1. Introduction

Underwater wireless communication (UWC) is essential for the development and exploration of underwater resources, but radio waves are heavily attenuated underwater, making radio-frequency (RF) communication difficult to employ [1]. The higher the frequency of the radio wave, the higher its attenuation. The acoustic waves, on the other hand, exhibit low attenuation underwater while propagating at a relatively slow speed of around 1500 m/s, and have a limited available bandwidth [2]. Underwater wireless optical communication (UWOC) has emerged as a viable alternative and garnered tremendous research interest due to its substantial available bandwidth, low transmission latency, and high secrecy [3–5]. Both light emitting diodes (LEDs) [6–8] and laser diodes (LDs) [9] can be used as the light source of UWOC systems. Although LD has a larger modulation bandwidth and a more concentrated beam, it is also accompanied by higher costs, fragility, and difficulty in alignment with photodetectors compared to LED. LED is sufficient to meet the communication application scenarios with medium distance and data rate requirements [10]. However, the limited bandwidth of commercial illuminating LEDs significantly impairs the performance of UWOC systems. Various strategies have been employed to handle the issue of bandwidth limitation, including high spectral efficiency modulation techniques such as orthogonal frequency division multiplexing (OFDM) [10–12], discrete multi-tone (DMT) [13,14]. Equalization techniques are also employed to extend the bandwidth of LEDs [14–16]. Nevertheless, the LED-based UWOC system also suffers from nonlinear impairments due to the highly nonlinear optical-power-versus-current (OPVC) characteristic of LEDs [17], thereby resulting in a narrow dynamic range to be used for optical communication. Consequently, high-order multi-carrier modulations, such as OFDM with high-order QAM, and DMT, are tough to utilize in a highly nonlinear LED-based system. In addition, OFDM exploits the high peak-to-average power ratio for intensity modulation, but the nonlinear distortions in the communication chain can severely undermine the performance of OFDM as they incur inter-channel interference [18]. In contrast, non-return-to-zero on-off keying (NRZ-OOK), being a binary modulation scheme, solely relies on the states of LEDs (on and off), thereby exhibiting immunity to LED nonlinearity [19]. Therefore, we utilized NRZ-OOK with intensity modulation/direct detection (IM/DD) for the real-time UWOC system due to its simplicity and cost-effectiveness, making it a choice for practical implementation.

Many previous studies focused on the improvement of the communication capacity and distance of point-to-point UWOC systems, while neglecting the significance of multi-user communication. In visible light communication (VLC) systems, researchers have employed the multiple access techniques that are widely used in wireless communication systems, such as time division multiple access (TDMA) [20,21], code division multiple access (CDMA) [22–24], and multi-user multiple input multiple output (MU-MIMO) [12,25] to enable multi-user communication. The TDMA system necessitates an adaptive time allocation scheme, which prohibits independent and simultaneous communication among users [26]. The use of optical orthogonal codes (OCC) in CDMA systems inevitably incurs a spectral resource cost, and the issue of inter-symbol-interference (ISI) in CDMA requires a high level of electrical power consumption [27]. To obtain the desired signal for each user in MU-MIMO systems, it is imperative to address the issue of signal interference caused by multiple users. Besides, the optical multiple access method, such as wavelength division multiple access (WDMA), has also been utilized in optical communication systems. In [28], a multi-user VLC system is achieved by WDMA. Unfortunately, the available wavelength range for UWOC system is limited to blue and green wavelength ranges, which poses challenges in using WDMA for UWOC systems.

Non-orthogonal multiple access (NOMA) has emerged as a spectrally efficient technology to achieve multi-user communication. NOMA exhibits superior spectral efficiency compared to orthogonal multiple access (OMA) due to its utilization of power or code domain multiplexing instead of frequency domain multiplexing [29]. In [30], Lin et al. demonstrated a VLC system based on NOMA-OFDM. In [31], the authors leveraged the difference in underwater attenuation between red light and green light to establish a two-user uplink UWOC system. The authors of [32] experimentally demonstrated a NOMA-OFDM-based UWOC system with green and blue polarization multiplexing. Chen et al. [33] proposed a user pairing scheme based on channel conditions and quality-of-service (QoS) that combines NOMA and OMA, aiming to further enhance the system capacity for accommodating more users. The error propagation (EP) problem arising from successive interference cancellation (SIC)-based NOMA due to unfair power allocation among users needs to be resolved. Besides, in a real-time UWOC system, the non-ideal received waveforms, characterized by long rise and fall time, have a detrimental effect on the user decoding process, especially for the SIC decoding technique. Therefore, a SIC-free decoding approach is of vital importance to the NOMA-based multi-user optical communication system. In [34], symmetric superposition coding and symmetric SIC decoding were proposed to deal with the EP in the downlink NOMA-based VLC system. The authors of Ref. [35] introduced a flexible-rate, SIC-free decoding method for downlink VLC systems. In [36], Hu et al. demonstrated an optical-spatial-summing-based NOMA downlink VLC system that utilized a large LED array to achieve fine-grained power allocation. The aforementioned optical communication systems are not suitable for practical underwater application scenarios due to their non-real-time nature. Additionally, an uplink optical communication system has a different power allocation scheme compared to that of the downlink one. However, there is scarce literature reporting the real-time, multi-user uplink UWOC system based on SIC-free NOMA.

In this paper, we propose a straightforward two-stage program judgment filter (PJF) to correct the received superimposed signal and an amplitude threshold (AT) decoding approach for the two-user uplink UWOC system. Specifically, we first utilize the two-stage PJF to improve the received signal, followed by obtaining corresponding amplitude sets of the two-user signal, and ultimately determining the amplitude thresholds for decoding. With the proposed signal waveform reshaping and AT user decoding methods, for the first time, we experimentally demonstrate a real-time, two-user uplink UWOC system based on NRZ-OOK modulation via field programmable gate arrays (FPGAs). The effect of the power allocation ratio (PAR) is also investigated to achieve optimal communication performance for both users. By applying the proposed method, user decoding can be accomplished without SIC, thereby avoiding the issues of EP and non-ideal received waveforms. As a result, by means of the AT decoding method and our previously proposed three-stage cascaded T-bridge equalization (TCBE) circuits [37], the real-time UWOC system can achieve a data rate of 30 Mbps for each user and bit error rates (BERs) of $7.8 \times {10^{ - 6}}$ and $3 \times {10^{ - \textrm{4}}}$ for user 1 and user 2 (when PAR equals 2:1 and users are symmetrically positioned), respectively. The BERs are below forward error correction (FEC) limit of $3.8 \times {10^{ - \textrm{3}}}$. With the proposed AT decoding method, the BER of user 2 (with lower power) is considerably decreased compared to that of the conventional SIC decoding method.

2. Principle

2.1. Power allocation

In NOMA-based UWOC systems, the multiple signals superimposed in the power domain can be distinguished by the allocated power levels, enabling multiple users to efficiently utilize the entire time-frequency resources. We employ NRZ-OOK modulation along with IM/DD due to its practicality and simplicity as a modulation technology. Assuming the UWOC system has two users, denoted as ${s_1}(t)$ and ${s_2}(t)$, which can be expressed as

 

Fig. 1. Transmitted signal waveform of (a) user 1, (b) user 2, and (c) ideal received superimposed signal, ${A_3} = {A_1} + {A_2},$ along with the received signal waveform (d) before PJF and (e) after PJF.

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2.2. PJF and AT decoding approach

In order to mitigate the impact of the sampling points located at the rising or falling edge of the signal waveform on user decoding, a two-stage PJF is employed to filter the sampled signal. The original output signal $y_i^{\textrm{(0)}}$ of the analog-to-digital converter (ADC), as shown in Fig. 1(d), is fed into the FPGA. The designed two-stage PJF is implemented on the signal $y_i^{\textrm{(0)}}$ in the FPGA, i.e., if the difference in amplitude between two adjacent (the previous and current) sampling points at the rising or falling edge exceeds or equals the defined threshold ${T_\textrm{1}}$ (note that ${T_\textrm{1}}$ is determined in the experimental process), then the amplitude of the current sampling point is adjusted to the same as that of the previous sampling point. Otherwise, it retains its original amplitude. The first-stage PJF is used to rectify the sampling points with significant variations at the rising or falling edge. For correcting the sampling points with minor fluctuations, a second-stage PJF is employed, whose threshold value ${T_\textrm{2}}$ is smaller than ${T_\textrm{1}}$. The results $y_i^{\textrm{(}j\textrm{ + 1)}}$ of the first-stage and second-stage PJF can be expressed as

3. Simulation and experiment

In order to verify the effect of the proposed AT decoding approach, offline simulations are conducted on the AT and SIC decoding methods. At the transmitter side (Tx), the symmetrically positioned users continuously send the same m-sequence with a period length of ${2^{14}} - 1,$ which is generated by the primitive polynomial expressed as

The m-sequence is generated by a linear feedback shift register (LFSR) in the FPGA. At the receiver side (Rx), the received signals in the FPGA are consecutively captured by the built-in IP core inline logic analyzer (ILA) tool. The captured superimposed signals are subsequently decoded offline via the AT and SIC decoding methods in MATLAB. As shown in Fig. 2(a), the BER of user 1 at different communication data rates obtained by the AT decoding approach closely approximates that of the SIC decoding method, and the BER of user 1 is far below the threshold of the FEC. It can also be observed that as PAR increases, user 1 exhibits improved BER performance, whereas user 2 experiences a deterioration in performance. This can be attributed to an elevated signal-to-noise ratio (SNR) for user 1 and a diminished SNR for user 2 with the increase in PAR. As depicted in Fig. 2(b), the BER of user 2 obtained by the AT decoding method is obviously lower than that obtained by the SIC decoding approach at different data rates. This is because the SIC decoding method suffers from the EP problem, and burrs can be caused by the non-ideal received waveform when decoding user 2. In contrast, the utilization of AT decoding effectively mitigates these issues and reduces the BER of user 2. With the AT decoding method and a PAR of 2:1, the BER of user 2 remains within the FEC limit when data rate reaches 30 Mbps.

 

Fig. 2. Simulated BER versus PAR under different data rates with AT and SIC decoding methods for (a) user 1 and (b) user 2.

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Figure 3 shows the schematic of the two-user NOMA-based uplink UWOC system. The experimental setup is presented in Fig. 4, which also illustrates the captured video transmission of user 2. At Tx, as depicted in Fig. 4(b), different information flows (video, picture) of user 1 (PC 1) and user 2 (PC 2) are first transmitted to the corresponding FPGA (Xilinx, ZYNQ7020) via the Ethernet UDP/IP protocol, where the signals are encoded and modulated. Then the signals are forwarded to the digital-to-analog converter (DAC, AD9767, maximum sampling rate: 125 MSample/s) to accomplish digital-to-analog conversion. Regarding power allocation, we can manipulate the amplitude of the user signal through the FPGA and DAC to achieve the corresponding power levels for user 1 and user 2. Subsequently, the pre-designed equalization circuits are employed to expand the bandwidth of the UWOC system. Meanwhile, a power amplifier (AMP, 37 dB, 100 kHz–75 MHz), along with a variable electrical attenuator (VEA, KT2.5–90/1S–2S) are used to adjust the signal amplitude. Note that the equalized circuits and amplification factor remain consistent for user 1 and user 2. Therefore, the signal amplitude difference between user 1 and user 2 can only be attributed to the power allocation process. Finally, the amplified analog signals are coupled with the direct voltage via the bias-tee (Bias-T, 50 kHz–60 MHz) to drive the green light emitting diodes (LEDs, Cree, XPE2). Two beam shaping lenses with a collimating angle of 15° are mounted in front of the LEDs to focus the transmitting light beams. After transmission through the water tank (length: 1 m, width: 0.4 m, height: 0.3 m) made from polymethyl methacrylate and filled with tap water. At Rx, as shown in Fig. 4(c), two convex lenses with a focal length of 10 cm are placed in front of the avalanche photodiode (APD, Hamamatsu, C12702–12) to collimate the respective lights. The lights are captured by the APD to complete photoelectric conversion, after which the superimposed signal is amplified by a trans-impedance amplifier (TIA, 0–50 MHz, 2 kΩ). The amplified signal is sampled by an ADC (AD9481, maximum sampling rate: 250 MSample/s), and the sampled signal is fed into the FPGA module at Rx to accomplish the synchronization and user decoding processes. The synchronization between users is unnecessary as their signals can be differentiated by their unique signal amplitudes. To achieve frame synchronization between transmitter and receiver, a synchronization header is utilized at the beginning of each valid data frame. The process of bit synchronization involves sampling the valid data and utilizing a counter to facilitate the process, which can be divided into the bit synchronization state and the decoding decision state. The bit synchronization state is established after the detection of five consecutive sampling points ‘11111’, followed by the decoding decision state. Ideally, an information bit ‘1’ can only be decoded when five continuous sampling points of ‘11111’ are detected. However, because the received signal waveform might be slightly distorted, errors may occur and cannot be completely avoided. Therefore, we stipulate that the information bit ‘1’ can be decoded when the number of ‘1’s exceeds or equals 3 in 5 consecutive sampling points. Meanwhile, a counter is utilized to monitor the occurrence of ‘1’s in five consecutive sampling points. Once the count reaches 3, the counter will increment by 1. Upon reaching the predetermined threshold of the count number, the decoding decision state will be paused to re-establish the bit synchronization state by searching for sampling points of ‘11111’. After synchronization, the FPGA at Rx enables online decoding of the signals from two users, which are then transmitted to the PC at Rx for real-time communication via the Ethernet UDP/IP protocol. The key experimental parameters are listed below in Table 1.

 

Fig. 3. Schematic of the two-user NOMA-based uplink UWOC system.

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Fig. 4. Photography of (a) the experimental setup, (b) transmitter side, and (c) receiver side.

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Table 1. Key experimental parameters

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4. Results and discussion

In order to evaluate the effect of the PJF and AT decoding approaches, we use the IP core ILA of the FPGA to capture the internal signals in the FPGA at Rx. For the purpose of clearly figuring out the decoding accuracy, at Tx, both users non-simultaneously and continuously send the same m-sequence (‘111101011001000’) with a short period length of ${2^4} - 1$. Figure 5 presents the output signal waveforms when utilizing the proposed AT decoding technique in the UWOC system. As shown in Fig. 5(a) and (f), it can be observed that a higher communication data rate leads to a longer rise and fall time, which results in more distorted signal waveforms and increased difficulty in the user decoding process. When the data rate of both users is 15 Mbps, comparing the filtering outputs shown in Fig. 5(b) and (c), the output of the first-stage PJF is the same as that of the second-stage PJF, which can be explained by the large variation of the sampling points at the rising or falling edge. Based on the filtering output, both users can be successfully decoded, as depicted in Fig. 5(d) and (e). However, as the data rate increases to 30 Mbps, the first-stage PJF fails to correct the sampling points with minor variations at the rising or falling edge. In such a case, the second-stage PJF plays a crucial role in correcting these sampling points, as shown in Fig. 5(g) and (h). The green arrows from Fig. 5(f) to (g) and from Fig. 5(g) to (h) indicate that the waveform changes at the sampling points with large and small variations, respectively. As a result, when the data rate reaches 30 Mbps, both users can be effectively decoded using the AT decoding method, as shown in Fig. 5(i) and (j).

 

Fig. 5. The output signal waveform (a, f) after ADC, (b, g) after first-stage PJF, (c, h) after second-stage PJF, (d, i) of user 1, and (e, j) of user 2 for 15 Mbps and 30 Mbps with the AT decoding method.

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On the contrary, when employing the SIC decoding method, user 1 can be successfully decoded based on the filtered signal shown in Fig. 6(b) and (g), while it is challenging to accurately decode user 2. The decoding results of user 1 are shown in Fig. 6(d) and (i) for data rates of 15 Mbps and 30 Mbps, respectively. When decoding user 2, we first reconstruct the signal of user 1, and then use the superimposed signal to subtract the signal of user 1. The resulting subtracted signals are depicted in Fig. 6(c) and (h), which are utilized for decoding user 2. It is evident that imperfections in the rise and fall time of the received signal waveform give rise to burrs in the subtracted waveform, leading to a higher BER for user 2 compared to that achieved through the AT decoding method. Under such circumstances, user 2 achieves correct decoding at a data rate of 15 Mbps, but encounters decoding failure at a higher data rate of 30 Mbps, as illustrated in Fig. 6(e) and (j). Therefore, the proposed AT decoding method demonstrates superior performance compared to the SIC decoding method in practical digital communication systems.

 

Fig. 6. The output signal waveform (a, f) after ADC, (b, g) after two-stage PJF, (c, h) of the subtracted signal, (d, i) of user 1, and (e, j) of user 2 for 15 Mbps and 30 Mbps with the SIC decoding method.

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The peak-to-peak voltage (Vpp) of the transmitted signal is crucial to the performance of the UWOC system. We investigate the BER performance of user 1 with respect to its Vpp. We vary the Vpp from 2 V to 6 V at the DAC module. Figure 7(a) depicts the measured BERs for different Vpp under varying data rates. When the Vpp of user 1 is about 4 V, the lowest BER can be obtained for each data rate. Under this condition, the BERs for the data rates of 5 Mbps, 10 Mbps, 15 Mbps, 20 Mbps, 25 Mbps, and 30 Mbps are $5.17 \times {10^{ - \textrm{5}}}$, $5.3 \times {10^{ - \textrm{5}}}$, $7.2 \times {10^{ - \textrm{5}}}$, $8.12 \times {10^{ - \textrm{5}}}$, $9.9 \times {10^{ - \textrm{5}}}$, and $5.7 \times {10^{ - \textrm{3}}}$, respectively. Therefore, in the following experiment, we maintain a Vpp of 4 V for user 1 and adjust the Vpp of user 2 to achieve power allocation. We subsequently analyze the effect of bias voltage of the LED on BER performance of UWOC system. A low bias voltage results in insignificant amplitude characteristics of the transmitted signal that render the decoding algorithm invalid, while a high bias voltage leads to oversaturation of the photodetector and even failure of communication. In the experiment, both users are subjected to equivalent bias voltages. For the sake of simplicity, we only measure the optimal bias voltage for user 1 and maintain it for both users throughout the experiment. We set the Vpp of user 1 at 4 V and adjust its bias voltage from 2.5 V to 3 V. As shown in Fig. 7(b), it can be found that the lowest BER can be obtained when the bias voltage is 2.8 V.

 

Fig. 7. BER versus (a) Vpp and (b) bias voltage under different data rates for user 1.

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In the following, we evaluate and compare the BER performance of the NOMA-based UWOC system when users are decoded by the AT and SIC methods. Figure 8 demonstrates the BER performance with respect to PAR under various communication data rates for both users. The power allocation is achieved by maintaining a constant Vpp of 4 V for user 1, while adjusting the Vpp of user 2 from 0.5 V to 4 V. As shown in Fig. 8(a) and (b), the increase in PAR contributes to a decrease in the BER of user 1, which can be explained by higher SNR resulting from increased power. The results are consistent with the simulated results in Fig. 2. With the AT decoding method, as shown in Fig. 8(a), the BERs of user 1 are $1.7 \times {10^{ - \textrm{6}}}$, $2.4 \times {10^{ - \textrm{6}}}$, $2.9 \times {10^{ - \textrm{6}}}$, $4.6 \times {10^{ - \textrm{6}}}$, $5.2 \times {10^{ - \textrm{6}}}$, and $7.8 \times {10^{ - \textrm{6}}}$ under a PAR of 2:1 for the data rates of 5 Mbps, 10 Mbps, 15 Mbps, 20 Mbps, 25 Mbps, and 30 Mbps, respectively. With the SIC decoding method, the BERs of user 1 exhibit a similar trend to those obtained with the AT decoding method, as depicted in Fig. 8(b). However, the BER of user 2 deteriorates as PAR increases due to the lower SNR. Based on the AT decoding approach, as can be seen from Fig. 8(c), the BERs of user 2 are $1.8 \times {10^{ - \textrm{6}}}$, $3.3 \times {10^{ - \textrm{6}}}$, $9.4 \times {10^{ - \textrm{6}}}$, $1 \times {10^{ - \textrm{4}}}$, $1.5 \times {10^{ - \textrm{4}}}$, and $3 \times {10^{ - \textrm{4}}}$ under a PAR of 2:1 for the data rates of 5 Mbps, 10 Mbps, 15 Mbps, 20 Mbps, 25 Mbps, and 30 Mbps, respectively. In contrast, when the data rate is 25 Mbps, the BER of user 2 exceeds the FEC threshold under a PAR of 2:1 with the SIC decoding method, as illustrated in Fig. 8(d). The BER performance of user 2 in the UWOC system that decodes via the SIC technique severely degrades compared to that of decoding through the AT decoding method.

 

Fig. 8. BER versus PAR under different communication data rates for (a) user 1 with AT decoding method, (b) user 1 with SIC decoding method, (c) user 2 with AT decoding method, and (d) user 2 with SIC decoding method.

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Regardless of PAR, we can find that the BER of user 1 remains lower than $1 \times {10^{ - \textrm{5}}}$ when the data rate is within 30 Mbps for both the SIC and AT decoding methods. However, PAR plays a significant role in the decoding of user 2. The optimal BER performance of user 2 is obtained when PAR is 2:1. To ensure that both users achieve a data rate of 30 Mbps with BER below the FEC threshold, an optimum PAR of approximately 2:1 is recommended for the proposed UWOC system. At a PAR of 2:1, the comparison between the simulation and experimental results is presented in Table 2. The simulation results can reflect the BER performance of users when conducting offline decoding in MATLAB. The simulation and experimental results exhibit consistent trends with respect to the changes in data rate. We can also find that the simulation results demonstrate superior performance compared to the experimental results, which can be attributed to the slight discrepancy in the precision of crystal oscillators utilized in FPGAs at both transmitting and receiving ends.

Table 2. Comparison between the simulation and experimental results

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Figure 9 presents the corresponding eye diagrams of the output signal of the two-stage PJF for the data rates of 15 Mbps and 30 Mbps. In an ideal scenario, there are three levels of eyes in the eye diagram for four types of signal amplitude in the two-user UWOC system. When data rate of both users is 15 Mbps, as depicted in Fig. 9(a)–(d), it can be observed that three levels of eyes are the most prominent when PAR is 2:1. Under such circumstances, the thresholds $T{h_\textrm{0}},\textrm{ }T{h_1},$ and $T{h_2}$ can be easily determined. Therefore, both users can be effectively decoded according to Eqs. (7) and (8), which is in line with the BER results shown in Fig. 8. As PAR increases, the inner eyes expand while the outer eyes shrink. The larger the inner eyes become, the easier the threshold $T{h_1}$ can be decided, resulting in the BER of user 1 decreasing with the increase of PAR, as depicted in Fig. 8(a) and (b). However, the decoding of user 2 turns increasingly challenging as $T{h_0}$ and $T{h_2}$ are more complex and difficult to discern. When the data rate increases to 30 Mbps for both users, as shown in Fig. 9(e)–(h), distinguishing the three levels of eyes turns arduous. As PAR increases, the inner eyes become more distinguishable, while the outer eyes gradually disappear, which indicates $T{h_1}$ can be easily determined while $T{h_0}$ and $T{h_2}$ fail to be determined. When PAR becomes large, user 1 can be successfully decoded but not user 2. Therefore, the optimum performance of user 2 can be achieved when PAR is set to 2:1, which aligns well with the BER results shown in Fig. 8(c). When the data rate is 30 Mbps, the lowest BER ($3 \times {10^{ - \textrm{4}}}$) of user 2 is obtained by the AT decoding method.

 

Fig. 9. Measured eye diagrams with a PAR of (a, e) 2:1, (b, f) 3:1, (c, g) 4:1, and (d, h) 4.5:1 for data rates of 15 Mbps and 30 Mbps, respectively.

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The BER performance of both users is also investigated when they are placed at different distances from the receiver. User 1 (with high allocated power) remains at the corner position of the water tank, while user 2 (with low allocated power) moves to the central position at the edge of the water tank. It can be observed from Fig. 10(a) that the decoding results of the AT decoding method are in close proximity to those of the SIC decoding method when decoding user 1, whereas in Fig. 10(b), it is evident that the AT decoding method still outperforms the SIC decoding method when decoding user 2. Compared to the BER performance of the case when users are symmetrically positioned, both users exhibit similar trends as PAR increases, i.e., the BER of user 1 decreases as PAR increases, while user 2 becomes worse. The BERs of user 1 exhibit a relative increase under various PARs when compared to the symmetrical position case, which can be attributed to the relative rise in its SNR. Conversely, at the same PAR, the BER performance of user 2 is enhanced in comparison to the symmetrical position case due to the improvement in its channel condition.

 

Fig. 10. When placing users at different distances from the receiver, measured BER versus PAR under different data rates with AT and SIC decoding methods for (a) user 1 and (b) user 2.

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5. Conclusion

In this paper, we propose, for the first time, a NOMA-based, real-time, and two-user uplink UWOC system, which can directly conduct real-time video transmission for practical applications. In the system, a straightforward two-stage PJF is employed to correct the signal waveform, and a SIC-free AT decoding approach is proposed to alleviate the issues related to EP and the non-ideal received signal waveforms. Based on the filtered outputs and AT decoding method, the UWOC system exhibits superior communication performance, particularly for user 2, as compared to that decoded based on SIC. At a data rate of 30 Mbps and a PAR of 2:1, the received signals of both users can be decoded successfully with BERs of $7.8 \times {10^{ - 6}}$ and $3 \times {10^{ - \textrm{4}}}$ for user 1 and user 2, respectively. We also find that the BER of user 1 decreases with the increase in PAR, while it deteriorates for user 2 in practical communication application scenarios. When the data rate is below 30 Mbps, the BER of user 1 remains at a low level of less than $1 \times {10^{ - \textrm{5}}}$. Therefore, the overall performance of the UWOC system is primarily dependent on user 2. It is recommended to utilize a PAR of approximately 2:1 for the proposed UWOC system in cases where users are positioned symmetrically. It should be noted that the utilization of the AT decoding method is most suitable for systems with two or three users, as the number of the superimposed signal amplitudes increases exponentially with each additional user. In the next step, we will conduct a thorough investigation on the user pairing scheme to accommodate a large number of users, and develop a multi-user downlink UWOC system to fulfill the demand for bidirectional communication in the subaqueous environment.