## Abstract

Due to the strong scattering characteristics, there are serious problems of inter-symbol interference (ISI) and transmission attenuation in the none-line-of-sight (NLOS) wireless ultraviolet communication system. In this paper, a wireless ultraviolet scattering channel estimation method based on deep learning is presented. The learning model structure is designed by combining the one-dimensional convolutional neural network (1D-CNN) and the deep neural network (DNN). In the training stage, the network optimization process is improved by the differential evolution (DE) algorithm. The computer simulation results show that the proposed deep learning channel estimation scheme has better mean square error (MSE) performance and bit error rate (BER) performance compared with the traditional algorithms. Furthermore, we verify the stability of this scheme in different communication environments, and the constructed neural network model has good generalization ability.

© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

## 1. Introduction

Wireless ultraviolet (UV) scattering communication is a kind of wireless communication technology based on atmospheric particle scattering. Due to its strong scattering characteristics, wireless UV can be applied to some special scenarios [1]. But the multipath effect is more obvious, which will lead to the serious pulse broadening phenomenon in the optical path. In the case of high data rate, the multipath effect will lead to the problem of inter-symbol interference (ISI) in the communication system [2], which will cause misjudgment of information transmission and the degradation of communication performance. In terms of none-line-of-sight (NLOS) wireless UV scattering channel, the Monte Carlo method has been used to study single scattering [3–5] and multiple scattering [6,7], through the modeling of UV scattering channel, the impulse response, path loss, channel bandwidth and other channel characteristics of NLOS UV scattering channel are studied.

Channel estimation is an effective solution to the problem of communication system performance degradation caused by scattering. When the channel is unknown, channel estimation can obtain the channel state information (CSI) of the receiving end, which is very important for improving the performance of the communication system. The traditional channel estimation methods include least square (LS) estimation [8], minimum mean square error (MMSE) estimation [9], and Bayesian estimation [10], etc. The channel estimation methods in Free Space Optical (FSO) communication are studied in [11] and [12], where the channel characteristics and optical fading are estimated by parametric analysis. There are also many pieces of research on channel estimation for wireless UV scattering communication. According to the received signal expression and channel parameter form of UV scattering communication, the channel estimation methods of LS estimation and maximum likelihood (MLE) estimation are studied in [13], the estimation performance is measured by the defined estimated signal-noise ratio (SNR). To eliminate the problem of ISI in UV communication, some joint estimation methods of channel parameters and communication signals are presented in [14] and [15], the improved estimation algorithms can effectively detect the communication signals and achieve reliable information transmission. However, the most of traditional estimation methods are not suitable for the special scenario of UV covert communication, which will lead to the performance degradation of the communication system. Moreover, most of the traditional channel estimation algorithms are nonlinear and have high computational complexity. In recent years, deep learning has been widely used in the physical layer of wireless communication [16], and it is a new idea to introduce deep learning (DL) technology into the channel estimation of wireless UV communication. Sufficient data iterative training can make the learning network infinitely approximate the actual channel model [17–19], and the DL-based channel estimation algorithms can be carried on the GPU, which greatly improve the operation efficiency.

Deep learning is one of the important means to improve the accuracy of channel estimation. The scheme of designing the channel estimator by using the Generative Adversarial Networks (GAN) and the autoencoder (AE) are proposed in [20] and [21], which can improve the accuracy of channel estimation. Deep neural network (DNN) has also been used in signal processing for wireless optical communication [22–24]. The signal processing part of the communication system is usually regarded as the black box, and the DNN is used to learn the nonlinear mapping relationship between its input and output, which has lower computational complexity compared with traditional methods. Aiming at the prediction problem of time series such as channel estimation, one-dimensional convolutional neural network (1D-CNN) can get better results with lower computational cost and higher data processing speed [25,26]. In summary, the application of neural networks for signal processing in wireless UV communication has certain research significance.

In this paper, we apply deep learning technology to wireless UV communication and propose a wireless UV scattering channel estimation method based on deep learning (DL-UVCE). The structure of the learning model designed in this paper is composed of DNN and 1D-CNN. The differential evolution (DE) algorithm is applied to the network training process. In the case of modeling the wireless UV single scattering channel model, the optimal mapping relationship between the channel pulse coefficient and the received signal is learned through the training of network. Then we accurately extract the statistical characteristics of the wireless UV scattering channel, which can provide the basis for the subsequent signal detection and channel equalization.

The rest of this article is arranged as follows: Section 2 describes the single scattering channel model of wireless UV communication, which provides the theoretical basis for the follow-up work. The proposed DL-UVCE scheme is presented in Section 3, include network structure and optimization process. The performance of DL-UVCE is illustrated with simulations in Section 4. Section 5 is conclusions and remarks on the work of this paper.

## 2. Wireless ultraviolet single scattering channel model

In this paper, the wireless UV single scattering channel model is taken as the research object. As shown in Fig. 1, the single scattering theory assumes that the photons emitted at the transmitter are scattered only once in the common scatterer before they are transmitted to the receiver, thus enabling NLOS communication.

In Fig. 1, ${T_X}$ is the transmitter, ${R_X}$ is the receiver, and the communication distance between the transmitter and receiver is *d*, ${\beta _T}$ and ${\beta _R}$ are the elevation angles of the transmitter and receiver, respectively, ${\theta _T}$ is the angle of beam divergence for the transmitter, ${\theta _R}$ is the receiver field of view, $V$ is common scattering volume, ${r_1}$ and ${r_2}$ are the distances from the transmitter and receiver to *V*, respectively, ${\theta _s}$ is scattering angle. All these scatterer parameters affect the statistical properties of the channel, so the relevant properties of the channel will be studied in the following by selecting different angular parameters.

#### 2.1 Channel impulse response of scattering channel

Channel impulse response (CIR) is an important channel statistical characteristic for studying ultraviolet scattering problems. According to the geometric model of single scattering, the ellipsoidal coordinate system is established [27]. The transmitter and receiver are respectively placed on the focal point of the ellipsoidal coordinate system. The transmitted photons are scattered on the ellipsoidal surface, so the sum of the distance from the scattering point to the transmitter and receiver is a fixed constant value, which simplifies the calculation of the UV NLOS single scattering channel model. As shown in Fig. 1, the overlap area between ${\theta _T}$ and ${\theta _R}$ is the common scattering volume that determines the channel characteristics, the lower limit of this area is ${\Phi _1}$ and the upper limit is ${\Phi _2}$. Let the transmitter send a pulse signal with the energy of ${E_T}$, and take the differential volume element $\delta V$ in *V*, which can be considered as the secondary radiation source after scattering occurs, according to the scattering theory in [27], the photon energy received per unit area at the receiver is

To facilitate the analysis of the statistical characteristics of the ultraviolet scattering channel, we assume that *V* is tiny enough and $\cos (\zeta )$ is approximated as a constant. The differential volume element $\delta V$ is converted in the ellipsoidal coordinate system, and the total energy of the receiver is obtained by integrating it into the ellipsoidal coordinate system. The approximate expression can be written as follows:

After the above analysis for the energy at the receiving end, $\xi $ is represented by ${{ct} / d}$, where *c* is the lightspeed. Then the simplified approximate expression of channel impulse response [28] is as follows:

The pulse broadening phenomenon is verified by simulation through the above model, and the parameters used are as follows: ${k_s} = 4.9 \times {10^{ - 4}}{m^{ - 1}}$, ${k_e} = 7.4 \times {10^{ - 4}}{m^{ - 1}}$, ${\beta _T} = {\beta _R} = {60^ \circ }$, ${\theta _T} = {30^ \circ }$, ${\theta _R} = {15^ \circ }$. The unit impulse signal is input at the transmitter, and the channel impulse response waveforms obtained at four different communication distances are shown in Fig. 2. It can be seen that the pulse spreading phenomenon of the wireless UV scattering channel is very obvious, the pulse half-height width reaches the microsecond level and increases with the increase of the communication distance.

#### 2.2 Path loss of wireless ultraviolet scattering channel

The NLOS link between the transmitter and the receiver can be regarded as the sum of the line-of-sight (LOS) links ${r_1}$ and ${r_2}$. Suppose the transmission power of the transmitter is ${P_t}$, and the power per solid angle is ${{{P_t}} / {{\Omega _t}}}$. Because of the path loss and signal attenuation in the scattering process, ${P_t}$ decays to $({{{{P_t}} / {{\Omega _t}}}} )\cdot ({{{{e^{\textrm{ - }{k_e}{r_1}}}} / {r_1^2}}} )$ after transmission in ${r_1}$, and becomes $({{{{P_t}} / {{\Omega _t}}}} )\cdot ({{{{e^{\textrm{ - }{k_e}{r_1}}}} / {r_1^2}}} )\cdot ({{{{k_s}{P_s}V} / {4\pi }}} )$ after scattering by *V*, then it will suffer from atmospheric attenuation ${e^{ - {k_e}{r_2}}}$ and space link loss ${({{\lambda / {4\pi {r_2}}}} )^2}$, and the receiver gain of the detector is ${{4\pi {A_r}} / {{\lambda ^2}}}$. In summary, the received optical power of the UV NLOS link [29] can be obtained as:

Therefore, the path loss is

Based on the above theoretical analysis, the effect of the angle parameters on the path loss is simulated, the parameters are set to ${P_t} = 50mW$, ${A_r} = 1.77c{m^2}$, ${k_s} = 4.9 \times {10^{ - 4}}{m^{ - 1}}$, ${k_e} = 7.4 \times {10^{ - 4}}{m^{ - 1}}$, $d = 200m$, $\lambda \textrm{ = }254nm$. The path loss curves for different geometric model angle parameters are shown in Fig. 3.

As can be seen from Fig. 3, the path loss increases as the communication distance increases. Figure 3(a) shows the effect of ${\beta _T}$ and ${\beta _R}$ on the path loss. Compared with the elevation angle of the transmitter, the increase of the elevation angle of the receiver results in greater path loss. In general, both the receiver and transmitter elevation angles are positively correlated with the path loss. Figure 3(b) shows that the beam divergence angle has little effect on the path loss, and the path loss decreases with the increase of the received field of view angle.

Therefore, the path loss of wireless UV communication can be reduced by increasing the received field of view and decreasing the elevation angle. The parameters of the channel model used for channel estimation are selected by the above analysis and are shown in Table 1.

## 3. Channel estimation method based on deep learning

This section presents a scheme for designing a UV scattering channel estimator by using the DNN and the 1D-CNN model. The core part is the training process of the network. With sufficient training data, the proposed neural network can keep close to the actual UV scattering channel by deep learning, and then we apply the optimal output to the channel estimation part of the wireless UV communication system intending to accurately estimate the channel response coefficients. The proposed scheme for UV scattering channel estimation is shown in Fig. 4.

As shown in Fig. 4, this scheme is mainly divided into the offline training part and the online estimation part. In the offline training part, 1D convolution and 1D max-pooling operations are performed on the input signals to obtain the low dimensional characteristic parameters which are suitable for the DNN. Then, the parameters are converted into the matrix form and input to the DNN by the fully connection layer. Through continuous linear activation operation, the network learns the mapping relationship between the received signal and the channel response coefficient. In the online estimation part, the network optimal output is applied to the channel estimation part of the communication system, and the transmitted signal is accurately recovered at the receiving end. The accuracy of channel estimation will directly affect the communication performance of the whole system.

#### 3.1 Neural network architecture

The structure of 1D-CNN is shown in Fig. 4, which is composed of four parts: input layer, 1D-Conv layer, 1D-Maxpooling layer, and fully connection layer. A fixed time window is used to process the transmission signal, the vector sampling points covered by each window movement are taken as an input of the neural network. The window length is set to be $M\textrm{ + 1}$, then the vector after the window moving *m* times is

For the signal sampling sequence ${{\textbf x}^{(n)}} = [{x(1),x(2), \cdots ,x(n)} ]$, the training data set can be expressed as:

The 1D convolution layer is used to filter the UV transmission signal, so as to achieve feature extraction. The length of the convolution kernel is less than the length of the input vector, and its parameter expression is ${\textbf s} = [{{s_1},{s_2}, \cdots ,{s_t}} ]_{t \times 1}^T,t < M + 1$. This scheme adopts the 1D Valid convolution method for operation processing, and the convolution step is set to 1. The output vector length of the convolution operation is less than the input vector length, which can be expressed as:

*k*is the output vector length of the convolution operation, and $k = M - t + 2$.

The pooling operation of the 1D-CNN designed in this paper adopts the 1D Maxpooling layer to reduce the data space and simplify the operational complexity of the network. The fully connection layer in the network integrates the extracted low-dimensional data features and sends the output value to the DNN for parameter optimization.

DNN is a neural network with multiple hidden layers, composed of basic neurons, as shown in Fig. 5.

For input data ${x^{(l)}} = ({{x_1},{x_2}, \cdots ,{x_n}} )$, the output of the neuron is as follows:

*b*is the bias coefficient. $\sigma $ is the activation function. This scheme chooses the sigmoid function as the activation function, which is defined as $\sigma (x )= \frac{1}{{1\textrm{ + }{e^{ - x}}}}$.

In this paper, the channel estimation of wireless UV communication is realized by constructing a neural network, and the deep learning method used belongs to a regression prediction problem. Therefore, we choose the Mean Square Error (MSE) function as the loss function, which is defined as:

where ${h^L}$ is the network actual output,*y*is the target output, ${||\cdot ||_2}$ is the 2-norm operation.

To prevent the problem of overfitting during the network training process, we adopt the Dropout method for regularization. Dropout is used to activate a part of the neurons in the hidden layer randomly so that the other neurons are in an inactive state, and then only the weights and biases of the activated neurons are updated. That is, assuming that each neuron is activated with probability *P*, the output value of this neuron needs to be multiplied ${1 / P}$ to ensure that the signal intensity input to the next layer of neurons remains stable. The setting of this probability should not be too small, otherwise, it will cause the underfitting phenomenon. Therefore, *P* is set to $0.6$ in this paper.

#### 3.2 Neural network optimization process

The multi-layer neural network has comparatively high computational complexity and is easy to fall into local optimum. To solve this problem, the neural network optimization process adopts the DE algorithm which has a large search space, thereby increasing the convergence speed of the system and reaching the global optimum [30]. The goal of the DE algorithm is to evolve a population of size $NP$, which is composed of D-dimensional individuals and is defined as ${{\textbf X}_{i,G}} = \{{x_{i,G}^1, \ldots ,x_{i,G}^D} \},i = 1, \ldots ,NP$. The DE algorithm mainly performs mutation, crossover, and selection operations in the population to find the optimal individual in the population.

- (1) Mutation: Two individuals are randomly selected in the population to calculate the difference, and a new individual is generated by summing the scaled difference vector and another random individual. The mutation operation can be expressed as follows:$${{\textbf V}_{i,G}} = {{\textbf X}_{{r_1},G}} + F \cdot ({{{\textbf X}_{{r_2},G}} - {{\textbf X}_{{r_3},G}}} )$$where ${r_1},{r_2},{r_3}$ are mutually exclusive integers in the range of $[1,NP]$. $F$ is the scaling factor.
- (2) Crossover: To increase the diversity of the population, the original individual ${{\textbf X}_{i,G}}$ and the mutation individual ${{\textbf V}_{i,G}}$ were recombined to produce new individuals, and the experimental individual ${{\textbf U}_{i,G + 1}} = \{{u_{i,G}^1, \ldots ,u_{i,G}^D} \}$ was generated. The crossover operation is as follows:$${{\textbf U}_{i,G + 1}} = \left\{ \begin{array}{l} {\textbf V}_{i,G}^j,{\kern 1pt} {\kern 1pt} [{rand(j) \le CR} ]or[{j = n(j)} ]\\ {\textbf X}_{i,G}^j,{\kern 1pt} {\kern 1pt} [{rand(j) > CR} ]and[{j \ne n(j)} ]\end{array} \right.$$where $rand(j)$ is a random number in the range of $[0,1]$. $CR \in [0,1]$ is the crossover rate, which is used to control the cross ratio. $n(j)$ is a random integer in the range of $[0,D]$.
- (3) Selection: The greedy search strategy is adopted to select the next generation of individuals. The larger the fitness value, the more preferred. The selection operation is as follow:$${{\textbf X}_{i,G + 1}} = \left\{ \begin{array}{l} {{\textbf X}_{i,G}},{\kern 1pt} {\kern 1pt} {\kern 1pt} fitness({{\textbf U}_{i,G}}) \le fitness({{\textbf X}_{i,G}})\\ {{\textbf U}_{i,G}},{\kern 1pt} {\kern 1pt} {\kern 1pt} fitness({{\textbf U}_{i,G}}) > fitness({{\textbf X}_{i,G}}) \end{array} \right.$$where $fitness$ is to find the fitness value of the vector.

In this paper, the parameter population is established for the connection weight and bias of DNN, and the parameters are updated by the DE algorithm. The training process is shown in Fig. 6.

The specific steps are as follows:

Step1: Initialization setting. DNN initialization includes the number of hidden layers and neurons in each layer, the activation function, the maximum number of epochs, and the training threshold. The initialization of the DE algorithm includes population size $NP$, vector dimension $D$, scaling factor $F$, and cross rate $CR$.

Step2: Initialization of the connection weight and bias.

Step3: Initialize the fitness value of the individual in the parameter population. In this scheme, the average value of the MSE generated in the process of parameter population training is used as the fitness value.

Step4: According to formulas (12), (13), (14), mutation, crossover, and selection operations are performed on the parameter population individuals.

Step5: Calculate the fitness value of the newly generated individual and retain the optimal individual.

Step6: Determine whether the termination condition is reached, if satisfied, proceed to Step7. Otherwise, return to step 4 to continue the differential evolution operation.

Step7: Combined with the optimal individual of the parameter population, the network training process is completed by judging the error threshold and updating the parameters. If the threshold error is not met, the parameters are further updated through the Stochastic Gradient Descent (SGD) method in backpropagation process until convergence, and finally the optimal model is obtained.

#### 3.3 Algorithm complexity analysis

The traditional LS and MMSE algorithms are both channel estimation methods based on training symbols, and the training symbol needs to be extracted after receiving the entire frame of signal for channel estimation, which will bring unavoidable time delay. In terms of algorithm calculation complexity, the structure of the LS algorithm is relatively simple, and the channel characteristics of the pilot position subcarriers can be obtained only by performing a division operation on each carrier, so the calculation amount is small. The MMSE algorithm considers the influence of noise on the basis of the LS algorithm, and can obtain a better channel estimation effect. But the calculation amount is large, and the matrix inversion operation needs to be performed multiple times with the increase of the number of system subcarriers, and each subcarrier requires $O({K^3})$ order multiplication operation, resulting in high computational complexity. The algorithm proposed in this paper is mainly neural network, which is similar to a blind estimation method. It makes full use of the internal information of the transmitted data to realize channel estimation. The core operation of the algorithm lies in the linear activation and optimization process of neurons, as follows:

The proposed 1D-CNN requires $({M + 1} )\cdot t$ multiplications to obtain the output vector of the convolution. As for DNN, the transition between the $l$ th layer and the $(l - 1)$ th layer requires ${n_l} \cdot {n_{l - 1}}$ multiplications, thus realizing the linear transformation. Besides, there are some simple algorithmic processes such as bias comparison, which can be neglected. Therefore, the computational complexity of the deep learning algorithm used in this scheme can be written as follows:

In general, this solution has acceptable computational complexity on the premise of obtaining better channel estimation accuracy, and the algorithm runs on the GPU, which has better computational efficiency.

## 4. Simulation results

In this section, we first optimize the parameters of the neural network model proposed in the previous section to obtain the optimal model parameters. Then we compare the channel estimation scheme proposed in this paper with other traditional effective channel estimation methods to evaluate the estimation performance from the perspective of BER and MSE. Finally, by changing the channel model, we make the channel parameters in the test part and the training part to be different, which is used to evaluate the robustness of DL-UVCE. This part of the computer simulation is based on the Linux operating system, and we use the Keras framework in the Python language to build the neural network model. The hyperparameter preset values for neural network training are shown in Table 2.

#### 4.1 DL-UVCE scheme performance and parameters adjustment analysis

This part mainly focuses on the adjustment of the model hyperparameters. According to the hyperparameter list, the batch size in this scheme is set to 50. Each time parameter update of deep learning is obtained from a set of data. The parameter optimization process is mainly completed by differential evolution algorithm. We simulate the MSE performance of the proposed DL-UVCE scheme from different perspectives: the number of hidden layers, and the number of neurons per hidden layer. In Fig. 7(a), we analyze the MSE performance of DL-UVCE by changing the number of hidden layers *L*. It can be seen that the MSE decreases with the increase of epochs. However, as the number of hidden layers increases, the MSE first decreases and then increases, i.e., the estimation performance first becomes better and then becomes worse. Figure 7(a) shows that the MSE is the minimum when $L = 5$, so the number of hidden layers is set to be 5 in this scheme.

Through the previous step, it is determined that the number of the hidden layer is set to 5, and then the number of neurons per hidden layer needs to be adjusted and optimized. Taking into account the computational complexity of the network training algorithm, the number of neurons per hidden layer is set to be the same, and it is defined as *n*. By changing *n*, the MSE performance of DL-UVCE is analyzed. As can be seen from Fig. 7(b), overall as the number of epochs increases, the MSE of channel estimation first decreases, then tends to flatten. However, as the number of neurons per hidden layer increases, the MSE gradually decreases, i.e., the estimation performance gets better and better. It should be noted that when *n* takes 10, 15, and 20, the corresponding MSE curves almost overlap. Therefore, considering the estimation performance and the training complexity of the neural network, we choose *n* to be 10.

To analyze the influence of the DE algorithm on the model convergence speed and global optimality, the proposed DL-UVCE is compared with the traditional DNN model optimized by the backpropagation algorithm, as shown in Fig. 8. Through two sets of different network structures for training, it can be seen that the convergence speed of DL-UVCE is faster than DNN with the same conditions, and the proposed scheme has better MSE performance during the entire training process.

#### 4.2 Comparative analysis

In this section, we compare the performance of the proposed algorithm DL-UVCE with LS algorithm, MMSE algorithm, and the traditional DNN model optimized by the backpropagation algorithm.

We first calculate the channel response coefficient estimated with different algorithms. By comparing with the real values, we can intuitively see the gap between the channel estimation results of different algorithms and the real values, as shown in Fig. 9. Compared with LS and MMSE algorithm, the DL-UVCE scheme is closer to the expected value, which can get better channel estimation result.

The communication experiments and simulations in this article are all carried out in OOK modulation mode. Taking the Mean-Square Error (MSE) and Bit Error Ratio (BER) as the measurement standard, we compare and analyze the performance of several channel estimation schemes, as shown in Fig. 10. It can be seen from Fig. 10(a) that the MSE as a whole gradually decreases with increasing the SNR, i.e., the estimation performance is getting better. Compared with LS and MMSE estimation, the performance of the DL-UVCE is significantly improved. Specifically, the MSE is reduced by 91.5% and 49.1%, respectively. Compared with the DNN scheme, the performance of DL-UVCE is improved obviously in the case of low SNR. And when the SNR increases, the MSE performance gradually approaches the same level. This is because the proportion of noise will affect the effect of the 1D convolution operation.

In Fig. 10(b), we compare and analyze the BER performance of several existing effective channel estimation algorithms. It can be seen that the BER of several estimation algorithms gradually decrease with the increase of the SNR. Compared with the LS estimation and MMSE estimation, the BER of DL-UVCE has been reduced by approximately 1 and 2 orders of magnitude, respectively. Furthermore, when the SNR is less than 15 dB, the BER performance of DL-UVCE has a certain improvement compared with the DNN scheme. The same is because the more noise, the more obvious the effect of the 1D convolution operation.

#### 4.3 Robustness analysis

In the above simulation experiment process, the channel statistical information used in the test phase and the training phase are all from the same channel model. However, in practical applications, there is a high probability that the channel environments in the training and testing phases will be different. So it is also necessary to verify the robustness of the proposed scheme, as shown in Fig. 11. We use the Monte Carlo simulation of the UV single scattering channel model and the weak atmospheric turbulence channel model for the test part of channel estimation. As can be seen from Fig. 11, the BER curves under these two channel models are close to the channel model used for the training of this scheme. Therefore, by changing the channel model used in the test phase, the corresponding BER levels are approximately equal, which proves that the proposed channel estimation scheme has good robustness.

## 5. Conclusions

Based on the model of wireless NLOS UV single scattering channel, we use 1D-CNN and DNN to design a channel estimator and then accurately estimate the channel statistical characteristics according to the optimal output results of the network, so as to compensate for the transmission attenuation at the receiving end. Through the network parameter adjustment and optimization process, the mapping relationship between the received signal and the channel response coefficient can be accurately learned, and the estimation result is close to the real channel. The proposed DL-UVCE scheme can accurately and quickly estimate the channel response coefficient, which can be used for subsequent signal detection and channel equalization in the wireless UV communication system. The simulation results indicate that the proposed DL-UVCE scheme has better channel estimation performance in contrast with the other traditional channel estimation methods. The neural network optimized by the DE algorithm has higher convergence speed and can stably realize channel estimation in the single scattering and the weak turbulence environments. So the deep learning channel estimator designed in this paper is suitable for the signal processing process of wireless UV communication. Future research will consider the possibility of applying deep learning to multiple-input multiple-output (MIMO) channel estimation and channel equalization of the wireless UV communication system.

## Funding

National Natural Science Foundation of China (61971345); Shaanxi Province Key R&D Program General Project (2021GY-044); Scientific Research Program of Education Department of Shaanxi Province (17-JF024); Technology Program of YuLin City (2019-145).

## Disclosures

The authors declare no conflicts of interest.

## Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

## References

**1. **H. Xiao, Y. Zuo, J. Wu, H. Guo, and J. Lin, “Non-line-of-sight ultraviolet single-scatter propagation model,” Opt. Express **19**(18), 17864–17875 (2011). [CrossRef]

**2. **R. Yuan and J. Ma, “Review of Ultraviolet Non-Line-of-Sight Communication,” China Commun **13**(6), 63–75 (2016). [CrossRef]

**3. **T. Shan, J. Ma, T. Wu, Z. Shen, and P. Su, “Single scattering turbulence model based on the division of effective scattering volume for ultraviolet communication,” Chin Opt Lett **18**(12), 120602 (2020). [CrossRef]

**4. **T. Cao, J. Song, and C. Pan, “Simplified Closed-Form Single-Scatter Path Loss Model of Non-Line-of-Sight Ultraviolet Communications in Noncoplanar Geometry,” IEEE J Quantum Elect **57**(2), 1–9 (2021). [CrossRef]

**5. **P. Song, C. Liu, T. Zhao, H. Guo, and J. Chen, “Research on pulse response characteristics of wireless ultraviolet communication in mobile scene,” Opt. Express **27**(8), 10670–10683 (2019). [CrossRef]

**6. **D. Han, X. Fan, K. Zhang, and R. Zhu, “Research on multiple-scattering channel with Monte Carlo model in UV atmosphere communication,” Appl. Opt **52**(22), 5516–5522 (2013). [CrossRef]

**7. **R. Yuan, J. Ma, P. Su, Y. Dong, and J. Cheng, “Monte-Carlo Integration Models for Multiple Scattering Based Optical Wireless Communication,” IEEE Trans. Wireless Commun **68**(1), 334–348 (2020). [CrossRef]

**8. **Z. Fang and J. Shi, “Least Square Channel Estimation for Two-Way Relay MIMO OFDM Systems,” ETRI. J **33**(5), 806–809 (2011). [CrossRef]

**9. **J. Fang, X. Li, H. Li, and F. Gao, “Low-Rank Covariance-Assisted Downlink Training and Channel Estimation for FDD Massive MIMO Systems,” IEEE Trans. Wireless Commun **16**(3), 1935–1947 (2017). [CrossRef]

**10. **S. Salari and F. Chan, “Joint CFO and Channel Estimation in OFDM Systems Using Sparse Bayesian Learning,” IEEE Commun. Lett **25**(1), 166–170 (2021). [CrossRef]

**11. **K. Wang, G. Chen, D. Zou, and Z. Xu, “Turbulence Channel Modeling and Non-Parametric Estimation for Optical Wireless Scattering Communication,” J. Lightwave Technol **35**(13), 2746–2756 (2017). [CrossRef]

**12. **D. Chen and J. Hui, “Parameter estimation of Gamma-Gamma fading channel in free space optical communication,” Opt. Commun **488**, 126830 (2021). [CrossRef]

**13. **C. Gong and Z. Xu, “Channel Estimation and Signal Detection for Optical Wireless Scattering Communication With Inter-Symbol Interference,” IEEE Trans. Wireless Commun **14**(10), 5326–5337 (2015). [CrossRef]

**14. **T. Zhao, L. Liu, L. Liu, and G. Zhang, “Differential evolution particle filtering channel estimation for non-line-of-sight wireless ultraviolet communication,” Opt. Commun **451**, 80–85 (2019). [CrossRef]

**15. **Z. Wei, W. Hu, D. Han, M. Zhang, B. Li, and C. Zhao, “Simultaneous channel estimation and signal detection in wireless ultraviolet communications combating inter-symbol-interference,” Opt. Express **26**(3), 3260–3270 (2018). [CrossRef]

**16. **T. Wang, C. Wen, H. Wang, F. Gao, T. Jiang, and S. Jin, “Deep Learning for Wireless Physical Layer: Opportunities and Challenges,” China Commun **14**(11), 92–111 (2017). [CrossRef]

**17. **Y. Lecun, Y. Bengio, and G. Hinton, “Deep learning,” Nature **521**(7553), 436–444 (2015). [CrossRef]

**18. **M. Soltani, V. Pourahmadi, A. Mirzaei, and H. Sheikhzadeh, “Deep Learning-Based Channel Estimation,” IEEE Commun Lett **23**(4), 652–655 (2019). [CrossRef]

**19. **Z. Mao and S. Yan, “Deep learning based channel estimation in fog radio access networks,” Chin Commun **16**(11), 16–28 (2019). [CrossRef]

**20. **T. Hu, Y. Huang, Q. Zhu, and Q. Wu, “Channel Estimation Enhancement with Generative Adversarial Networks,” IEEE Trans. Cogn Commun **7**(1), 145–156 (2021). [CrossRef]

**21. **J. Kang, C. Chun, and I. Kim, “Deep-Learning-Based Channel Estimation for Wireless Energy Transfer,” IEEE Commun Lett **22**(11), 2310–2313 (2018). [CrossRef]

**22. **H. Sun, X. Chen, Q. Shi, M. Hong, X. Fu, and N. D. Sidiropoulos, “Learning to Optimize: Training Deep Neural Networks for Interference Management,” IEEE Trans Signal Process **66**(20), 5438–5453 (2018). [CrossRef]

**23. **E. Balevi, A. Doshi, and J. Andrews, “Massive MIMO Channel Estimation with an Untrained Deep Neural Network,” IEEE Trans. Wireless Commun **19**(3), 2079–2090 (2020). [CrossRef]

**24. **X. Cheng, D. Liu, C. Wang, S. Yan, and Z. Zhu, “Deep Learning-Based Channel Estimation and Equalization Scheme for FBMC/OQAM Systems,” IEEE Wirel Commun Le **8**(3), 881–884 (2019). [CrossRef]

**25. **B. Wu, S. Yuan, P. Li, Z. Jing, S. Huang, and Y. Zhao, “Radar Emitter Signal Recognition Based on One-Dimensional Convolutional Neural Network with Attention Mechanism,” Sensors **20**(21), 6350 (2020). [CrossRef]

**26. **J. M. Kang, C. J. Chun, and I. M. Kim, “Deep Learning Based Channel Estimation for MIMO Systems with Received SNR Feedback,” IEEE Access **8**, 121162–121181 (2020). [CrossRef]

**27. **T. Wu, J. Ma, P. Su, R. Yuan, and J. Cheng, “Modeling of Short-Range Ultraviolet Communication Channel Based on Spherical Coordinate System,” IEEE Commun Lett **23**(2), 242–245 (2019). [CrossRef]

**28. **M. R. Luettgen, J. H. Shapiro, and D. M. Reilly, “Non-line-of-sight single-scatter propagation model,” J. Opt. Soc. Am. A **8**(12), 1964–1972 (1991). [CrossRef]

**29. **Y. Zuo, H. Xiao, J. Wu, Y Li, and J. Lin, “A single-scatter path loss model for non-line-of-sight ultraviolet channels,” Opt. Express **20**(9), 10359–10369 (2012). [CrossRef]

**30. **S. Gao, Y. Yu, Y. Wang, J. Wang, and M. Zhou, “Chaotic Local Search-Based Differential Evolution Algorithms for Optimization,” IEEE T Syst Man CY-S **51**(6), 3954–3967 (2021). [CrossRef]