Research on Rate Adaptation of Underwater Optical Communication with Joint Control of Photoelectric Domain

Abstract

As the communication distance changes, the received signal strength of an underwater optical communication system will change, and the range of its variation may not only exceed the dynamic range of the photoelectric detection device but also cause the reliability of communication to change due to the change in the received signal-to-noise ratio. In order to maintain better communication over a longer distance, this paper proposes a rate-adaptive method for underwater optical communication with joint control in the photoelectric domain. In the optical domain, the incident light’s power is adaptively adjusted by controlling the transmittance of the liquid crystal light valve to reduce saturation distortion. In the electrical domain, the constellation distribution is optimized according to the desired probability mass function, and the modulation order is adjusted in real time by estimating the received signal-to-noise ratio of the link. The simulation results show that under the forward error correction (FEC) threshold, the proposed method increases the dynamic range of the photomultiplier tube (PMT) by about 10 dB and expands the dynamic range of the system’s communication distance.

1. Introduction

With the continuous growth of global economic and military needs, the development and utilization of marine resources has become one of the main driving forces of the new scientific and technological revolution. The demand for higher transmission rates and longer distances in underwater wireless communication technologies is increasing [1]. Compared with more mature underwater acoustic communication, underwater wireless optical communication (UWOC) has the advantages of high speed, small delays and low power consumption over short distances. However, the optimal transmission window for optical beams in seawater is limited to the blue–green spectrum. The optical properties of the each component in seawater are mainly determined through the absorption and scattering properties of light [2]. As the distance between the transmitter and receiver increases, light experiences greater absorption and scattering, which severely affects signal quality. The degree of attenuation affects the transmission rate and range of the communication system, making UWOC transmission more challenging. Therefore, a key challenge for the next generation of UWOC systems is optimizing the system to achieve maximum transmission capacity based on the transmission distance between the receiver and transmitter [3]. This paper studies an adaptive control technology that can adapt to changes in the underwater communication environment.

In recent years, adaptive transmission technology has been widely used in UWOC systems, with the main focus on power, modulation mode, coding efficiency or a combination of these parameters. In [4], an algorithm was designed to adaptively adjust the beam width and transmitter power to achieve reliable real-time long-distance video transmission. Autonomous underwater vehicles (AUVs) are used to establish reliable communication, addressing the shortcomings of relay technology in emergency situations and enhancing the stability of optical links. However, increasing power and expanding the beam width may reduce communication efficiency. In order to reduce the transmission power required and solve the significant attenuation of light during underwater transmission, in [5], a photomultiplier tube (PMT) with a strong low-light detection capability was used to receive signals. Experiments in a 10 m indoor water tank verified the system’s reliability; it is reasonably predicted that the PMT has the potential to achieve long-distance underwater communication. When the incident power is too high, the PMT may be saturated, leading to signal distortion. Neutral density filters can attenuate the incident optical power, but their operation accuracy is low. In [6], it is pointed out that the transmittance of a liquid crystal light valve (LCLV) can theoretically achieve continuous variation between 0% and 100%, allowing for more precise power control. By dynamically adjusting the LCLV and the PMT gain, the dynamic range of the received optical power is extended by 68 dB. The study employed on–off keying (OOK) modulation. However, considering the requirements for transmission efficiency and interference resistance, more complex modulation schemes are needed. In [7], an integrated binary phase shift keying (BPSK)/quadrature phase shift keying (QPSK) switchable transmission and reception method was proposed for free-space optical (FSO) communication. It adaptively switches between BPSK and QPSK based on different channel conditions. Stable communication is achieved and the channel’s capacity is improved. The distance between the transmitter and receiver is one of the key factors affecting signal quality. In [8], for visible light communication (VLC), a system was designed to select pulse-position modulation (PPM) or pulse-amplitude modulation (PAM) based on the signal-to-noise ratio (SNR) to meet bit error rate (BER) requirements. The effectiveness of the algorithm was verified within a communication distance of 6 m. In [3], a time-domain hybrid pulse–amplitude-modulation (TDHP) scheme is proposed for the first time in a UWOC system, achieving a maximization of transmission capacity and distance. When the transmitting power is 0.5 W and the wavelength is 450 nm, the communication distance is kept between approximately 11 m and 100 m by changing the generation ratio of different modulation methods, the receiver field of view, etc. Due to the complexity of the propagation environment, orthogonal frequency division multiplexing (OFDM) has gradually become a research hotspot because of its high reliability and stability. Given the limitations of single quadrature amplitude modulation (QAM) in terms of its rate and communication distance [9,10], in [11], a joint power adaptation and adaptive QAM scheme is proposed. It optimizes the transmission efficiency of the system under channel variations, allowing each user to achieve the maximum transmission rate at high SNRs. In [12], the bit power loading method combined with wavefront shaping technology results in a 30.7% increase in the transmission rate. However, it is also unable to reduce the distance to the Shannon limit to achieve maximum rate optimization. In recent years, constellation probabilistic shaping (CPS) technology has gradually been applied to this problem. This technique converts uniformly distributed input bits into non-uniform, Gaussian-like, distributed constellation symbols. It not only reduces the distance to the Shannon limit but also allows for rate adaptability by adjusting the information entropy, achieving flexible rate adaptation [13]. In [14], it is verified that the probabilistic optimal solution for constellation points in an additive white Gaussian noise (AWGN) channel is Maxwell–Boltzmann (MB) distribution. In [15], a distance-based rate-adaptive VLC system is proposed by adding CPS. The shaping factor is adaptively changed according to the SNR, achieving a finer-grained rate adjustment, with the total capacity increased by up to 28%. In [16], an entropy loading technology based on CPS is proposed. In indoor downlink application scenarios, the appropriate bit rate is selected by estimating the received SNR of different users. This method achieves data rates of 26 to 46 Gbps over a communication distance of 0.5 to 2 m. In [17], in order to improve the transmission rate of VLC, an adaptive spatial modulation scheme based on CPS is proposed. In [18], it is proven that CPS can also increase the transmission distance, with probabilistic shaping 64QAM (PS−64QAM) providing at least a 40% improvement over uniform 64QAM (UN−64QAM). However, most of this technology is focused on VLC, and there is less research on UWOC systems.

In order to provide a clearer and more concise overview of the above literature and the method proposed in this paper, the key features of these methods, such as their modulation method, link distance, etc., are summarized in

Table 1. Comparison between the method proposed in this paper and the references above.

Ref.	CPS	Optical/Electrical Domain	Modulation Method	Transmit Power	Link Distance	Optimization Objective
Proposed	Yes	Both	QAM	80 mW	7–48 m	Distance; rate
[3]	No	Electrical	TDHP	0.5 W	11–100 m	Distance
[5]	No	Both	OOK	10–30 mW	10 m	Distance
[6]	No	Optical	OOK	80 mW	2 m	Power
[8]	No	Electrical	PAM/PPM	4 W	0.5–6 m	Distance
[12]	No	Electrical	QAM	-	0.15–0.3 m	Rate
[15]	Yes	Electrical	QAM	-	1–20 m	Rate
[16]	Yes	Electrical	QAM	-	0.5–2 m;	Rate

. In UWOC, light experiences severe attenuation, which limits the communication distance. However, CPS optimizes symbol distribution, reducing the BER and enhancing system reliability. Compared to uniformly distributed input signals, CPS can extend the communication distance under the same conditions. Moreover, by adjusting the shaping degree, the information rate can be flexibly controlled and spectral efficiency improved. Different from existing schemes, the adaptive method proposed in this paper not only integrates CPS into its electrical domain but also controls the incident power in the optical domain.

In order to adapt to the changing channel conditions and the dynamic range of the PMT, this paper first proposes a uniform QAM rate-adaptive control strategy in the electrical domain. Based on the link conditions, the modulation scheme is adaptively adjusted among BPSK, 4QAM, 16QAM, 64QAM, and 256QAM. In order to comprehensively consider the system’s reliability and transmission rate performance, CPS technology is added on the basis of the above method to make up for a certain amount of rate loss. In the optical domain, the LCLV is combined with the PMT. Based on the magnitude of the incident light’s power, it judges whether the PMT has reached saturation and then determines whether to change the transmittance of the LCLV. The simulation results show that the proposed algorithm improves the reliability and efficiency of the system. The use of LCLV increases the dynamic range of the PMT by about 10 dB and expands the dynamic range of the communication distance of the system.

2. System Model

Underwater channels have a serious impact on an optical signal, resulting in a limited communication distance. In order to expand the communication range, the transmitter selects a laser (LD) with a smaller divergence angle, and the receiver selects a PMT with a higher detection capability. The transmitter and receiver are aligned along the line of sight [4]. In the case of fixed transmission power, the optical signal’s attenuation is more serious when the communication distance is longer. Under the premise of ensuring communication quality, a single QAM cannot meet the changing channel status and the dynamic range of PMT. Therefore, under different link conditions, the adaptive selection of the modulation mode and the control of LCLV can expand the dynamic range of the communication distance and the PMT-received power and improve the reliability and efficiency of the system.

The impact of various components contained in water on the optical signal is mainly manifested in two aspects, namely absorption and scattering [19]. The attenuation effect on the optical signal caused by these two factors can be represented by the attenuation coefficient $c(\lambda )$, which can be expressed as follows:

$$c(\lambda )=a(\lambda )+b(\lambda ),$$

(1)

where $a(\lambda )$ represents the absorption coefficient, $b(\lambda )$ represents the scattering coefficient and $\lambda$ represents the wavelength.

According to the Beer–Lambert law, when the distance of the light beam propagating underwater is $d$, the path loss model is expressed as follows:

$$L_{loss}={\mathrm{e}}^{-c(\lambda )d}.$$

(2)

Assuming the transmitter and receiver are aligned and considering geometric losses, the underwater channel’s DC gain can be expressed as follows [20]:

$$H(0)={\displaystyle \frac{m+1}{2\pi }}{\cos }^m(\varphi )A_{eff}(d,\psi ),$$

(3)

$$A_{eff}(d,\psi )={\displaystyle \frac{\pi D_r^2\cos (\psi )/4}{\pi {(L\tan ({\varphi }_{1/2})+D_t/2)}^2}},$$

(4)

where $m=(-\ln 2)/\ln (\cos ({\varphi }_{1/2}))$ is the Lambertian radiation order, ${\varphi }_{1/2}$ is the half-power angle of the light source, $\varphi$ is the irradiation angle, $\psi$ represents the incidence angle of the beam to the detector surface, $D_t$ represents the diameter of the light source condenser lens, $D_r$ represents the diameter of the receiving surface, $d$ represents the beam propagation distance and $A_{eff}(d,\psi )$ represents the effective area of the detector.

The process of light transmission underwater can be regarded as a cumulative loss process. Multiple factors work together to reduce the signal’s power [21]. The maximum communication distance is closely related to the received power. Therefore, considering the photoelectric conversion efficiency of the transmitter and receiver, the DC gain, and the path loss, the underwater channel gain model can be expressed as follows:

$$h={\eta }_t{\eta }_{r}H(0)L_{loss}={\eta }_t{\eta }_r{\displaystyle \frac{m+1}{2\pi }}{\cos }^m(\varphi )A_{eff}(d,\psi )e^{-c(\lambda )d},$$

(5)

where ${\eta }_t$ and ${\eta }_r$ represent the conversion efficiency of the transmitter and detector, respectively. The simulation values of the above key parameters are shown in

Table 2. Key parameters of underwater channel model.

Parameter	Value/Unit
$c(\lambda )$	0.0145 m−1
${\varphi }_{1/2}$	5°
$\varphi$	0°
$\psi$	0°
$D_t$	50 mm
$D_r$	50 mm
${\eta }_t$	0.1289
${\eta }_r$	0.9500

[20].

Since the light source can only emit non-negative optical signals with real values, the signals generated by traditional QAM are no longer applicable to the UWOC system. Therefore, this paper adopts the asymmetrically clipped optical orthogonal frequency division multiplexing (ACO-OFDM) system [22] and adds a feedback link for the selection of the modulation mode and the adjustment of the LCLV. A block diagram of the adaptive system used in this paper is shown below.

3. Rate-Adaptive Scheme of Joint Control of Photoelectric Domain

3.1. Rate-Adaptive Control of Electrical Domains

When the transmitter and receiver communicate, the receiver estimates the SNR and feeds back the next set of modulation information to the transmitter to ensure the optimal performance of the system. A block diagram of the UWOC adaptive control system is shown in Figure 1. When the system performs rate-adaptive control, it is assumed that the channel will change when the distance between the transmitter and receiver changes. In the simulation, the transmission power is set to 80 mW. When the system sends a signal, the received signal can be expressed as $y(t)=x(t)h+n(t)$ according to (4). Under the assumption that the noise and transmitted signal are statistically independent, the received signal power is expressed as follows [8]:

$${\sigma }_y^2={\left|h\right|}^2{P}_x+{\sigma }_{\omega }^2,$$

(6)

where $h$ represents the underwater channel gain and $P_x$ represents the transmitting signal power.

When the system does not send signals, only the noise is captured at the receiver [23], and then the variance, that is, the noise’s power, can be measured. The expression is as follows:

$${\sigma }_y^2={\sigma }_{\omega }^2={\displaystyle \frac{1}{N}}{\displaystyle \sum _{k=1}^N{\left|y_n(k)\right|}^2}.$$

(7)

Therefore, the estimated SNR can be expressed as follows:

$$\widetilde{SNR}={\displaystyle \frac{{\sigma }_y^2-{\sigma }_{\omega }^2}{{\sigma }_{\omega }^2}}={\displaystyle \frac{{\sigma }_y^2}{{\sigma }_{\omega }^2}}-1.$$

(8)

When the receiver obtains link state information at this time, it can select the appropriate modulation mode under the premise of satisfying the set BER threshold, thereby extending the dynamic range of the communication distance and enhancing the system’s flexibility. When the distance between the transmitter and receiver increases, leading to a decrease in the SNR, the system adaptively selects a lower-order modulation scheme. This change sacrifices the rate and improves the BER performance. In order to make up for this rate loss, CPS technology is combined with the above method; by reducing the probability of constellation points with high energy in the outer circle and increasing the probability of constellation points with low energy in the inner circle [24], the average power of the constellation diagram is effectively reduced. Under the premise of ensuring consistent power, the signal after probability shaping has a higher fault tolerance rate and longer communication distance. The specific reasons for this will be explained below.

The signal probability distribution that best matches the AWGN channel is MB distribution, which can be expressed as follows [25]:

$$P_X(x_k)={\displaystyle \frac{\exp (-v(\mathrm{Re}{(x_k)}^2+\mathrm{Im}{(x_k)}^2))}{{\displaystyle \sum _{i=1}^M\exp (-v(\mathrm{Re}{(x_i)}^2+\mathrm{Im}{(x_i)}^2))}}},$$

(9)

where $x_i$ represents the $i\text{-}\mathrm{th}$ constellation point of the complex MQAM and $v$ is a probability shaping factor that determines the probability distribution of the constellation points. The size of information entropy is determined by the probability of the occurrence of each symbol, and the unit is bit/symbol. The expression is as follows:

$$H(X)=E[I(X)]={\displaystyle \sum _{i=1}^{M}p(x_i)I(x_i)}=-{\displaystyle \sum _{i=1}^{M}p(x_i){\log }_{2}p(x_i)},$$

(10)

therefore, when $v$ decreases, the degree of probability shaping decreases; conversely, when $v$ increases, the degree of shaping increases, and the information entropy decreases. The probability distributions of PS−16QAM and PS−64QAM signals with different $v$ values are shown in Figure 2.

The average relative power of the signal is $\overline{P}={\displaystyle \sum _i{\left|X_i\right|}^{2}P(X_i)}$. As shown in Figure 2, the CPS technology increases the probability of constellation points that are closer to the origin and decreases the probability of constellation points that are far away from the origin, thus saving power. In order to ensure that the average power of the signal remains consistent before and after shaping, the constellation diagram of the reshaping signal is amplified by multiplying the coefficient $\alpha$. The expression is as follows:

$$E[{\left|\alpha \cdot X\right|}^2]=E[{\left|X_0\right|}^2].$$

(11)

Take the PS−16QAM signal as an example, and let $v=0.2$. The probability distribution of each constellation point can be obtained according to (9), and then the average relative power calculated after shaping is 4.7. The average relative power of the UN−16QAM signal is 10. According to (10), we obtain $\alpha \approx 1.459$, that is, the amplitude of each symbol of PS−16QAM increases by a factor of 1.459. As shown in Figure 3, the Euclidean distance between the points of each constellation becomes larger after shaping and the error tolerance is higher, so the communication distance is longer under the desired BER threshold.

As shown in Figure 4, the constellation diagrams at the receiver and the BER performance before and after shaping are shown. Specifically, (a) and (c) are the constellation diagrams of UN−16QAM and PS−16QAM when the SNR = 10 dB. Correspondingly, (b) and (d) are the constellation diagrams when the SNR = 15 dB. It can be seen from the simulation diagram that the constellation points of the shaped signals are concentrated in the inner circle, which reduces the average transmission power of the system and reduces the power demand. Figure 4e shows a comparison of the BER performance before and after shaping. It can be seen that at the FEC threshold, when comparing the same modulation orders, the SNR is improved by approximately 4 dB after shaping when the entropy loss is 1. This indicates that the shaped signals significantly enhance the BER performance. Figure 4f shows a comparison of signals at different shaping levels, and the results indicate that a higher degree of shaping leads to a better performance.

The probability of each symbol calculated by (9) is the ideal distribution $P_A$. In practice, the number of occurrences of each symbol is an integer and the sum is the total number of symbols. For the same $P_A$, there may be a variety of symbol numbers with different values, and then there are different probability combinations. To identify the actual probability distribution that is closest to the ideal probability distribution, ref. [26] uses Kullback–Leibler (KL) divergence to measure the degree of proximity between the two. The shaping signal can be obtained by the above process. In order to transmit more information at the same SNR, CPS is combined with the uniform QAM rate-adaptive algorithm; by switching between the uniform QAM signal and the shaping signal, the rate and spectral efficiency switching mechanism achieve a higher granularity, and the communication distance of the shaped signal is longer. The specific simulation results are shown in Section 4.

3.2. Power-Adaptive Control of Optical Domains

When the distance between the transmitter and receiver is small, the incident optical power is strong, which leads to saturation distortion of the PMT. Therefore, the incident optical power needs to be controlled. Compared with the attenuator plate, the LCLV has a higher regulation precision of light, and the light’s transmittance can be controlled only by changing the voltage applied at both ends of the LCLV [6].

According to Section 3.1, after the signal arrives at the receiver, the received signal’s power needs to be estimated. When the incident optical power approaches or exceeds the saturation threshold, the PMT will exhibit a complex nonlinear performance, resulting in the distortion of the received signal and a limited dynamic range [27]. In order to expand the dynamic range of the PMT, an LCLV is used to control the incident optical power when a short distance between the transmitter and receiver leads to PMT saturation. To ensure that the SNR is at its maximum and the signal is not distorted, the received power should be maintained at the maximum value in its linear region. Therefore, the transmittance of the LCLV needs to be adaptively adjusted according to the incident light’s power. The expression is as follows:

$$T={\displaystyle \frac{P_{optimal}}{P_{in}}},$$

(12)

where $T$ represents the light transmittance of the LCLV, $P_{optimal}$ represents the maximum power of the PMT in its linear region and $P_{in}$ represents the incident light’s power. Based on the relationship between the transmittance of the LCLV and the driving voltages at both ends summarized in [6], the relationship between the LCLV driving voltage and the incident light’s power can be further derived.

In summary, the above methods are combined to design a rate-adaptive algorithm for joint control of the photoelectric domain. First, the power and SNR at the current distance are estimated using a test signal. The receiver determines whether the PMT is saturated based on the estimated power and then decides whether to adjust the transmittance of the LCLV. Secondly, the modulation method to be used is determined based on the estimated SNR. When $H\ne {\log }_2(M)$, the shaped signal is transmitted. Based on Equation (9) and the KL divergence, the probability mass function is calculated, and then the corresponding symbol sequence is generated. Otherwise, uniform QAM signals are transmitted. The specific flow chart is shown in Figure 5.

4. Simulation Result Analysis

In this section, the performance of the proposed rate-adaptive control strategy is verified by simulation. Based on the above channel model and system, the information rate, reliability, spectral efficiency and throughput performance of the rate-adaptive control strategy are analyzed.

As shown in Figure 6, the BER and communication distance before and after shaping are compared under the same spectrum efficiency. Specifically, (a) and (c), respectively, represent the performance comparison between UN−16QAM and PS−64QAM when the information entropy is 4, while (b) and (d) show the performance comparison between UN−64QAM and PS−256QAM when the information entropy is 6. The simulation results show that under the same spectral efficiency, the signal after shaping has better a BER performance and longer communication distance. Therefore, PS−64QAM (H = 4) and PS−256QAM (H = 6) are selected in the subsequent simulated adaptive control experiment and combined with PCS technology.

The performance comparison of the communication distance of the uniform adaptive QAM and the joint regulation rate adaptation in the photoelectric domain is shown in Figure 7. The simulation results show that under the FEC threshold, when the communication distance is short and the received power is too high, the PMT is saturated and distorted and the BER is close to 0.5. When the LCLV is used to regulate the incident power, the communication distance is reduced by approximately 6 m, which can alleviate the influence of saturation distortion to a certain extent. Compared with a single high-order modulation mode, the adaptive modulation method can select the best modulation mode based to the channel’s state and improve the communication distance. PS−256QAM increases the communication distance by approximately 47% compared to UN−256QAM, PS−64QAM increases it by about 41% compared to UN−64QAM, and PS−16QAM extends the communication distance by around 18% compared to UN−16QAM. It can be seen that when the communication distance changes, resulting in changes in the underwater channel, the adaptive modulation algorithm effectively extends the dynamic range of the communication distance and maintains the system’s reliability.

The performance comparison of the information rate (a) and spectral efficiency (b) between uniform adaptive QAM and joint regulation rate adaptation in the photoelectric domain is presented in Figure 8. The simulation results show that with the uniform adaptive QAM strategy, when the modulation mode changes from 256QAM to 64QAM, the information rate decreases from 15.36 Mbps to 11.52 Mbps and the spectrum efficiency decreases from 2 bps/Hz to 1.5 bps/Hz. In the photoelectric domain joint control strategy, PS−256QAM with an information entropy of 7 can increase the rate to 13.44 Mbps and the spectral efficiency to 1.75 bps/Hz within the same communication distance. Similarly, the information rate and spectral efficiency of other signals after probability shaping are improved within some distance ranges.

As shown in Figure 9, the performance comparison of the throughput between uniform adaptive QAM and the joint regulation rate adaptation in the photoelectric domain is presented. The simulation results show that under the FEC threshold, the throughput of the photoelectric domain’s joint regulation is improved compared with that of uniform adaptive modulation. When the PMT is not saturated, an increase in received power corresponds to a higher order of QAM, resulting in an increase in throughput. Conversely, when the PMT is saturated, performance will decline sharply. The use of the LCLV extends the dynamic range of the PMT by about 10 dB. In summary, the rate-adaptive technology controlled by the photoelectric domain extends the dynamic range of the communication distance and the PMT, and the CPS technology used, combined with adaptive modulation, makes up for the rate loss.

5. Conclusions

The received signal strength of the underwater optical communication system changes with the change in the communication distance, resulting in a single modulation mode that does not match the channel loss and the dynamic range of the PMT. Therefore, this paper studies a rate adaptation scheme of underwater optical communication with joint control of the photoelectric domain. By estimating the channel conditions, the SNR and incident power can be obtained, allowing for the adaptive adjustment of the modulation scheme and the transmittance of the LCLV. The simulation results show that under the FEC threshold, the proposed algorithm extends the dynamic range of the communication distance and PMT, improves the throughput and verifies the effectiveness and reliability of CPS technology.