It has been widely noticed that visible light communication (VLC) has the advantages of anti-electromagnetic interference, abundant spectrum resources, and low cost. This paper introduces an efficient asymmetrically clipped optical orthogonal frequency division multiplexing (ACO-OFDM) modulation method to accommodate visible light communication systems using orthogonal frequency division multiplexing (OFDM) with positive real number constraints. However, the signal is easily distorted by multi-path interference of the channel during transmission, which results in poor communication quality of the VLC system. The VLC system mainly recovers the signal by obtaining the channel state information, and how to provide accurate feedback on the high-dimensional state information is particularly important to improve the communication quality of the VLC system. The commonly employed channel estimation method is based on the guide frequency assisted method. Among the existing methods, least squares (LS) method treats the channel as an ideal one and ignores its noise for channel estimation. Despite low complexity, the estimation accuracy is not high. Minimum mean square error (MMSE) is utilized for channel estimation due to the assumption that the second-order statistical information of the channel is known and adopted for channel estimation, but the estimation accuracy increases with the complexity. Deep learning provides a new solution for accurate feedback of channel state information, but few deep learning methods for channel estimation in ACO-OFDM systems have been reported. To improve the problems of low estimation accuracy and efficiency, and a large number of leads in channel estimation of ACO-OFDM systems, this paper proposes a deep neural network channel estimation method to improve the communication quality of the system.

A deep neural network (DNN)-based channel estimation method is proposed for the channel estimation of the ACO-OFDM visible light communication system. Within this scheme, an end-to-end approach is applied to implicitly estimate channel state information and directly recover distorted signals. The DNN network is divided into an offline training phase and an online implementation phase. In the offline training phase, the fast Fourier-transformed received signal at the receiver is leveraged as the input of the DNN network, and the original transmitter signal is the ideal output of the network. The mean square error (MSE) is adopted as the loss function of the network to minimize the MSE between the network output and the ideal output. The well-trained DNN model is then implemented in the ACO-OFDM system for online deployment. In addition, with an aim to accelerate the DNN network training and ensure that the model can make accurate predictions on the test data, the DNN network is optimized through gradient centralization (GC), which is embedded in the optimizer for processing and acts on the gradient of the weight vector to constrain the loss function. The estimation accuracy of the DNN-based ACO-OFDM channel estimation method is further improved to enhance the communication performance of the system.

The effectiveness of the proposed method is verified by the relationship between the performance indexes of bit error rate (BER) and MSE and signal noise ratio (SNR). The conventional methods of least squares (LS) and MMSE are selected as the comparison algorithms. The parameters of the system are set as shown in Tables 1 and 2. The convergence speed and MSE of the DNN network after the introduction of the gradient concentration (GC) method are better than those of the DNN network using the classical gradient descent method (Fig. 5). When channel estimation is performed at 8 pilots and 64 pilots, the method in this paper shows the best BER performance compared with other methods. At 8 pilots, the LS and MMSE methods are no longer effective for channel estimation. At 64 pilots and BER of 10^-1, the proposed method improves the SNR gain by 10 dB and 4.2 dB compared to LS and MMSE (Fig. 6). The proposed method also exhibits the best MSE performance at different pilots, which indicates that the proposed method is robust to the pilots and can obtain better estimation performance at fewer pilots, thus improving the spectrum utilization (Fig. 7). The robustness of the pilots is analyzed, and the BER and MSE performances of the proposed method are not affected by the pilots (Fig. 8). Cyclic prefix (CP) is important for OFDM systems, but the CP inclusion in the system reduces the data transmission rate and wastes time and efforts. The BER performance of the proposed method is not affected when analyzing with/without CP, but the conventional method can no longer work properly without CP. The proposed method improves the SNR gain by 19.1 dB and 11.9 dB at a BER of 0.266 compared to the LS and MMSE methods respectively (Fig. 9). This shows that the proposed method does not significantly affect the channel estimation by removing CP and reduces the dependence of inter-symbol interference and inter-carrier interference on CP. The gradient centralization optimized DNN method outperforms the DNN method with the classical gradient descent method in terms of BER and MSE performances.

To address the problems of low accuracy and inefficient channel estimation facing traditional methods, this paper proposes a DNN-based channel estimation method. The simulation results show that the BER and MSE performances of this method are significantly improved compared with the traditional methods of LS and MMSE. The method is applicable to the channel estimation of the visible light communication system and is important to improve the performance of the visible light communication system. Additionally, it still works well under less guide frequency and removing. The proposed method has better spectral utilization and stronger robustness than the DNN model optimized by the classical gradient descent algorithm, and the DNN model optimized by gradient centralization has higher convergence speed and better MSE performance than the DNN model optimized by the classical gradient descent algorithm. In summary, the proposed method provides an effective channel estimation reference scheme for visual light communication systems to achieve high spectrum utilization and reliability.