize the dynamic allocation of OFDM multiuser system resources. The magnetic induction link in the underwater transmission process was studied, a com- pact and easy-to-deploy autonomous submarine wireless communication system was designed, and an adaptive circuit based on OFDM multicarrier modulation was proposed to expand the link bandwidth (De Paillette and Gaugue, 2020).

The above studies revealed that although the research on underwater inductively coupled current communication technology is relatively mature, the OFDM technology is already being applied to underwater inductively coupled current communication. However, studies on this problem combined with adaptive technology for the allocation of different bits and power to various subcarriers are limited. A previous study established a seawater multipath transmission channel of the inductively coupled mooring chain. This channel was built based on MATLAB, and when the length of the steel cable was 300 m, its amplitude-fre- quency characteristics were analyzed to determine the chan- nel bandwidth. The use of OFDM technology was proposed to overcome the multipath effect of seawater channels, and adaptive technology was integrated into the OFDM to realize resource allocation of multiple underwater sensor node users.

The second part of the article provides a brief overview of the inductively coupled seawater channel and establishes the main transmission parameters of the OFDM system. The third part combines the adaptive algorithm with the OFDM, designs an adaptive allocation scheme based on an inductively coupled seawater channel, and proposes an im- proved joint subcarrier and bit power allocation algorithm for the application of the OFDM to seawater channel trans- mission. First, based on the improved subcarrier allocation algorithm, the problem of subcarrier allocation in the OFDM system during the simultaneous transmission by multiple underwater node users is solved. On this basis, an improved greedy algorithm is proposed for the dynamic allocation of the appropriate number of transmission bits and power values to the subcarriers allocated by each user. The fourth section initially verifies the effectiveness and re- lated performance of the improved greedy algorithm when applied to underwater single-user bit and power allocation. Then, based on the improved joint subcarrier and bit and power allocation algorithm, simulation analysis of the re- source allocation results of underwater multiuser subcarriers, bits, and power based on the seawater channel is per- formed. A conclusion is drawn at the end of the article.

This paper proposes the application of the adaptive resource allocation algorithm and OFDM technology, which can adaptively allocate subbands of appropriate width to each user in accordance with the CSI in the seawater chan- nel transmission process. The application eliminates the dis- advantages of traditional frequency division multiple access or time division multiple access (TDMA) methods and can dynamically allocate appropriate bits and power for each user, improve bandwidth use and channel capacity, and further enhance the system transmission performance.

2 Seawater Channel and Parameter Selection

2.1 Inductively Coupled Seawater Channel

The multipath effect of electrical signal transmission in seawater is verified based on COMSOL. The length of the steel cable is 300 m, the seawater dimensions are 1200 m × 1200 m × 1200 m, and the grid division method is used to divide the channel path into 10 diameters. The results show that the shortest path of electrical signal transmission on the steel cable is 300 m, and the longest is 523 m. The pro- pagation speed in seawater is approximately 3.3 × 107m s?1, the calculated 10-path time delaysare (0, 0.246, 0.504, 1.07, 1.55, 2.17, 2.91, 3.88, 5.47, and 6.76), and the unit is (μs). A frequency excitation of 10 kHz is applied to this model, and the simulation of transmission steel cables at dif- ferent depths is conducted. The depth ranges from 300 m to 2000 m, and the interval is 100 m. The current value is ob- tained by the integration of the current line density on the transmission steel cable. Then, the current values at various depths are normalized to the standard at a depth of 300 m. At the electrical signal frequency of 10 kHz, the path loss parameters of the transmission steel cables at different dep- ths are obtained, and the function is fitted, as shown in Eq. (1). Then, the current line density is integrated to obtain the channel output current value at frequencies of 10 kHz to 10 MHz and normalized to 10 kHz to determine the attenuation parameters of the current signal at different frequencies and perform a function on it (Eq. (2)). Based on the finite impulse response mathematical model method, the established seawater channel multipath transmission model is shown (Eq. (3)) (Zheng., 2019b, 2021b):

whereis the signal frequency,is the cable depth,() is the frequency attenuation parameter,() is the path loss parameter,is the number of paths,gis the path weight factor, τand is the path delay.

Then, a channel model is built based on the MATLAB platform (hardware environment central processing unit (CPU): Intel(R) Core(TM) i7-7700HQ @ 2.80 GHz and RAM: 8.00 GB; software environment: Windows 10 Professional Edition operating system; MATLAB version: R2016a). When the steel cable length is 300 m, a standard sine wave with frequencies of 10 kHz to 10 MHz is passed in, and its amplitude-frequency characteristic curve is analyzed. With the frequency corresponding to the amplitude attenuation of ?20 dB as the cutoff frequency, the effective bandwidth at a depth of 300 m equals 2 MHz.

2.2 Parameter Selection

The parameter design of the OFDM system transmission based on an inductively coupled seawater channel mainly includes determining the seawater channel bandwidth, de- termining the multipath delay, selecting the cyclic prefix (CP) length, selecting the OFDM symbol period, determining the data bit rate, and determining the number of subcarriers. The analysis in the previous section shows that the effective bandwidth B of the seawater channel is 2 MHz, and the maximum delaymaxis 6.76 × 10?6s when the length of the steel cable is 300 m. In general, the CP length of the OFDM system should meet the condition of≧maxto overcome the influence of intersymbol interference. An ex- tremely lengthy and large CP will cause the loss of signal- to-noise ratio (SNR) performance. Thus, the selected CP length is also 6.76 × 10?6s. The CP length is generally 1/5 of the OFDM symbol period. Therefore, the OFDM sym- bol period is 3.38 × 10?5s. Subcarrier spacing is the reciprocal of the symbol period without a CP, and the number of subcarriers is the effective bandwidth of the seawater transmission channel divided by the subcarrier spacing. In the OFDM system, the number of fast Fourier transform (FFT) points must be an integer power of 2, and the sampling period of the system is the symbol period when the OFDM system has no CP divided by the number of FFT points. Table 1 shows the designed transmission parame- ters of the OFDM system based on the inductively coupled seawater channel and the abovementioned OFDM parameter design method.

Table 1 Transmission parameters of the OFDM system for inductively coupled seawater channels

3 Adaptive Resource Allocation Scheme and Realization Principles of Underwater Sensor Node Users

3.1 Design of Adaptive Resource Allocation Scheme Based on Inductively Coupled Seawater Channels

The OFDM system resource allocation scheme based on inductively coupled seawater channel sensor node users is as follows. First, the seawater transmission channel can be regarded as a slow-fading channel. The physical and conductivity characteristics of seawater channels are relatively stable in a short period, and thus, the fixed-point observation communication platform based on the inductive coupling mooring chain of the fixed-point buoy observation platform does not have the Doppler effect caused by platform motion. In the transmitter, the ideal channel estimation method is used to estimate the real-time CSI of subcarriers. Then, the transmitter can use the CSI combined with adaptive bit and power allocation technology to dyna- mically adjust the bit and power allocation of each subcarrier. The adaptive modulator modulates each subchannel, performs IFFT on the modulated frequency domain symbols, and adds a guard interval of appropriate length. Then, these time domain data symbols reach the receiving end through the seawater channel. Finally, the inverse trans- form corresponding to the transmitting end is performed at the receiving end. First, the guard interval is removed, and FFT is performed. Then, the data are demodulated based on the carrier modulation information obtained by the transmitting end, and the original transmitted data signal is recovered. Fig.2 shows a single-node user resource allocation scheme based on seawater channels.

Fig.2 Adaptive resource allocation scheme based on seawater channels 94.

3.2 Improved Joint Subcarrier and Bit and Power Allocation Algorithm

3.2.1 Improved multiuser subcarrier allocation algorithm

In the actual application process, the resource allocation of multiuser systems cannot completely allocate resources, such as bits and power, to subchannels with good channel conditions as a single user does. This paper proposes an im- proved multiuser subcarrier allocation scheme that limits the number of subcarriers allocated for each user. This scheme can be performed strictly and accurately in accordance with the set user ratio constraint under the condition that the subcarriers allocated by each user are guaranteed to have a high SNR. Assuming that the number of subcarriers in the multiuser OFDM system is, the number of users is, the channel bandwidth is, and the total transmit power istotal,0represents the noise power spectral density,2,denotes the channel gain of theth user on itsth subcarrier,p,nindicates the power value allocated by theth user on itsth subcarrier,H,n=2,/0refers to the SNR of the useron itsth subcarrier, andc,nassigns matrix elements to the subcarriers. The objective function can be expressed as Eq. (4) (Shen., 2005):

The constraint condition is given in Eq. (5):

where (a) indicates whether subcarrieris allocated to user; (b), the same subcarrier can only be used by one user; (c), the power value assigned to each subcarrier shall not be less than 0; (d), the total power value allocated by all subcarriers must meet the power constraints and must not exceed the set total transmit power value. In (e), {}|=1 is the preset user rate ratio constraint that ensures user fairness, and {R} is the expected rate value of theth user, which can be expressed by Eq.(6), whereNis the number of subcarriers allocated by theth user, andb,nindicates the number of bits allocated by theth user on itsth subcarrier.b,ncan be obtained in accordance with the Shan- non theorem, as shown in Eq.(7).

The improved multiuser subcarrier allocation algorithm is as follows:

1) Initially, letR= 0, Ω= ?,c= 0,= {1, 2, ···,},p,n=total/,N=×∑, Λ= {1, 2, ···,},, and∈ {1, 2, ···,}, whererepresents the set of all subcarriers,Ndenotes the number of subcarriers allocated to the user, and Λ is the set of all users.

2) Find the subcarrierswith the largest SNR for user 1 to userin turn and assign them to the corresponding users; that is, for all users∈ {1, 2, ···,}, find the subcarriersthat satisfy the conditions |H,n| ≥|H,j| and assign them to userand∈.

5) Complete the allocation of subcarriers for each user.

3.2.2 Bit and power allocation algorithm for each user subcarrier

Under the constraint of limited total power, the total power allocated to each user when maximizing the channel capacity of an individual user is computed and determined by constructing the Lagrangian equation, as shown in Eqs. (8) – (10). Then, the per-user bit and power allocation problem can be transformed into a single-user bit and power allocation problem. The application of an improved greedy algorithm to the inductively coupled channel transmission is proposed to complete the bit and power allocation for each user subcarrier. Specifically, the improved greedy algorithm can be summarized as follows: Based on the channel gain of the subchannel, find the channel gain corresponding to the subchannel allocated by each user, cal- culate the average value of the subchannels in ascending order, and directly allocate the average number of bits to the subchannel higher than the average value of channel gain. The remaining bits are then allocated in accordance with the allocation steps of the traditional greedy algorithm. Ensure the rational and efficient use of resources.

where {λ}|=1 is the Lagrangian factor. When ?/?p,n0, Eqs. (9) and (10) are obtained:

Next, the transmission power value of the subchannel allocated for each user is temporarily not considered. First, the total power of all subchannel transmissions allocated for each user is calculated. Assuming that the total power allocated to useris P,tot,1,totcan be obtained by derivation (Eq. (11)):

In the above formula,canddare coefficients that satisfy the known conditions. The total transmission power allocated to each user is obtained by using the nonlinear equation method, as shown in Eq. (12):

After the allocation of the total power to each user, the power of the user is allocated to the subchannel allotted by each user. Then, the problem of subchannel power allocation for each user can be transformed into a problem similar to that of single-user power allocation. After further derivation, Eq. (13) can be obtained:

The specific allocation steps are as follows:

1) Initially, the number of subcarriers in the OFDM system is, the total number of bits to be allocated isR, the number of bits allocated for theth subchannel isR, the allocated bit step size is 2, and the maximum number of allocated bitsmaxfor a subchannel is 6.

2) Calculate the total user power allocated to each user by constructing the Lagrangian equation.

4) Calculate the total number of allocated bitsand determine whether the condition<Ris established. If so, allocate the remaining subcarriers; otherwise, output the allocation result.

5) Allocate the remaining subcarriers of the user; that is, calculate the power increment required to increase 2 bits for all subcarriers: ?p(b+ 2) =p(b+ 2) ?p(b). Then, search for the subcarrier with the smallest increment, that is, ?p(b+ 2). Next, find the corresponding subchannel number defined asand allocate 2 bits to the corresponding subchannel; that is,b=b+ 2. Finally, repeat the pro- cess for iteration 3.

6) Under the condition that the total power allocated to the user in step 2 is satisfied, calculate the power required by each subcarrier according to Eq. (14):

7) Continue assigning the next user until all users’ power and bits are allocated.

4 Analysis of Simulation Results

4.1 Improved Greedy Algorithm to Realize Subcarrier Bit and Power Allocation for Single Users

First, the results of bit and power allocation for single- user subcarriers using the improved greedy algorithm are verified. The seawater channel bandwidth is 2 MHz, and the channel is divided into 64 subchannels. A total of 216 bits are transmitted in one OFDM symbol. A maximum of six bits are allowed to transmit in a subchannel, and the total power constraint satisfied is not greater than 1 W. Fig.3 shows the bit and power allocation results when the improved algorithm is used. The results show that the improv- ed algorithm can allocate high bits and power to subchan- nels with high channel gains and allocate fewer bits and power to subchannels with poor channel gains. Meanwhile, it does not allocate bits and power to subchannels with poor channel attenuation. Thus, the improved algorithm can be correctly applied to the seawater channel data transmission process and dynamically allocate bits and power to it. In addition, the sum of bits allocated to all subchannels satisfies the preset constraints.

For the further study of the performance of the improved algorithm, we compare and analyze the results of algorithm complexity, normalized channel capacity, and transmission bit error ratio (BER) of the water-filling algorithm (Cho., 2010), greedy algorithm (Tase., 2006), Chow algorithm (Chow., 1995), Fischer algorithm (Fischer and Huber, 1996), and the improved algorithm proposed in this paper when applied to inductively coupled seawater channel transmission. First, the CPU running times of different algorithm programs are compared on the basis of the MATLAB platform to analyze the complexity of algorithms. The SNR ranges from 0 dB to 30 dB, and the increment in value is every 2 dB. Under the conditions of the 16 SNRs, the operation is repeated 10 times to obtain the average value, and the CPU running time required to complete the data transmission process of the entire OFDM system is obtained. Then, we further simulate and calculate the normalized channel capacity of different algorithms, that is, the information transmission rate of the unit frequency band. After obtaining the channel capacity of the OFDM system, we divide it by the bandwidth of the OFDM system and the number of subcarriers to obtain the normalized channel. Table 2 shows the average CPU running times of the above algorithms under different SNRs and the simulation results of the normalized subchannel capacity under the same SNR of 30 dB. Next, we compare the average BER results obtained after 100 iterations of statistics under the SNR using different algorithms for transmission in inductively coupled seawater channels. Fig.4 shows the result. A total of 216 bits are transmitted in one OFDM symbol, and a maximum of 6 bits are allowed to transmit on a subchannel.

Fig.3 Bit and power allocation results obtained when using the improved algorithm.

Table 2 Comparison of normalized channel capacity and complexity of different algorithms

The water-filling and Fischer algorithms require a short- er average CPU time to complete the data transmission pro- cess in the OFDM system compared with the other algorithms. Thus, both algorithms have lower complexities. However, their normalized channel capacity is also low; that is, their frequency band utilization rates are low. The greedy and Chow algorithms have higher normalized chan- nel capacities, but their complexity is also higher. The im- proved greedy algorithm introduced in this paper has improved normalized channel capacity and algorithm complexity. When completing one OFDM system data transmission, the algorithm complexity is reduced by 0.18126 ×10?2s, and the normalized channel capacity is improved by 0.012 bit s?1Hz?1. Moreover, when the BER result is the same, that is, 10?3, the improved algorithm in this paper can improve the BER performance of inductively coupled seawater channel data transmission by approximately 6 dB compared with the greedy algorithm.

4.2 Results Obtained When Using the Improved Multiuser Subcarrier Allocation Algorithm

Fig.5 shows the specific subcarrier allocation results of the unimproved Shen algorithm and the improved multiuser subcarrier allocation algorithm in the OFDM multinode user system based on the inductively coupled seawater channel. The selected number of users is 4, the user ratio constraint is [1:1:1:1], and the total number of carriers allocated for four users is 64. Fig.6 shows the CSI of different users through the inductively coupled seawater channel. The simulation results shown in Fig.5 indicate that under the preset user ratio constraints, the number of sub- carriers allocated to each user by the unimproved algorithm is [12:17:14:21]. The number of subcarriers allocated to each user by the improved algorithm is [16:16:16:16]. The improved algorithm can abide more strictly by the preset user ratio constraints. In addition, the validity and accuracy of the improved algorithm in the OFDM multiuser system based on the inductively coupled seawater channel are verified.

4.3 Bit and Power Allocation Results for Each User Subcarrier

On this basis, the improved greedy algorithm is applied to the bit and power allocation of subcarriers allocated by each user. The unimproved Shen algorithm and the improved algorithm are used to allocate appropriate transmission bits for each user’s subcarriers (Fig.7). Fig.6 reveals that the CSI of the four users is users 1, 3, 2, and 4 in order from good to bad. As shown in Fig.7, when the Shen algorithm is used, the subchannels allocated to users 1 and 3 can be used normally and are allocated with more transmission bits. In addition, the subchannels allocated to user 2 (5/17) are not used due to severe fading, and the proportion of subchannels that are not used due to severe fading in the channel allocated to user 4 is 6/21. When the improved algorithm is used, the subchannels allocated to users 1 and 3 can be used normally, and more transmission bits are allocated. Meanwhile, 1/4 of the subchannels allocated to user 2 are not used due to severe fading, and the proportion of subchannels that are not used due to severe fading in the channel allocated to user 4 is 3/16. The performance of the improved algorithm is significantly enhanced, which greatly reduces the nonusage of channels caused by subchannel fading and improves the utilization rate and bandwidth utilization rate of the subchannels.

Fig.5 Comparison of subcarrier allocation results between the Shen algorithm and the improved algorithm for each user.

Fig.6 CSI for different users.

Fig.7 Comparison of the results of the Shen algorithm and the improved algorithm for subchannel bit allocation of each user.

Fig.8 shows that when the improved subcarrier allocation algorithm is used to allocate subcarriers to each user, the improved greedy algorithm is applied to allocate suitable bits and power to each user subcarrier to further improve the transmission performance of the system. Under the constraint condition of total transmission power equal to 1 W, the total transmission powers of user subcarriers allocated for user 1 to user 4 are 0.31926 W, 0.25855 W, 0.19974 W, and 0.22245 W, respectively.

Fig.8 Subchannel power allocation results for each user.

4.4 Performance Analysis of Multiuser Cotransmission

To further analyze the performance of the improved al- gorithm in this paper, we compare and analyze the algori- thm complexity, normalized channel capacity, and transmission BER results of the subcarrier and bit power allocation algorithms before and after the improvement in inductively coupled seawater channel transmission. Fig.9 shows the CPU running time required to realize the allocation of mul- tiuser subcarriers and total user power based on the MATLAB platform. The improved algorithm requires a shorter CPU running time than the traditional algorithm. Thus, the lower complexity of the improved algorithm is verified.

Fig.10a shows the simulation result of the normalized subchannel capacity of the system under the same conditions. The number of users is 4, and the SNR is 30 dB. The figure shows that the improved algorithm can increase the normalized subchannel capacities by 1.092 and 0.471 bit s?1Hz?1compared with the traditional TDMA method and the unimproved Shen algorithm, respectively. Fig.10b dis- plays the result obtained when the number of users is 8. The figure shows that the improved algorithm can increase the normalized subchannel capacities by 2.440 and 0.910 bit s?1Hz?1compared with the traditional TDMA method and the unimproved Shen algorithm, respectively. The im- proved multiuser resource allocation algorithm can improve the channel capacity of the system and bandwidth utilization rate, and the higher the number of users, the more evident the improvement effect.

Then, we analyze the results of the BER transmitted by each user on the relevant subcarriers. Fig.11 shows the transmission BER results of each user when the traditional Shen algorithm and the improved algorithm are used. The results show the higher BER performance of users 1, 3, and 2 than users 3, 2, and 4, respectively. This BER performance results are mainly determined by the users’ CSI. The comparison reveals that the improved algorithm can improve the BER transmission performance of users. When the SNR is 30 dB (Fig.11a), the BER results of users 1 – 4 are 0.05, 0.16, 0.08, and 0.23, respectively. As displayed in Fig.11b, when users 1 – 4 achieve the same BER results, the corresponding SNRs are 24, 25, 25, and 23 dB, respectively. Thus, under the same conditions, the improved Shen algorithm can improve the transmission BER performance of the traditional Shen algorithm by approximately 6 dB.

Fig.9 Comparison of CPU runtime results obtained with different algorithms.

Fig.10 Comparison of normalized subchannel capacity of different algorithms. (a), the number of users is set to 4; (b), the number of users is set to 8.

Fig.11 Transmission BER results for each user of different algorithms when the number of users is set to 4. (a), Shen algori- thm; (b), improved algorithm.

5 Conclusions

Starting from the development and practical significance of underwater sensor networks in three-dimensional marine monitoring, this study fully investigates the research status of underwater inductive coupling communication technology. Based on the established inductively coupled seawater channel, the use of the OFDM technology is proposed to overcome the multipath effect of the seawater channel, and adaptive technology is applied to it. A multiple underwater sensor node user resource allocation sche- me is designed, and an improved subcarrier allocation sche- me is proposed for the dynamic allocation of subcarriers to underwater multinode users. In addition, an improved greedy algorithm is proposed to dynamically allocate the number of transmission bits and power values for the subcarriers allocated to each user. When the improved multiuser resource allocation algorithm completes one OFDM system data transmission, the algorithm complexity can be reduced by 0.363×10?2s. Under the condition that the user corresponds to the same BER, the performance can be improved by approximately 6 dB. Therefore, the effectiveness of the proposed improved algorithm to the OFDM multiuser system with an inductively coupled seawater chan- nel is verified, and the system performance is improved.

The proposed adaptive modulation algorithm is implemented under an ideal channel model, but it still differs from the actual seawater channel model. Therefore, conti- nuous testing is required to improve the accuracy of the channel model. Although the improved algorithm performs better than traditional ones, it places higher demands on hardware performance and power consumption as the signal bandwidth and subcarrier count increase.

Acknowledgements

This paper was supported by grants from the National Natural Science Foundation of China (No. 62071329), and the National Science Foundation of Tianjin (No. 20JCYB JC00130).

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(January 25, 2021;

April 23, 2023;

May 22, 2023)

? Ocean University of China, Science Press and Springer-Verlag GmbH Germany 2023

. E-mail: zhengyu@tiangong.edu.cn

(Edited by Chen Wenwen)