1. Introduction

Visible light communication (VLC) is a short-range optical wireless communication technique that sends data with an intensity modulation of visible light at an ultrahigh-frequency band. VLC represents a possible alternative to the overloaded radio frequency (RF) communication technology for the sixth-generation wireless communication (6G) [1]. Compared with existing RF communication systems, VLC utilizes existing illumination systems and has the advantages of high efficiency, energy-saving, authorization-free, and harmless to the human body [1–3]. Light-emitting diode (LED) based communication has become a popular VLC communication method due to its fast-switching characteristics, high-quality luminescence, and high market share. LED-based VLC (LED-VLC) system is not only used for indoor downlink communication, but also for sensing [4], localization [5], and vehicular communication [6].

In LED-VLC systems, the signal suffers from intersymbol interference (ISI) and nonlinear interference due to the limited bandwidth of LEDs [7,8] and the nonlinear response of optoelectronic devices. Many works discuss the compensation methods for signal impairments, including pre-equalization, precoding, or receiver-side post-equalization [9–13]. On the transmitter side, digital pre-processing methods enhance signal resistance to channel impairments without additional noise enhancement [9–11]. The nonlinear post equalizers can effectively estimate and mitigate the nonlinear distortion by using the Volterra series [12] or multi-layer activations [13]. However, full compensation of the signal attenuation will increase the peak-to-average power ratio (PAPR), strengthen the signal nonlinearity, then bring more processing pressure on the receiver [10,11]. These digital signal processing (DSP) blocks consist of the traditional communication system. Although this structure is flexible to implement, it is unclear whether the individually optimized blocks can lead to the global optimization of the communication systems. Literature [14] recommends optimizing the entire system as an end-to-end (E2E) solution rather than individual modules to coordinate the optimization between the transmitter and receiver. The transmitter and receiver are constructed by two annual neural networks (ANNs), between which is a parametric transformation layer simulating the channel impairments. The gradient back-propagation (BP) helps jointly optimize the weights in the transceiver ANNs and combat the impairments. The E2E structure can be seen as autoencoder neural networks (AE), which are extended to software-defined radios [15,16] and optical fiber system [17]. In [15], the experimental performance of the autoencoder-based communication system is suboptimal due to the mismatch between the stochastic channel model used for training and the actual channel. In [16], the reinforcement learning over the actual channel enables approximately 1.3 dB BER gain compared with the 256-QAM baseline. The results in [15] and [16] reveal the importance of an accurate channel model in the actual communication experiments.

Recent works also investigate the E2E structure in VLC systems. In [18], a hybrid AE is used to solve the high PAPR problem of orthogonal frequency division multiplexing (OFDM) signal in the VLC system. By adaptively adjusting the mapping and demapping of constellations in the AE framework, the PAPR of OFDM signals is significantly reduced, alleviating the linearity requirements of transceiver devices. Recent studies [19,20,2,21] investigate the viability of using the AE framework to design dimmable VLC systems. A multi-colored VLC scenario is considered in [19] where the whole VLC communication system is modeled as an autoencoder. The E2E symbol recovery process includes the VLC transceiver pair and a channel layer characterizing the optical channel. In [20], an ANN transmitter of the OOK-modulated VLC is designed to generate the set of feasible OOK pulses. A multi-stage training strategy is adopted to anneal the continuous-valued encoder output into an OOK signal. But the ISI is not considered in the channel model. In [2], the authors propose a convolutional autoencoder structure for image sensor communication. The random rotation effect is taken into account during the training phase, allowing blind detection for the convolutional autoencoder with imperfect CSI at the receiver. A deep learning transceiver design with dimming support is studied in [21]. Multiple dimming constraints are used by trained the ANN transceiver through a dual formulation of the target function. The simulation results show that the ANN transceiver with the known nonlinear transfer function outperforms the baseline method in an ISI and nonlinearity-affected environment. In [22], the authors suggest deep learning-based E2E VLCnet to support flicker reduction and dimming. The flicker reducing activation unit limits the number of active nodes and the run length of the same brightness level for flicker reduction. The channel model refers to the channel impulse responses for VLC in [23] and considers the input-dependent noise originating from the shot noise. However, the aforementioned E2E VLC works are just validated in a simulation environment. Establishing a practical E2E LED-VLC system should consider more interference from the external drive circuit [24]. To simultaneously realize efficient lighting and high-speed communication, multiple devices including LED, bias-tee, photodetector, and amplifiers are commonly adopted to compose the physical channel of the LED-VLC system [8,24]. The combined influence of all these physical devices with low-pass or band-pass filtering effects creates strong low-frequency noise (LFN) in the received signal of the LED-VLC system [25,26]. The LFN strongly degenerates the signal-to-noise ratio (SNR) of the received signal in the low-frequency area, which causes the channel response in the low-frequency area to be inaccurately estimated. As a result, in actual VLC systems, the low-frequency area always contains no information [27,28]. It remains a challenge to design a reliable channel modeling method and a feasible deep learning E2E framework for practical LED-VLC systems to combat the LFN.

This work focuses on mapping the whole LED-VLC system as an ANN-based AE structure and introducing a novel channel modeling strategy to satisfy real LED-VLC practice. This is the first deep learning-based E2E framework applicable in a real VLC system to the best of our knowledge. The channel filtered signal, of the frequency band higher than the upper edge of the LFN-dominated region and lower than the cut-off frequency of the LED-VLC system, is down-converted to the baseband to train the channel model of our E2E framework. In this way, the data-driven modeling strategy is robust to the LFN and bandwidth limitation effect. We call the channel model, trained with the selected frequency band data, the in-band channel model (IBCM). With the IBCM, our AE can learn a representation robust to the in-band channel perturbations. The encoded message of the transmitter ANN should then be up-converted to the frequency range where the IBCM was trained for a real transmission. At the receiver, the received signal should be down-converted to the baseband for the receiver ANN to recover the transmitted message. Simulating and experimental results show the proposed deep learning-based LED-VLC system can efficiently combat the interference from the LFN. Compared with single-carrier pulse amplitude modulation (PAM), the proposed E2E framework achieves 1.875 Gbps transmission, 325 Mbps faster than the PAM-8 single carrier modulation scheme (SCM) under the 7% hard-decision forward error correction (HD-FEC) threshold (3.8E-3). The received signal can be near-errorless recovered by the HD-FEC with a 7% overhead if the BER before HD-FEC is lower than 3.8E-3 [29]. Moreover, the trained transceiver ANNs suggest more robust to ISI and nonlinearity than the PAM-8 SCM transmission scheme under varying drive voltage, signal amplitude, and baud rate.

2. Principle of deep learning-based autoencoder for LED-VLC system

2.1 Channel modeling strategy for LED-VLC system

The E2E system learns to optimize the transmitter and receiver ANNs. However, the channel blocks the gradient BP process, which updates the weights of ANNs, prohibiting the training of the transceiver neural network. To solve this problem, we use an ANN to emulate the channel response and connect the computation graph between the transceiver chain for the gradient to propagate. The ANN structure is motivated by the two tributaries ANN channel emulator proposed in [30]. Our channel model also uses two tributaries to separately learn the linear and nonlinear channel responses. The transmission equation of the entire ANN can be expressed as,

We first explain how the LFN influences the accuracy of the conventional data-driven channel model. As Fig. 1 shows, frequency fading, additive noise, and nonlinear distortions are the main interference in the LED-VLC channel. The signal with equal power spectral density (PSD), which is indicated by the Tx₁ in Fig. 1, will be transformed to the Rx₁ in Fig. 1 after the channel effect. The red area of the Rx₁ spectrum denotes the strongly polluted low SNR frequency components, due to the LFN and high-frequency bandwidth limitation effect. Once directly using the polluted data to train a network to emulate the channel response, the low SNR components disturb the weights updating direction and lead the ANN to spread the prediction error to all frequency components. However, if the signal Tx₁ is upconverted to a higher frequency band to get the Tx₂ signal, the LFN cannot influence the transmitted message.

 

Fig. 1. Schematic of the channel modeling strategy

Download Full Size | PDF

The frequency band, starting from the upper edge of the flicker-noise-dominated region and stopping at the cut-off frequency of the LED-VLC system, is depicted by the blue area in the spectrum of the received signal Rx₂ in Fig. 1. We choose this frequency band to transmit messages and call the transmitted messages the in-band signal. The in-band signal has high SNR, allowing less perturbed learning for the ANN. Therefore, as is shown in the lower yellow area in Fig. 1, the in-band signal is extracted and down-converted to the baseband to get the label data Rx₂’. The in-band signal of Tx₂ is also through the same process to get the input data Tx₂’. The time-domain input data Tx₂’ and label data Rx₂’ are then used to train the ANN. After applying this modeling strategy, the ANN can be trained to emulate the in-band channel effect. We call the trained ANN the IBCM. Then we fix the weights of the IBCM and embed the IBCM into our deep AE network. In the training process of IBAE, the fix-weights IBCM can apply the learned channel effect onto the transmitted signal and output the signal for the receiver ANN, while the weights of the transmitter and receiver are updated to combat the channel effect from the IBCM.

2.2 IBCM connected deep learning-based AE

With the trained IBCM, gradients BP can process from the receiver ANN to the transmitter ANN. Figure 2 depicts the AE structure consisting of a transmitter, an IBCM, and a receiver. This is an in-band autoencoder (IBAE) for it only learns to combat the in-band channel effect with the IBCM. In this section, the E2E AE framework for LED-VLC is described, as well as the training details for each module.

2.2.1 System overview

 

Fig. 2. The (a) training phase and (b) deployment phase of the proposed AE structure for LED-VLC.

Download Full Size | PDF

The structure of the framework is illustrated in Fig. 2(a). The random transmitted symbol m$\; \in \; ${1, …, M} is translated into an M×1 one-hot vector, ${\boldsymbol s}$, in which the m-th element is equal to 1. The transmitter learns to represent the one-hot vector with a fixed-length data sequence and sends the sequence to the IBCM while the receiver learns to reconstruct information, $\hat{{\boldsymbol s}}$, according to the received signal from the IBCM. The output $\hat{{\boldsymbol s}}$ of the receiver is a probability vector over the M possible classes, in which the largest probability item is trained to have the same index as the “1” item in the corresponding one-hot input ${\boldsymbol s}$ of the transmitter. Thus, the label of the receiver is the same as the input of the transmitter. Serving as the target function to evaluate the similarity between $\hat{{\boldsymbol s}}$ and ${\boldsymbol s}$, the cross-entropy loss is calculated at the receiver, which is defined as

As discussed in Section 2.1, the IBCM is trained in advance with experimental data before becoming part of the proposed IBAE network. In contrast, the training data set of IBAE, the one-hot vectors, are translated from the randomly generated transmit symbols m. These vectors are treated as both inputs and labels for the IBAE. The target of IBAE is to minimize the E2E cross-entropy loss when training the transceiver ANNs. Since we only need to take the randomly generated one-hot vector as the input and output label, the training of IBAE can be regarded as an unsupervised learning process. A similar expression can also be found in the literature [32]. We apply the modified stochastic gradient descent algorithm Adam [33] to train the IBAE. In the training process, Adam uses the cross-entropy loss to calculate the gradient of each network path and update the weights of IBAE.

In the deployment stage, the E2E communication performance is evaluated using the learned transmitter and receiver with a physical channel. As shown in Fig. 2(b), the random symbol sequence represented by one-hot vectors is fed into the transmitter ANN to generate the encoded signal (Tx’). A different seed of pseudo-random bit sequences (PRBS) is used in the deployment stage to avoid overfitting due to PRBS pattern recognition in the training stage. The signal Tx’ is then serial-to-parallel (SP) transformed, upconverted by a series of frequency-domain processing, 2× up-sampled, and parallel-to-serial (PS) transformed to get the transmitted signal (Tx) for the DAC. The received signal (Rx) is PS transformed, down-converted through the inverse frequency domain processing, 2× down-sampled, and SP transformed to obtain the to-be-decoded data (Rx’) for the receiver ANN. We use 30% of the Rx’ and one-hot vectors to fine-tune the receiver ANN to compensate for the unconsidered impairments in the IBCM. Figure 3 shows the typical training process when fine-tuning the receiver in our experimental and simulation environments. We find that the training can be stopped after 10 epochs in most cases, which is enough to demonstrate satisfactory convergence. The rest 70% of the data is used to test the performance of the fine-tuned receiver ANN. The output of the receiver ANN is converted to binary vectors and used to calculate the bit-error-ratio (BER) performance.

2.2.2 Training channel model

 

Fig. 3. The learning curve when fine-tuning the receiver ANN in our experimental and simulation environments.

Download Full Size | PDF

The channel model is trained with the in-band signal obtained in a real transmission experiment. We generate the baseband random signal Tx’ with 64 amplitude levels in a dense and evenly distributed. The baseband signal also has an equal PSD. The distribution and PSD characteristic of Tx’ promise a sufficient observation of the channel response to signals with different amplitudes and frequencies. Before transmitting, the signal Tx’ is up-converted to a higher frequency band to reduce the influence of the LFN. On the receiver side, the in-band signal is extracted and down-converted to produce the baseband signal Rx’. The normalized baseband Tx’ and Rx’ data are used to create the final training and label data for the ANN-based IBCM.

As is mentioned in Section 2.1, the IBCM uses two tributaries to learn the linear and nonlinear channel responses separately. One tributary uses ReLU as the activate function to fit the nonlinear part. The other tributary uses no activation function to fit the linear part. The output of the two tributaries is added together to get the output of the channel model. We use mean square error (MSE) as the loss function to train the IBCM. Then the IBCM is integrated into the autoencoder network as the bridge layer to propagate gradients and generate impairments on the signal. The weights of the IBCM will not be updated while training the autoencoder.

2.2.3 Training transmitter

At the transmitter ANN, the transmit message m ${\in} \; ${1, …, M} represented by a one-hot vector ${\boldsymbol s}$ is input to two subsequent hidden layers both with 4M neurons. The output layer has n neurons generating the data sequence for transmission. In other words, an M×1 one-hot vector is encoded to an n×1 data sequence by the transmitter ANN. Each one-hot vector carries log₂(M) bits of information. The parameter n determines the oversampling rate of the transmitted signal. Both M and n influence the data rate of the E2E system. Since the channel effect introduces ISI between consecutive samples, multiple transmitted sequences need to be considered to simulate realistic transmission. The output sequences of 2N+1 adjacent transmitters are concatenated by a flatten layer to form a sequence of (2N+1)·n samples. All these 2N+1 transmitter ANNs have identical hyperparameters. The tanh activation function is used in the hidden layers and the output layer to generate normalized encoded sequences for the input layer of the IBCM.

During the training, the weights of the transmitter and receiver are updated simultaneously with the Adam algorithm. The E2E cross-entropy loss is calculated at the autoencoder network’s output in (3), and the gradients are propagated back to the transmitter via the IBCM. The well-trained transmitter encoded the input messages into patterns that the receiver could easily recognize.

2.2.4 Training receiver

At the receiver ANN, the received input is the output signal of the IBCM. After propagation in two hidden layers both with 4M tanh nodes, the output layer gives the approximation $\hat{{\boldsymbol s}}$ with the softmax function. The approximation $\hat{{\boldsymbol s}}$ is a probability vector containing the largest probability item expected to have the same index as the “1” item in the corresponding one-hot input ${\boldsymbol s}$. The difference between ${\boldsymbol s}$ and $\hat{{\boldsymbol s}}$ is measured by the cross-entropy with (3). Then the difference triggers the BP to update the gradient of the receiver ANN. The well-trained receiver could combat the channel impairment and make accurate detection with the received signal.

3. Simulation

In this section, we provide the deployment details of the proposed E2E system in a simulation environment. Performance comparisons between the conventional AE and the IBAE are provided. No matter whether the LFN exists, the IBAE achieves better results than the conventional AE using a data-driven channel model.

3.1 Simulation setup

3.1.1 Implementation details

As mentioned in Section 2, the hyperparameters of the IBAE are summarized in Table 1. The weights of all ANNs are optimized by Adam and the training batch size is 256. We have used grid search for hyperparameter tuning on the parameters M, n, the input length, and the output length of the IBCM. According to the empirical setup in [17], the number of hidden nodes in the transceiver and IBCM is respectively set to be proportional to M and n for simplicity. Figure 4 summarizes the grid search results in the simulation environment. The IBCM input length is optimized to emulate the longest channel memory of the LED-VLC channel. The IBCM output length is also desired to approach the memory of the channel for the receiver to consider the ISI in the received signal. As shown in Fig. 4(a), the training loss of IBCM is lower with a shorter output length, while a shorter output length cannot provide enough information on ISI. Under an acceptable MSE loss, we select the optimal IBCM input and output pair, nearing (100, 33), in the circled-out area of Fig. 4(a). When training the transceiver ANNs of the IBAE, the input and output length of IBCM vary in the near-optimal range according to the value of n we choose. In Fig. 4(b), we can find the BER of the IBAE decreases as n increases, and increases as M decreases. Since parameter n determines the oversampling rate of the transmitted signal, it should be small enough to promise a high data rate. At the same time, M is required to be large enough to carry more information bits. We choose n = 4, and M = 64 to ensure the data rate required under the 7% HD-FEC threshold. The parameter N is chosen upon the principle that (2N+1)·n should approach the optimal length of the channel memory. Thus, we choose N = 12 to construct the IBCM input layer with (2N+1)·n =100 nodes to emulate enough channel memory. To be clear, we introduce the minor revision in Table 1 of our manuscript. The IBCM output length depends on the multiplication of parameters l and n. Parameter l is used to flexibly adjust the IBCM output length when parameter n had been optimized. The output length of the IBCM is set to 36 (i.e., l = 9) to fully consider the ISI in the received signal. The conventional AE has the same structure and parameters as the IBAE. The difference between the two types of AE is that their embedded channel model layers are trained in very different strategies. The IBCM is trained with the in-band signal while the conventional data-driven channel model is directly trained with the noise polluted received data.

3.1.2 Channel Types

 

Fig. 4. Parameters optimization results of the (a) IBCM and (b) transceiver ANNs of the IBAE in the simulation environment.

Download Full Size | PDF

Table 1. Structure and parameters of the IBAE

View Table

We consider two types of channels in the simulation. The 1-st type of channel is the simulated LED-VLC channel, in which the relationship between the transmitted signal X and the received signal Y_i can be expressed in frequency domain as

The LFN is included in the 1-st type of channel. The LFNs in semiconductors are found to be inversely proportional to f [26]. We generate the LFN in n_f by reshaping the PSD of an additive white Gaussian noise n_wgn. The frequency-domain n_f can be expressed as

In the 2-nd type of channel, only additive white Gaussian noise n_wgn is included. The performance of the conventional AE in the 2-nd type of channel severs as the baseline in the simulation. We send the baseband signal Tx’ and upconverted signal Tx to the two types of channels to generate the received data. Then we transform the received data to the time domain for the data-driven channel models.

3.2 Numerical results

Figure 5 illustrates the frequency domain emulated results and mismatch of the two data-driven channel models trained with different strategies at the SNR of 24 dB. The mismatch between each emulated spectrum and the received spectrum is calculated as

 

Fig. 5. Frequency response of channel emulator (a) trained with the LFN; (b) trained without the LFN in the simulation environment.

Download Full Size | PDF

After training the data-driven channel models, the conventional AE and the IBAE embed the conventional channel model and IBCM to their channel layers, respectively. Their weights in the transmitters and receivers are optimized in an unsupervised manner. The optimized transmitter and receiver are tested through the process of Fig. 2(b) with a new generated random symbol sequence. The performance of the optimized conventional AE and IBAE are summarized in Fig. 6. In the 2-nd type of channel, without the influence of the LFN, the conventional AE shows a similar performance to the IBAE as the SNR increases. The performance gap between them is because the conventional AE allocates excessive transmitted power in the high-frequency area where attenuation is severe after the channel. In the 1-st type of channel, the LFN causes misleading modeling of the channel response in the conventional AE. The transmitter and receiver are trained with the mismatch channel information. Thus, the BER performance of the conventional AE is far worse than the IBAE in all SNR conditions.

 

Fig. 6. BER performance of conventional AE and IBAE. (i) is the spectrum of the encoded signal from the conventional AE; (ii) is the spectrum of the encoded signal from the IBAE;

Download Full Size | PDF

4. Experiment

The training process of the IBAE has been introduced in Section 2. In this section, we will further explore the influence of the LFN on the performance of conventional AE and validate the superiority of the proposed IBAE in a real LED-VLC demonstration. We perform our experiment in a normal indoor lighting environment, under the influence of ambient light noise.

4.1 Experimental setup

The experimental setup of our LED-VLC system is shown in Fig. 7. We also exhibit the noise spectrum in the inset of Fig. 7 when turning on all devices and transmitting no signal. From the inset, we can find strong noise power in the low-frequency band. Thus, we should avoid the influence of the LFN when generating transmitted signals. According to the experimental setup in Fig. 7, the random symbol sequence is represented by one-hot vectors and fed into the transmitter ANN to generate the encoded baseband signal (Tx’). A different seed of PRBS is used in this deployment stage to avoid overfitting due to PRBS pattern recognition in the training stage. After an SP transformation, the signal is upconverted by a series of frequency-domain processing, 2× up-sampled, and PS transformed to obtain the transmitted signal (Tx). The Tx is amplified by the electrical amplifier (EA), loaded on a bias voltage, and transmitted by a blue LED. After 1-meter free-space transmission, the optical signal is then transformed into an electrical signal by a commercially available photodiode (PD). A transimpedance amplifier (TIA) amplifies and outputs the received signal (Rx) to the oscilloscope for offline processing. The Rx signal is SP transformed, down-converted, 2× down-sampled, and PS transformed to get the final baseband signal (Rx’) for the receiver ANN. To compensate for the unpredictable channel impairments in the IBCM, we employ 30% of the Rx’ and Tx data to fine-tune the receiver ANN. Ten epochs of training are sufficient to establish good convergence. The remaining 70% of data is used to evaluate the fine-tuned receiver ANN’s performance. The corresponding symbols of the receiver’s output probability vectors are converted to binary vectors and used to calculate the BER performance.

 

Fig. 7. The experimental setup of the E2E LED-VLC system. (i) is the noise spectrum when the LED turns on and transmits no signal.

Download Full Size | PDF

The detailed structure of the IBAE is provided in Table 1. We set the training batch size to 256 and use the Adam optimizer to update the weights of the IBAE. Figure 8 summarizes the grid search results in the experimental environment. To consider enough channel memory length, the optimal IBCM input and output pair should locate near (160, 34), which is circled out in Fig. 8(a). Similar to the analysis in simulation, we find that n = 4 and M = 64 is the optimal combination in our experiment to fulfill the data rate requirement. Then, we select N = 20 and l = 9 to construct the IBCM input and output layer with 164 nodes and 36 nodes to consider enough channel memory. With 2× up-sampling and 2 GHz sample rate of DAC, the bitrate of the E2E system can be calculated as log₂(M)×2/n/2 = 1.5 Gbps. Because the conventional AE and the IBAE have the same hyperparameter, they will achieve the same data rate regardless of BER performance.

 

Fig. 8. Parameters optimization results of the (a) IBCM and (b) transceiver ANNs of the IBAE in the experimental environment.

Download Full Size | PDF

In addition, the performance of the PAM-8 SCM scheme is used as the baseline, for the IBAE and PAM-8 SCM both transmits one-dimensional modulated signal. Literature [8] contains the detailed DSP procedure for the PAM-8 SCM scheme. At the transmitter side, the original PAM-8 symbols are up-sampled and filtered by a pulse-shaping filter to produce Nyquist PAM-8 signals. The spectral bandwidth and undesired out-of-band power leakage can be effectively suppressed by the pulse-shaping filter, which is a square-root raised cosine filter with a roll-off factor. The roll-off factor generally ranges from 0 to 1 [8]. A smaller roll-off factor leads to higher spectral efficiency, while a more serious ISI will be introduced. Figure 9(a) summarizes the BER results of the PAM-8 signal under different roll-off factors. We set the roll-off factor to 0.2 to ensure the performance. At the receiver side, a third-order Volterra nonlinear equalizer (VNE) is used to mitigate the linear and nonlinear distortions [34]. Figures 9(b) and (c) show the BER changes as we adjust the memory lengths of the 1-st, 2-nd, and 3-rd order Volterra kernels. We can find the optimal combination of the 1-st, 2-nd, and 3-rd order memory lengths as (23, 7, 3). Based on the above optimization results, we have tried our best to select the optimal parameters in the transmitter and receiver to ensure the PAM-8 SCM scheme reaches its best performance.

 

Fig. 9. Parameters optimization results of (a) the roll-off factor, (b) the 1-st, (c) 2-nd, and 3-rd order memory lengths of the Volterra kernels in the PAM-8 SCM scheme.

Download Full Size | PDF

4.2 Experimental result

4.2.1 Channel model

Before training the E2E LED-VLC system, we should first obtain the differentiable surrogate channels. The ANN channel models are all trained with the experimental data obtained in the LED-VLC platform shown in Fig. 7. Figure 10 shows the frequency domain emulated results and mismatch of the data-driven channel models trained with different strategies when the LED is biased at 3V with a 0.5 Vpp signal. Due to the severe LFN influence in the near-zero frequency band, using the received signal as the label of the neural network channel model directly will degenerate the prediction accuracy of the channel response. The maximum mismatch value of 158.1 occurs in the near-zero frequency band. By applying the in-band signal training strategy, the ANN channel model only learns the channel response from the high-SNR frequency band. The prediction error of the IBCM is reduced by 54.5%. The trend of the frequency fading in the emulated received signal is similar to that of the real received signal, which suggests that the IBCM has the potential to model the in-band channel response. In Fig. 11(a), the training and testing loss of the IBCM are also lower than that of the LFN-influenced channel models. In the next part, we will validate whether the IBCM helps the trained transmitter and receiver combat the impairment from the real LED-VLC channel.

4.2.2 Performance evaluation

 

Fig. 10. Frequency response of channel emulator (a) trained with the LFN; (b) trained without the LFN in the experimental environment.

Download Full Size | PDF

 

Fig. 11. Training and testing loss of the (a) IBCM and (b) IBAE under different signal conditions. The notation (A, B, C) means the bias, amplitude, and data rate of the signal are A V, B Vpp and C Gbps, respectively.

Download Full Size | PDF

In this section, we compare the performance of the proposed IBAE with conventional AE in the E2E LED-VLC transmission experiment. Before starting the performance evaluation, we first analyze the convergence of the IBAE. Figure 11 shows the training and testing loss of the IBCM and IBAE under different signal conditions. We can find that the training and testing loss of the IBAE and IBCM stop decreasing simultaneously. Thus, we can ensure the convergence of the IBAE and IBCM by stopping the training when the training loss no longer decreases. During the training phase, training the IBCM and IBAE for 20 epochs and 80 epochs is enough to converge, respectively. At the deployment phase, training the receiver ANN with 30% of the experimental data for 10 epochs is enough, which has been discussed at the end of Section 2.2.

Training the IBAE with the signal under 3.4 V bias voltage and 0.5 Vpp, Fig. 12(a) shows the spectrum of the encode baseband signal Tx’, upconverted transmitted signal Tx, and the received signal Rx. The LFN, which is located in the near-zero frequency band, can be observed in the received signal. The in-band signal avoids the influence of the LFN by the upconvert process. The upconverted signal Tx appears a chaotic distribution in Fig. 12(c) compared to the baseband signal in Fig. 12(b). The 64 types of the encoded data sequences are shown in Fig. 12(d). Four pulses with different amplitudes and phases form the distinguishable pattern of each encoded sequence.

 

Fig. 12. (a) Spectrum of the signal Tx’, Tx, and Rx; Constellation of the signal (b) Tx’ and (c) Tx; (d) The encoded data sequences of all the 64 symbols

Download Full Size | PDF

We then test the BER of the E2E schemes and the SCM scheme by adjusting the bias voltage and amplitude of the signal transmitted by the LED. The transmission bitrates of the three schemes are both 1.5 Gbps. The results are summarized in Fig. 13(a)(b). The IBAE achieves a significantly lower BER than the other two schemes. Owing to the inaccurate estimation of the channel response, the conventional AE achieves the worst performance in all conditions. In Fig. 13(a), the BER decreases as the bias voltage and signal amplitude increase until an optimal value is reached. This is because the saturation of the PD response will introduce nonlinearity in the received signal if the bias is too large. The BER of the IBAE reaches the lowest at 3.4 V bias, when the SCM scheme’s BER has already exceeded the 7% HD-FEC threshold, indicating that the IBAE scheme is superior in terms of nonlinearity resistance. When the signal amplitude is too large, the EA will get saturated and generate nonlinearity. In Fig. 13(b), the BER also reaches the lowest value in the middle of the Vpp increasing process. At the amplitude of 0.3 Vpp, the IBAE achieves the best BER of 5.5E-4, far below the 7% HD-FEC threshold. In contrast, the BER of the SCM scheme is below the 7% HD-FEC threshold in a lower range of Vpp.

 

Fig. 13. The BER performance of the three schemes under different (a) bias voltages, (b) signal amplitudes, and (c) bitrates

Download Full Size | PDF

After investigating the BER performance in Fig. 13(a)(b), we fixed the bias and amplitude of each scheme to their optimal values. Figure 13 exhibits the performance of the three schemes under different bitrates, in which we can find a 0.325 Gbps bitrate improvement of the IBAE compared to the SCM scheme at the 7% HD-FEC threshold. The IBAE achieves the highest transmission speed of 1.875 Gbps in the real LED-VLC platform.

4.2.3 Robustness of the IBAE

The IBCM and the IBAE are repeatedly trained once the signal condition changes in the above experiment. This part will discuss the robustness of the IBAE by testing a fixed IBAE in varying signal conditions. The weights of the transmitter ANN and the IBCM will not change while the receiver ANN needs to fine-tune for 10 epochs in every signal condition. We first train the IBCM and IBAE when the transmitted signal has an amplitude of 0.5 Vpp and a bias of 3.4 V. Then we summarize the BERs of the fixed trained IBAE under different bias voltages in Fig. 14(a). The performance of the fixed trained IBAE is very similar to the performance of the IBAE repeatedly trained under every bias voltage. Then we change the signal amplitude and obtain the BERs of the fixed trained IBAE in Fig. 14(b). As the amplitude increases, the fixed IBAE has maintained a similar performance to the repeatedly trained IBAE. Finally, we analyze the performance of the fixed trained IBAE by increasing the transmission speed in Fig. 14(c). The marginal difference between the blue curve and the grey curve suggests that the fixed trained IBAE can adapt to different signal conditions once fine-tuning the receiver ANN for a few training epochs.

 

Fig. 14. The performance of the fixed trained IBAE under different (a) bias voltages, (b) signal amplitudes, and (c) bitrates

Download Full Size | PDF

As the IBAE is robust to the bias and amplitude changes, we further investigate the dimming support of the proposed IBAE since users in practice may change the illumination level of the indoor environment [22]. In our E2E framework, the dimming control method we use belongs to the analog dimming (AD) technique, which is the simplest approach by adjusting the bias (or current) of the light source [35,36]. The equally spaced PAM signal is commonly used in VLC with dimming support [35–37]. In Fig. 13(a) and Fig. 14(a), we have shown the performances of our E2E scheme and the PAM-8 scheme under different biases. To clearly illustrate the LED brightness concerning the bias voltage, we use an optical power meter to measure the brightness of the LED under different biases. Figure 15(a) shows the relationship between the received optical power and the bias voltage when the 0.5 Vpp signal is transmitted by the LED. The LED has the maximum brightness as the bias voltage reaches 3.6 V. Since the IBAE achieves transmission under the 7% HD-FEC threshold from 2.8 V to 3.6 V bias in Fig. 13(a) and Fig. 14(a), it supports over 6.26 dB brightness change, covering 76.3% brightness variation range. In contrast, the PAM-8 SCM scheme only achieves a 33.2% brightness variation range under the 7% HD-FEC threshold. Moreover, in Fig. Figure 15(b) we find less than 0.03 dB brightness fluctuation when the 0.5 Vpp signal is transmitted, 0.6% of the mean power. As a proof of concept, the results in Fig. 15 suggest the proposed IBAE has the potential to support dimming control.

 

Fig. 15. The received optical power versus (a) bias voltage and (b) signal amplitude; The front face of the optical power meter when the LED is biased at (c) 3.6 V and (d) 2.8 V.

Download Full Size | PDF

5. Conclusion

In this work, we investigate the E2E deep learning-based LED-VLC communication system in the experimental environment. The LFN induced by multiple devices severely influences the signal quality in the real LED-VLC system, which restricts the data-driven E2E method to be implemented in the practical situation. To solve this problem, we proposed a novel channel modeling strategy to bypass the influence of the LFN in the LED-VLC system. By upconverting the baseband signal before the transmission and down-converting the in-band signal to the baseband at the receiver side, we can obtain the high SNR training data for the ANN-based IBCM. Thus, the IBAE embedded with the IBCM can be trained to combat the precise-estimated channel impairment while avoiding performance degeneration due to the influence of the strong LFN. The IBAE achieves the highest bitrate of 1.875 Gbps under the 7% HD-FEC threshold, 0.325 Gbps faster than the PAM-8 SCM scheme. Moreover, the IBAE is robust to bias, amplitude, and bitrate changes, which reveals its potential to adapt to dynamic signal conditions and support dimming control in the indoor environment.