Underwater visible light channel estimator based on ensemble network learning

Abstract

The present invention belongs to the field of visible light communication technology, specifically an underwater visible light channel estimator based on integrated network learning. The underwater visible light channel estimator of the present invention includes three branch networks of machine learning for estimating the underwater visible light channel. Specifically, based on existing prior knowledge, the channel estimator is split into three sub-networks: a linear estimator, an SSBI estimator, and a ReLU estimator, which are used to estimate the linear noise, quadratic noise, and higher-order noise of the channel, respectively. The three sub-networks are then integrated and trained to obtain the overall underwater visible light channel estimator. The present invention reduces the complexity of the entire network and the number of neurons, while still achieving the desired effect and providing more accurate channel estimation.

Description

Technical Field

[0001] The present invention belongs to the technical field of visible light communications, and in particular relates to an underwater visible light channel estimator. Background Art

[0002] As wireless communication capacity continues to expand, spectrum resources are gradually becoming depleted, so there is an urgent need to find alternative spectrum resources in higher frequency bands. Visible light communication has attracted widespread attention from the international community due to its unique advantages and has become a very promising technology for the future 6G [1-2]. It combines communication and lighting, has many advantages such as anti-electromagnetic interference, large potential bandwidth, and good security. Visible light communication can be used in many electromagnetically sensitive scenarios, such as cabins and hospitals, or in indoor communications that require high-speed access. In underwater communication scenarios, radio waves are difficult to transmit in seawater due to the skin effect. [3] mentioned that the attenuation of visible light underwater has a strong wavelength dependence, and blue-green light is very little absorbed by water molecules, becoming a window for underwater communication. Therefore, visible light communication is a key technology for underwater wireless communication and has become a research hotspot at home and abroad.

[0003] Although blue-green light can be transmitted underwater, it still faces the problem of optical power attenuation. Increasing the transmitted optical power is one of the solutions, but high power will also inevitably bring nonlinear noise. Therefore, it is particularly important to estimate the transmission function of the underwater visible light channel. A good channel estimator is conducive to signal simulation analysis, post-equalization and even pre-equalization of the signal. In the past few decades, researchers have focused more on underwater acoustic channel estimation, but this also has many reference significance for visible light channels. In 1991, Feder et al. proposed a joint channel estimation algorithm and demonstrated the application of phase recovery equalization in underwater communications [4]. In 2018, Gang Qiao et al. studied the sparse Bayesian learning framework for channel estimation in underwater acoustic orthogonal frequency division multiplexing communication systems [5]. However, the rate of underwater acoustic communication is very low and is easily affected by multipath effects, time-varying effects, etc. [6]. In recent years, underwater visible light communication has gradually developed. Recently, Xu Ma et al. proposed a channel estimation method based on compressed sensing, which assumes that the visible light channel attenuation is linearly related to frequency [7]. Zhongya Li et al. used an in-band channel modeling strategy to pre-equalize the signal[8]. However, the biggest problem facing the visible light channel is the nonlinear effect caused by optoelectronic devices, which is difficult to estimate and compensate using traditional methods.

[0004] In recent years, artificial intelligence (AI) has become a research hotspot in the field of communication due to its powerful nonlinear fitting ability. In our previous research, [9] proposed a nonlinear compensation method based on a bidirectional recurrent gate unit. Chen H et al. proposed a nonlinear elastic learning method based on joint time-frequency image analysis

[10] . Hu F et al. proposed another nonlinear compensation method in a multi-band visible light system based on polynomial functions combined with ANN

[11] . Therefore, it will be a trend to apply advanced AI technology to communication channel estimation. Yiheng Zhao et al. studied the underwater visible light system channel simulator based on heterogeneous neural networks for two tributaries

[12] . Zhang Yonglin et al. tested the performance of deep neural network assisted channel estimation for underwater acoustic OFDM communication

[13] . Lu Huaiyin et al. conducted related research on deep learning assisted robust joint channel classification, channel estimation and signal detection

[14] . With the help of a neural network-based channel estimator, J. Shi et al. developed the best adaptive waveform design using end-to-end learning

[15] .

[0005] However, previous research has left many unresolved issues. Using a single large-scale neural network is like using a black box, with poor interpretability. Even if the loss converges to a low level, it may simply find a compromise within the limited training set and fail to truly learn the channel characteristics. Furthermore, existing techniques lack a detailed analysis of the components of nonlinear noise, making it difficult to estimate.

[0006] References

[0007] [1]Chi N, Zhou Y, Wei Y, et al. Visible Light Communication in 6G: Advances, Challenges, and Prospects[J]. IEEE Vehicular Technology Magazine, 2020, 15(4): 93-102.

[0008] [2]Chi N,Haas H,Kavehrad M,et al.Visible light communications:demandfactors,benefits and opportunities[Guest Editorial].IEEE WirelessCommunications,2015,22(2):5-7.

[0009] [3]B.Cochenour,L.Mullen,and J.Muth,“Effect of scattering albedo onattenuation and polarization of light underwater,”Opt.Lett.35(12),2088–2090(2010).

[0010] [4]Feder,Meir,and Josko A.Catipovic."Algorithms for joint channelestimation and data recovery-application to equalization in underwatercommunications."IEEE journal of oceanic engineering 16.1(1991):42-55.

[0011] [5]Qiao,Gang,et al."Sparse Bayesian learning for channel estimationin time-varying underwater acoustic OFDM communication."IEEE Access 6(2018):56675-56684.

[0012] [6]Pompili D,Akyildiz I F.Overview of Networking Protocols forUnderwater Wireless Communications[J].IEEE Communications Magazine,2009,47(1):97–102.

[0013] [7]Ma,Xu,et al."Channel estimation for wideband underwater visiblelight communication:a compressive sensing perspective."Optics express 26.1(2018):311-321.

[0014] [8]Zhongya Li,Jianyang Shi,Yiheng Zhao,Guoqiang Li,Jiang Chen,JunwenZhang,and Nan Chi,"Deep learning based end-to-end visible light communicationwith an in-band channel modeling strategy,"Opt.Express 30,28905-28921(2022).

[0015] [9]J.Cai,X.Lin,G.Qin,R.Jin and N.Chi,"Nonlinear Compensation based onBidirectional Gate Recurrent Unit in Underwater Visible Light CommunicationSystem,"2022 31st Wireless and Optical Communications Conference(WOCC),2022,pp.30-34,doi:10.1109 / WOCC55104.2022.9880586.

[0016]

[10] Chen H,Zhao Y,Hu F,et al.Nonlinear Resilient Learning MethodBased on Joint Time-Frequency Image Analysis in Underwater Visible LightCommunication[J].IEEE Photonics Journal,2020,PP(99):1-1.

[0017]

[11] Hu,Fangchen,et al."Non-linear Compensation based on PolynomialFunction Linked ANN in Multi-band CAP VLC System."2019 26th InternationalConference on Telecommunications(ICT).IEEE,2019.

[0018]

[12] Yiheng, Zhao, Peng, et al. Two tributaries heterogeneous neural network based channel emulator for underwater visible light communication systems. [J]. Optics express, 2019, 27(16): 22532-22541.

[0019]

[13] Zhang, Yonglin, et al. "On the performance of deep neural networkaided channel estimation for underwater acoustic OFDM communications." OceanEngineering 259(2022):111518.

[0020]

[14] Lu, Huaiyin, Ming Jiang, and Julian Cheng. "Deep learning aidedrobust joint channel classification, channel estimation, and signal detection for underwater optical communication." IEEE Transactions on Communications 69.4 (2020): 2290-2303.

[0021]

[15] J.Shi et al., "Optimal Adaptive Waveform Design Utilizing an End-to-End Learning-Based Pre-Equalization Neural Network in an UVLC System," in Journal of Lightwave Technology, doi:10.1109 / JLT.2022.3225335. Summary of the Invention

[0022] The purpose of the present invention is to provide an underwater visible light channel estimator based on integrated network learning with low system structure complexity and high channel estimation accuracy.

[0023] The underwater visible light channel estimator based on integrated network learning provided by the present invention includes three branch networks designed by machine learning to estimate the underwater visible light channel. Specifically, based on existing prior knowledge, the channel estimator is split into three sub-networks (three branch networks of machine learning): a linear estimator, an SSBI (Signal Countermeasures Interference) estimator, and a ReLU estimator, which are respectively used to estimate the linear noise, quadratic noise, and high-order noise of the channel. The three sub-networks are then integrated and trained to obtain the overall underwater visible light channel estimator.

[0024] The linear noise is caused by the use of root cosine filters in pulse shaping technology, which brings inter-symbol interference (ISI); the quadratic noise is caused by the system using intensity modulation, including direct modulation and direct detection, and square-law detection of the photodetector (PD) at the receiving end; the high-order noise comes from the nonlinear distortion caused by high-power transmission of optoelectronic devices.

[0025] (1) Linear estimator for estimating the linear noise of the channel,

[0026] Due to the limited bandwidth of the visible light system, pulse shaping requires the use of a root-raised cosine filter, which inevitably results in ISI. ISI is a signal that is affected by the interference of the preceding and following signals. The length of the crosstalk signal depends on the actual channel. This linear superposition process can be simply estimated using a linear neural network, such as Figure 1 (b) shows an input layer, a hidden layer, and an output layer. The hidden layer nodes do not use nonlinear activation functions, that is, all nodes are connected only by linear weights. The linear neural network adopts a multi-input and single-output structure. The multi-input is the process of simulating ISI. The number of input nodes is the number of taps of crosstalk. The single output is to ensure the accuracy of data prediction as much as possible. The transmitted signal (Tx data) is shaped with a sliding window of length (2n+1) and then sent to the linear neural network. The process of linear neural network simulation of ISI is shown in the following formula (1),

[0027]

[0028] Where n represents the crosstalk length of the unilateral signal, that is, the tap length of ISI, which is (2n+1); s and o are the input and output signals respectively. 1 is the weight of each signal, Yes 1 The weight, s i is the component of s, i = Tn, T-n+1,,,T+n; T is the time corresponding to each signal, and n is the crosstalk length of the unilateral signal.

[0029] This simple linear estimator can simulate most of the characteristics of the channel, but it is still powerless against nonlinear distortion, so more estimators are needed.

[0030] (2) SSBI estimator for estimating channel quadratic noise

[0031] In addition to linear distortion, the system will also suffer from the quadratic distortion of SSBI at the receiving end. Since intensity modulation direct detection is widely used in visible light communication systems, SSBI occurs in the square law detection of the PD receiver. The normalized detection signal V DD (n) can be written as formula (2):

[0032]

[0033] Among them, the first term is the DC quantity that will not be detected by the oscilloscope, the second term is the desired signal, and the third term is the quadratic noise SSBI. carrier is the amplitude of the DC carrier, and E0(n) is the amplitude of the signal.

[0034] Since SSBI is the square of the signal in the time domain, it is the convolution of two Nyquist filtered square signals in the frequency domain. Therefore, SSBI is theoretically a triangular signal with the same bandwidth as the signal, such as Figure 1 As shown in (a). Eliminating SSBI by spectrum shifting will reduce spectrum efficiency by 50%, greatly affecting the communication capacity. Many algorithms for eliminating SSBI have been proposed in previous studies. In contrast, the present invention uses a neural network to estimate the SSBI generated by the receiver. The neural network includes an input layer, a hidden layer, and an output layer. The hidden layer uses a quadratic function as an activation function to simulate the quadratic distortion caused by the estimated signal. Linear weight connections are used between the input layer, hidden layer, and output layer. Consistent with the aforementioned linear estimator, the SSBI estimator adopts a multi-input single-output structure. ; As shown Figure 1 As shown in (d), the neural network takes into account the crosstalk of SSBI on the time scale, where the neurons in the hidden layer use the square function instead of the traditional activation function. Since SSBI noise is the product of two signals, the number of neurons in the hidden layer is set to Where (2m+1) is the number of taps of SSBI. If the input layer and the hidden layer are fully connected, a lot of redundancy will be generated. Therefore, based on the above ideas, the dropout probability of the network is set to (2m-1) / (2m+1) to randomly discard the connection between neurons. The predicted output of the hidden layer data after linear regression can be expressed as formula (3):

[0035]

[0036] Among them, ω 2 ,ω3 are the weights of the connections between neurons, and o is the input to the SSBI estimator. Yes 3 The weight, Yes 2 The weight, o i are the components of o, j = 1, 2,,,,m(2m+1), i = tm, t-m+1,,,t+m.

[0037] (3) ReLU estimator for estimating channel high-order noise

[0038] Taking into account the nonlinear effects produced by optoelectronic devices, a ReLU estimator is designed to predict nonlinear responses. Since visible light power is greatly attenuated underwater, it is necessary to increase the transmission power of LEDs. Since the electro-optical conversion curve of LEDs is not linear, nonlinear distortion is inevitable under large signal transmission. At the receiving end, the response curve of PD is also nonlinear. Therefore, these nonlinear effects will ultimately affect the accuracy of the channel model. Noting that traditional algorithms are difficult to predict high-order nonlinearities, the present invention adopts a neural network, which includes an input layer, a hidden layer, and an output layer. The hidden layer uses a nonlinear activation function ReLU to simulate the nonlinear noise of the estimated channel. Linear weight connections are used between the input layer, the hidden layer, and the output layer. Consistent with the aforementioned estimator, the ReLU estimator adopts a multi-input single-output structure, taking into account the temporal crosstalk of the signal. , such as Figure 1 (c) As shown. Taking Tx data as input, the predicted Rx data is expressed as formula (4):

[0039]

[0040] Among them, ω 4 ,ω 5 is the connection weight between neurons, (2p+1) is the tap length of the ReLU estimator; the ReLU activation function can be expressed as formula (5):

[0041]

[0042] r is the input signal of the ReLU estimator, Yes 5 The weight, ω 4 The element r i is the component of r, j = 1, 2,,,, (2p+1) 2 ,i=tp,t-p+1,,,t+p;

[0043] To ensure that the neural network has sufficient interleaving, the number of neurons in the hidden layer should be at least the square of the number of neurons in the input layer, that is (2p+1). 2.

[0044] Even though both the linear estimator and the ReLU estimator can predict the input and output data, neither of them can fully consider the characteristics of the underwater visible light channel. Therefore, an integrated estimator with more functions is needed.

[0045] (4) Estimator Ensemble

[0046] Although a single neural network can estimate the channel, the black box neural network not only lacks interpretability but also faces many potential risks. Therefore, the structure of the estimator needs to be redesigned based on certain prior knowledge. Figure 1 As shown in (a), it includes a linear estimator, an SSBI estimator, and a ReLU estimator. The Tx data is sent to different linear layers of the linear estimator (linear neural network) at different times t. The output of the linear layer is reduced in dimension through the flatten layer. This data is then input to the SSBI estimator (quadratic neural network) and superimposed with the intermediate term output by the linear layer. The process of signal superposition with SSBI is simulated here, as shown in Equations (2) and (6).

[0047] r(t)=o(t)+s(t) (6)

[0048] Where o(t) is the signal and s(t) is the predicted SSBI. All outputs are fed into the flatten layer again and then into the higher-order nonlinear layer. It can be seen that all linear ISI, quadratic SSBI, and higher-order nonlinearity are considered simultaneously in the integrated estimator. According to equations (1)(3)(4)(6), the predicted Rx data at time t can be expressed as equation (7),

[0049]

[0050] In the present invention:

[0051] In the linear estimator, the linear neural network includes an input layer, a hidden layer and an output layer, wherein the number of nodes in the input layer is 53, the number of nodes in the hidden layer is 212, and the number of nodes in the output layer is 1.

[0052] In the SSBI estimator, the neural network used includes an input layer, a hidden layer and an output layer, wherein the number of nodes in the input layer is 9, the number of nodes in the hidden layer is 36, and the number of nodes in the output layer is 1.

[0053] In the ReLU estimator, the neural network used includes an input layer, a hidden layer, and an output layer, wherein the number of nodes in the input layer is 53, the number of nodes in the hidden layer is 212, and the number of nodes in the output layer is 1.

[0054] (5) Ensemble estimator training

[0055] (a) Design of loss function

[0056] When neural networks are used for regression, the minimum mean square error (MSE) is often used as the loss function to evaluate the training performance, as shown in formula (8),

[0057]

[0058] Among them, d is the label of data training, and N is the amount of data in the training set.

[0059] (b) Adjustment of network connection weights

[0060] In order to automatically train the estimator, the back propagation (BP) algorithm is applied to adjust the connection weights of each network. According to the gradient descent and link rule, the adjustment formula of each weight is as shown in Equations (9)-(13):

[0061]

[0062]

[0063]

[0064]

[0065]

[0066] Where ReLU' is the derivative of the ReLU function and η is the learning rate for training.

[0067] (c) Selection of tap parameters

[0068] In order to select the suboptimal solutions of linear, quadratic and high-order taps, that is, the above-mentioned (2n+1), (2m+1) and (2p+1) parameters, a trade-off needs to be made between complexity and accuracy. A large tap value can make the result more accurate, but it will also increase the complexity of the system and make it difficult for the network to converge. Therefore, the present invention proposes an algorithm to find the local minimum. The first step is to fix the values of two of the taps, traverse the third tap, and find its minimum value. The second step is to use the minimum value to update the value of the third tap. The third step is to fix the other two tap values and repeat the above two steps until convergence.

[0069] Figure 2The final convergence results of the MSE and the corresponding number of taps are shown. The linear and high-order MSEs gradually decrease with the increase in taps, and the number of taps at the inflection point is selected to be 33 and 41, respectively. The MSE of the quadratic tap number has a clear extreme value at 9, because the increase in SSBI complexity affects the weights of the other two networks and is ultimately reflected in the MSE. The convergence result is that when the linear tap is 33 and the quadratic tap is 9, the suboptimal value of the high-order tap is 41; when the linear tap is 33 and the high-order tap is 41, the suboptimal value of the quadratic tap is 9; when the quadratic tap is 9 and the high-order tap is 41, the suboptimal value of the linear tap is 33.

[0070] Complexity Analysis

[0071] The computational complexity of neural networks is mainly contributed by multipliers. Therefore, other addition operations are omitted and the number of real-valued multipliers (RVMs) required to generate a sample output is calculated. The number of RVMs for an estimator with several hidden layers can be defined as:

[0072]

[0073] Where d is the number of layers including the input and output layers, and c refers to the neural network designed with ci neurons in the i-th layer. In order to reduce the complexity of the entire network, the theoretical number of neurons can be appropriately reduced while still achieving the desired effect. The number of nodes and the number of RVMs required for each estimator are shown in Table 1. The total memory occupied by the network includes the input and output scale, forward / backward pass scale, and parameter size. For a fair comparison, we align the number of RVMs of the single network estimator with the ensemble estimator. It is worth noting that the ensemble estimator requires massively parallel operations rather than serial processing, and therefore requires larger memory than the single network estimator. Despite the increased hardware resource requirements, the ensemble estimator can provide more accurate channel estimation. BRIEF DESCRIPTION OF THE DRAWINGS

[0074] Figure 1 are the neural network-based estimators. (a) is the ensemble estimator. (b) is the linear estimator. (c) is the ReLU estimator. (d) is the SSBI estimator.

[0075] Figure 2 The MSE performance of the three networks with different tap numbers.

[0076] Figure 3 The experimental setup and photos of the underwater visible light communication system. (a) is the system block diagram. (b) is a photo of the transmitter. (c) is a photo of the channel. (d) is a photo of the receiver.

[0077] Figure 4are the channel responses and response errors of the three estimators.

[0078] Figure 5 BER performance of the three estimators and the actual channel under different Vpp. (i) Constellation diagram of the actual channel. (ii) Constellation diagram of the linear estimator. (iii) Constellation diagram of the ReLU estimator. (iv) Constellation diagram of the integrated estimator.

[0079] Figure 6 MSE performance of the three estimators under different Vpp.

[0080] Table 1 shows the number of neural network nodes and computational complexity analysis of the three estimators. DETAILED DESCRIPTION

[0081] The present invention is further described below through specific examples and drawings.

[0082] To accommodate the characteristics of the passband channel, transmit data is typically carrier-modulated. The original binary bit stream is converted to a baseband signal through quadrature amplitude modulation (QAM), 4x upsampling, and Nyquist filtering. To convert the complex signal to a real signal, after I / Q separation, the real and imaginary components of the signal are multiplied by cosine and sine carriers, respectively. This carrier modulation yields a bandpass signal. Given the strong low-frequency noise inherent in underwater visible light systems, the signal is upshifted by 25 MHz to reduce noise interference. At the receiver, this solution applies offline DSP techniques to recover the original data. After equalization, demodulation, filtering, downsampling, and QAM demapping, the receive data is converted to a binary signal, where the bit error rate (BER) is calculated.

[0083] Figure 3This paper demonstrates an experimental underwater visible light communication system. The single-carrier modulated transmit signal, or Tx data, is generated offline using Matlab. This system includes the aforementioned steps of QAM mapping, upsampling, Nyquist filtering, I / Q separation, and wave-carrier modulation. The data is then loaded into an arbitrary waveform generator (AWG, Tektronix AWG710B, 4.2GSa / s) with a sampling rate of 2GSa / s to convert the digital signal into an analog signal. The data is amplified by an amplifier (EA, ZHL-2-8-S+) and then passed through a bias tee (ZFBT-4R2GW-FT+). Because the LED drive voltage must be positive and exceed the threshold voltage, the bias tee is controlled by an 180mA constant current power supply (GDP-4303S). This scheme uses a green LED as the signal source due to its low attenuation underwater. The light is focused into quasi-parallel light by a lens assembly and transmitted through a 1.2-meter-long water tank. At the receiver, the signal is focused by a lens and detected by a PIN-based photodetector (PD). The PD outputs two opposing signals, which are observed on a 2 GHz oscilloscope (OSC, DS09404A, 4 GHz). The two signals are amplified, synchronized, and then subtracted to remove common-mode noise. The received data from the underwater channel is processed using Matlab offline DSP technology, including equalization, demodulation, filtering, downsampling, and QAM demapping.

[0084] Next, we trained the aforementioned linear estimator, ReLU estimator, and ensemble estimator using the transmitted data as the training set and the received data as the labels, comparing their results. The training results show that the ensemble estimator achieves the best performance and can truly learn the channel characteristics. Therefore, a well-trained three-branch ensemble estimator can accurately predict the channel's input and output data.

[0085] Result analysis of the present invention

[0086] (1) The integrated estimator has the smallest channel response error among the three estimators, which is 0.3222dB at 300mV and 0.7861dB at 900mV.

[0087] In order to better display the channel characteristics, the channel response function is used to describe it in the frequency domain, as shown in the following formula (15):

[0088] Y(ω)=H(ω)·X(ω)+N(ω) (15)

[0089] Where H is the channel response function, N is the channel noise, and X and Y are the spectra of the transmitted and received waveforms, respectively, obtained by FFT transformation.

[0090] Since the time average value of the noise is zero, it can be eliminated by multi-sample averaging and smoothing techniques. The processed signals can be recorded as X' and Y'. Therefore, the channel response H can be calculated by Y' / X'. The channel response obtained from the experimental waveform is as follows Figure 4 The black line is shown. Notice that the channel response decreases gradually with increasing frequency and drops sharply after reaching 400MHz. This is because the modulation rate of the LED is limited by the carrier lifetime. In addition, the channel response has a peak at low frequencies, which is the result of the combined effect of low-frequency noise and SSBI, as shown in Figure 2. Figure 1 (b) shown. Figure 4 The figure compares the H values of three estimators with the actual channel response at Vpp of 300mV and 900mV. The figure shows that the linear, ReLU, and ensemble estimators exhibit mismatch with the channel response at low frequencies. When Vpp is 300mV, the mismatch values are 3.11dB, 2.88dB, and 1.68dB, respectively. The ensemble estimator outperforms the other two because the SSBI estimator is designed separately to predict quadratic distortion. Although the ReLU estimator can handle nonlinear effects, it is still limited by the constraints of a single network. The remaining mismatch primarily comes from unavoidable and unpredictable system noise, which is why the spectrum is shifted by 25MHz to minimize H mismatch. At high frequencies, significant fluctuations in the estimators are observed because the LED's modulation limit makes it difficult for the neural network to find channel regularities. Similar results are observed when Vpp is 900mV, with H mismatch values of 5.21dB, 4.91dB, and 3.55dB, respectively. Different from low driving voltage, the larger the Vpp, the more noise there is, which will reduce the accuracy of channel estimation.

[0091] In addition, the figure also shows the errors between the H values of the three estimators and the actual channel response, further demonstrating the performance of the integrated estimator proposed in this invention. The three straight lines in the figure describe the average values of the H errors of the linear estimator, the ReLU estimator, and the integrated estimator, respectively. When Vpp is equal to 300mV, the average values of the H errors are 0.9741dB, 0.7553dB, and 0.3222dB, respectively. When Vpp is equal to 900mV, the average values of the H errors are 1.1417dB, 0.8149dB, and 0.7861dB, respectively. Similar phenomena can be observed in other cases. The H error of the integrated estimator is the lowest among the three estimators. The H errors of the three estimators are relatively low in the mid-frequency region, and the errors at both ends are larger, which is consistent with our previous analysis.

[0092] (2) The integrated estimator can learn the “V”-shaped characteristics of the channel, while the other two estimators can only find a compromise solution to minimize the BER in a limited training set.

[0093] The received waveform signal after transmission through the channel is processed by the offline DSP. After equalization, demodulation, downsampling and demapping, it can be Figure 5 The bit error rate performance is calculated as shown. The BER performance curve for a real channel exhibits a "V" shape, with Vpp equal to 300mV at the lowest BER. Reducing Vpp reduces signal power, resulting in a lower SNR. Increasing Vpp introduces nonlinear noise, also reducing SNR. Both scenarios result in a lower BER, hence the "V" shape. It is worth noting that while all three estimators can converge to a low MSE, only the ensemble estimator can learn the "V"-shaped characteristics of the channel. Furthermore, as Vpp moves away from 300mV (the bottom of the "V"), the bit error rate error between the ensemble estimator and the channel increases. This is also because the decrease in SNR makes channel estimation difficult. The constellation points for a Vpp of 300mV are shown in the figure. Clearly, only the ensemble estimator's constellation points are similar to those of the channel. Therefore, the ensemble estimator exhibits greater robustness than the other single-network estimators, effectively addressing potential risks of MSE convergence.

[0094] (3) The MSE value of the integrated estimator convergence is much lower than that of the other two estimators, and the minimum MSE value is 2E-4.

[0095] Figure 6 The MSE performance of the ensemble estimator is compared with that of the linear and ReLU estimators. We loaded Tx data into each estimator and calculated the MSE performance based on the predicted output and the actual Rx data from the experiment. Clearly, the ensemble estimator has the lowest MSE of the three estimators, reaching a minimum of 2E-4 when Vpp equals 300mV. Because nonlinear effects gradually increase with Vpp, the ReLU estimator's MSE performance outperforms the linear estimator, as evidenced in the range of 500mV to 900mV. When Vpp is less than 300mV, the linear estimator's MSE performance slightly outperforms the ReLU estimator because linear noise dominates at low Vpp. Generally, lower Vpp results in lower SNR, making it difficult for the estimator to predict results. Therefore, the MSE curve also exhibits a "V" shape.

[0096] Table 1. Neural network nodes and computational complexity analysis

[0097]

[0098]

Claims

1. An underwater visible light channel estimator based on integrated network learning, characterized in that: The method involves designing three machine learning branch networks to estimate underwater visible light channels. Specifically, based on existing prior knowledge, the channel estimator is split into three sub-networks: a linear estimator, an SSBI estimator, and a ReLU estimator, which are used to estimate the linear noise, quadratic noise, and higher-order noise of the channel, respectively. The three sub-networks are then integrated and trained to obtain the overall underwater visible light channel estimator. The linear noise is caused by the use of root-spurious cosine filters in pulse shaping technology, which brings inter-symbol interference (ISI); the quadratic noise is caused by the square-law detection of the photodetector (PD) at the receiving end when the system adopts intensity modulation direct modulation and direct detection; the high-order noise comes from the nonlinear distortion caused by high-power transmission of optoelectronic devices; (1) A linear estimator for estimating the linear noise of the channel; The linear estimator uses a linear neural network, which consists of an input layer, a hidden layer, and an output layer. The hidden layer nodes are connected by linear weights. The linear neural network adopts a multi-input and single-output structure. The multi-input is used to simulate the ISI process. The number of input nodes is the number of crosstalk taps. The single output is to ensure the accuracy of data prediction as much as possible. The transmitted signal (Tx data) is shaped using a sliding window of length (2n+1) and then fed into a linear neural network. The process of simulating ISI using a linear neural network is shown in the following equation (1): Where n represents the crosstalk length of the unilateral signal, and the tap length of ISI is (2n+1); s and o are the input and output signals respectively; ω 1 is the weight of each signal, Yes 1 The weight, s i is the component of s, i = Tn, T-n+1,,,T+n; T is the time corresponding to each signal, and n is the crosstalk length of the unilateral signal; (2) SSBI estimator for estimating channel quadratic noise The system will be affected by the quadratic distortion from SSBI at the receiving end; the normalized detection signal V DD (n) is written as: in, It is a DC quantity that cannot be detected by an oscilloscope. carrier ·E0(n)] is the desired signal, |E0(n)| 2 is the quadratic noise SSBI; E carrier is the amplitude of the DC carrier, E0(n) is the amplitude of the signal; The SSBI estimator uses a neural network to estimate the SSBI generated by the receiver. The neural network consists of an input layer, a hidden layer, and an output layer. The hidden layer uses a quadratic function as the activation function to simulate the quadratic distortion caused by the estimated signal. Linear weights are used between the input layer, the hidden layer, and the output layer. The SSBI estimator adopts a multi-input single-output structure. The neural network takes into account the crosstalk of SSBI on the time scale. The neurons in the hidden layer use a square function instead of the traditional activation function. Since SSBI noise is the product of two signals, the number of neurons in the hidden layer is set to Where (2m+1) is the number of taps of SSBI; the dropout probability of the neural network is set to (2m-1) / (2m+1) to randomly discard the connections between neurons; the hidden layer data is subjected to linear regression to obtain the predicted output, which is expressed as formula (3): Among them, ω 2 ,ω 3 is the weight of the connection between neurons, and o is the input of the SSBI estimator; Yes 3 The weight, Yes 2 The weight, o i are the components of o, j = 1, 2,,,,m(2m+1), i = tm, t-m+1,,,t+m; (3) ReLU estimator for estimating channel high-order noise The ReLU estimator uses a neural network, which consists of an input layer, a hidden layer, and an output layer. The hidden layer uses a nonlinear activation function ReLU to simulate the nonlinear noise of the estimated channel. The input layer, hidden layer, and output layer are connected by linear weights. The ReLU estimator adopts a multi-input single-output structure, taking into account the temporal crosstalk of the signal. With Tx data as input, the predicted Rx data is expressed as: Among them, ω 4 ,ω 5 is the connection weight between neurons, (2p+1) is the tap length of the ReLU estimator; the ReLU activation function is expressed as: r is the input signal of the ReLU estimator, Yes 5 The weight, ω 4 The element r i is the component of r, j = 1, 2,,,, (2p+1) 2 ,i=tp,t-p+1,,,t+p; To ensure that the neural network has sufficient interleaving, the number of neurons in the hidden layer should be at least the square of the number of neurons in the input layer, that is (2p+1). 2 .

2. The underwater visible light channel estimator based on integrated network learning according to claim 1, characterized in that The estimator integration is to fuse the linear estimator, SSBI estimator, and ReLU estimator. The Tx data is sent to different linear layers of the linear estimator according to different time t. The output of the linear layer is reduced in output dimension through the flatten layer. Then this data is input to the SSBI estimator and superimposed with the intermediate item output by the linear layer. Here, the process of signal superposition with SSBI is simulated, as shown in formula (6). r(t)=o(t)+s(t) (6) Where o(t) is the signal and s(t) is the predicted SSBI. All outputs are fed into the flatten layer again and then into the higher-order nonlinear layer. In the integrated estimator, linear ISI, quadratic SSBI, and higher-order nonlinearity are considered simultaneously. According to equations (1), (3), (4), and (6), the predicted Rx data at time t is expressed as equation (7).

3. The underwater visible light channel estimator based on integrated network learning according to claim 2, characterized in that Ensemble estimator training, including: (a) Design of loss function The minimum mean square error (MSE) is used as the loss function to evaluate the training performance, as shown in formula (8), Among them, d is the label of data training, N is the amount of data in the training set; (b) Adjustment of network connection weights The back propagation (BP) algorithm is applied to adjust the connection weight of each network. According to the gradient descent and link rule, the adjustment formula of each weight is as follows: Where ReLU' is the derivative of the ReLU function, and η is the learning rate of training; (c) Selection of tap parameters In order to select the suboptimal solutions for linear, quadratic, and high-order taps, i.e., the (2n+1), (2m+1), and (2p+1) parameters mentioned above, the following algorithm is used to find the local minimum: the first step is to fix the values of two of the taps, traverse the third tap, and find its minimum value; the second step is to update the value of the third tap using the minimum value; the third step is to fix the values of the other two taps and repeat the above two steps until convergence.

4. The underwater visible light channel estimator based on integrated network learning according to any one of claims 1 to 3, characterized in that: In the linear estimator, the number of input layer nodes of the linear neural network used is 53, the number of hidden layer nodes is 212, and the number of output layer nodes is 1; In the SSBI estimator, the number of input layer nodes of the neural network used is 9, the number of hidden layer nodes is 36, and the number of output layer nodes is 1; In the ReLU estimator, the number of input layer nodes of the neural network used is 53, the number of hidden layer nodes is 212, and the number of output layer nodes is 1.

Images