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Abstract
This paper proposes a novel two tributaries heterogeneous neural network (TTHnet) based channel emulator, which is suitable for both estimating single-carrier and multi-carrier modulated channels of underwater visible light communication (UVLC). Compared to traditional neural networks, the TTHnet channel emulator has only 1932 trainable parameters, which is only 0.8% of multilayer perceptron (MLP) based channel emulator and 1% of a convolutional neural network (CNN) based channel emulator. Furthermore, it provides a more accurate estimation of the UVLC channel and greater interpretability than MLP and CNN. The experiments in this paper use carrier-less amplitude/phase modulation (CAP) and discrete multi-tone modulation (DMT) as representative examples of single-carrier and multi-carrier modulation, respectively. The experiment proves that the TTHnet based channel emulator could effectively emulate the channel response of UVLC systems both in time and frequency domain. To the best of our knowledge, this is the first time that the single-carrier and multi-carrier modulated UVLC channel is emulated by the deep neural networks based channel emulator, which will effectively accelerate the research progress of UVLC and reduce research costs of UVLC systems.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
In recent years, high-speed underwater wireless communication has received continuous growth of attention, which contributes to the development of submarine oil exploration, seabed geomorphology, and seawater quality testing [1–3]. Although acoustic communication has been widely used underwater, its limited bandwidth cannot meet up with the increasing demand for high bit-rate [4,5]. Light emitting diode (LED) based and laser diode based visible light communication systems can provide both long-distance and high bit-rate transmission for underwater wireless communication, which is in the interests of relevant companies [6–9]. In order to design a system that is stable and wideband for a practical UVLC channel during the simulation process, it is essential to emulate the UVLC channel. However, the Ocean is a complex system composed of creatures and non-organisms [10]. Different marine environmental parameters, particulate matter, and solute have complex characteristics for light absorption and scattering diffraction at different wavelengths [11]. As a consequence, the complicated UVLC channel leads to great difficulties for channel estimation. Especially in high-order modulated CAP and DMT UVLC system, it is difficult to emulate high nonlinear distorted UVLC channel, due to various factors such as impulse response of electronic devices, scattering of water and turbulence underwater.
The channel of static UVLC system emulated by Mohammed Elamassie, Chadi Gabriel, and Xu Ma could be used as a reference to set the system parameters that guarantee the best and most stable system performance [4,12,13]. Since the real underwater channel is turbulent, H. M. Oubei and E. Zedini et al. modeled the UVLC channel with temperature induced weak turbulence [14]. Recently, A. Huang demonstrated a UVLC channel model that takes both temperature and pressure induced week turbulence in to account [15]. However, the above researches on channel estimation focus only on different kinds of path loss of light propagation in water. In fact, in the process of channel estimation, it is essential to take characteristics, such as impulse response of electrical amplifiers, bias current and nonlinear response of LEDs, and modulation formats into account. To be specific, the same signals with different modulation format, such as signal-carrier and multi-carrier, will experience different distortion. To be specific, due to the limited dynamic range of led and the nonlinear response of the drive current and voltage of LED, systems with higher PAPR have higher distortion. Multi-carrier modulations such as OFDM and DMT have higher PAPR than single carrier modulations such as PAM and CAP. Consequently, signal-UVLC channel model that takes both temperature and pressure induced week turbulence into account suffer less nonlinear distortion than multi-carrier modulated systems [16,17]. Changes in bias current of LED and peak-to-peak voltage (Vpp) of signals also cause changes in the channel impulse response. Therefore, the estimation of a complete UVLC channel is a complicated process, including the channel response of the electronic devices and the modulation of the signal, which is more than just path loss of light. In the field of wireless communication, early efforts proved that DNN, as an artificial intelligence algorithm, could be used for channel estimation [18–20].
The proposed TTHnet based channel emulator has been proven to be useful for estimating both single-carrier and multi-carrier UVLC channels. We have discussed the design and optimization process of TTHnet based channel emulator in detail. Furthermore, in comparison with MLP and CNN based channel emulators, we experimentally proved that TTHnet based channel emulator not only provides a better estimation of the UVLC channel but also has a simpler network structure and less computational complexity. The innovations of this paper are summarized as follow:
- a) We propose a novel self-designed the TTHnet based channel emulator, which is the first application of the neural network with a two-tributary structure in the field of channel estimation.
- b) The TTHnet based channel emulator could precisely emulate both single carrier and multi-carrier UVLC channels.
- c) The experiment proved that the TTHnet based channel emulator emulated channel is closer to real channel than CNN and MLP based channel emulator.
Finally, we experimentally verified the robustness of the TTHnet based channel emulator for UVCL systems with different modulation formats (single-carrier modulation and multi-carrier modulation), various bias currents, and various Vpps.
2. Principle
Through the study of traditional neural networks, we notice that traditional neural networks are not only difficult to emulate the channel response of UVLC system very accurately but also occupy huge computing resources. This is because the research on neural networks mainly focuses on the fields of computer vision and natural language processing. However, scientists have very limited research on neural networks in channel estimation. The effect obtained by borrowing neural networks applied to other fields directly in the field of channel estimation is not satisfactory. Therefore, we propose TTHnet that includes prior knowledge in the field of channel estimation for VLC channel estimation, which provides high-precision channel estimation with low computational complexity.
Figure 1 describes the forward propagation process of TTHnet in detail. Before the transmitted signal is input to the TTHnet based channel emulator, it needs to be normalized to ensure the robustness of the channel emulator. The normalization function utilized in our TTHnet is expressed as,
where x indicates the transmitted signal.Then, the serial transmitted signals are converted into parallel signals before they are input into the input layer of TTHnet. It is worth noting that in order to simplify the flow chart of the forward propagation process, we set the length of the sliding window to 3. We have learned through experiments that in the current UVLC system, 191 is the best value for the sliding window. The values of all hyperparameters in TTHnet will be provided in Fig. 2.
After that, the signal is sent to two different tributaries. In the 1st tributary, a CNN with one convolution layer and one dense layer is utilized to emulate the linear distortion in the signal bandwidth. In the 2nd tributary, hollow MLP with a hollow operator layer and two dense layers is applied to emulate the nonlinear distortion out of the signal bandwidth. In other words, the output of 2nd tributary Y2 will act as a nonlinear correction for the output of 1st tributary Y1. Finally, in order to imitate the real time-varying UVLC channel, additive white Gaussian noise (AWGN) is added on the output signal of the whole TTHnet, . The transmission equation of the entire network can be expressed as,
where, and are trainable weights and biases, respectively; is the emulated signal; represents the operation to remove the center feature (the 96th feature in our case); could be expressed as [21],The represents the operation to remove the center feature, which ensures that 2nd tributary is focused on estimating out-of-band nonlinear distortion, which is given by,
where is an odd number represents the length of the slide window.After experiencing the forward propagation, we use the minimum mean square error (MSE) as the loss function to calculate the difference between the distributions of received signals and emulated signals. The weight and can be obtained by the following equation,
where, is the received signal of the transmitted signal, and is the corresponding emulated signal; is the number of all signals in a batch.
In order to make the experiment more informative, we compare TTHnet with traditional CNN and MLP in the experiment. The structures and hyperparameters of TTHnet, CNN and MLP are shown in Fig. 2. Where, FS, AF and FN are abbreviations of the filter size, active function and number of filters, respectively. In terms of the TTHnet, we input 191 features into TTHnet and pass them to the 1st tributary and 2nd tributary at the same time. In the 1st tributary, we convolve the features with a filter with 32 elements. Then, the output of the convolutional layer is passed through a fully connected layer to generate one scalar output. In the 2nd tributary, the hollow operation will eliminate the center feature (the 96th feature). Then, the output of the hollow layer will go through two hidden layers, the first hidden layer has 9 nodes, using tanh as the activation function; the second hidden layer has one node, using tanh as the activation function. The output of the 2nd hidden layer is a scalar. Finally, the output from the two tributaries is added to the appropriate additive white Gaussian noise (AWGN) to obtain the emulated signal. The trainable parameters of TTHnet are 1932. The CNN and MLP utilized for comparison have 194945 and 251491 parameters, respectively. In other words, TTHnet's space complexity is only 1% of CNN and 0.8% of MLP. The structure and trainable parameters of MLP are learned from the previous study in [18]. Since there is no research on CNN in the field of channel estimation, we designed a CNN based channel emulator with better performance than MLP based channel emulator. Since the number of trainable parameters directly determines the computational complexity of the model, the proposed TTHnet consumes least computing resource.
3. Experimental setup
According to the experimental setup in Fig. 3, the CAP64 modulated or DMT64 modulated signals are transmitted into an arbitrary waveform generator (AWG) as the transmitted signals. Meanwhile, every 191 adjacent signals are input to the neural network as features. In terms of real underwater channel, the signal output from the AWG is equalized, amplified and coupled with a DC current through the Bias Tee, which will be used to drive the blue LED. Then, LED converts electrical signals into optical signals that will be collimated into parallel light by a convex lens. Then, the light passes through the 1.2m water tank that which is filled with 3% salt water at a water temperature of 25 degrees Celsius. At the receiving end, we use a convex lens to converge the parallel light signals onto the PIN that could convert optical signals into electrical signals. Then, we use an oscilloscope (OSC) to sample the electrical signal to obtain the corresponding digital signal. The synchronized signals are sent to TTHnet as labels. Meanwhile, the synchronized signals are sent to the corresponding demodulation algorithm (offline processing) as received signals. The offline processing will demodulate the received signals and calculate the bit error rate (BER). Due to limited experimental conditions, we have not yet estimated the UVLC channel with turbulence. In the next study, we will emulate the UVLC channel affected by turbulence based on neural network algorithms.
In terms of the emulated UVLC channel, features X and the corresponding labels are combined and utilized as the training set in the backpropagation process. The backpropagation process will find out the best and that minimize the MSE according to Function (5). Then, and will determine the trained neural network based channel emulator. In order to prevent over-fitting and improve the robustness of the neural network, we used new independent signals to test the trained neural network based channel emulator (calculation of MSE and BER). In brief, the real UVLC channel, the backpropagation process and the testing (channel estimating) are represented by black, red, green arrows, respectively.
4. Experimental results
Since the AWG normalizes the signal with the maximum absolute value, we assume that maximum absolute normalization function (1) can bring the best performance and robustness to the channel emulator. We experimentally compare function (1) with other normalized equations, such as,
Max-Min normalization [22],
and Z-Score normalization [23],
According to Fig. 4(a), in comparison with other normalization base estimation, the emulated spectrum based on Max-Abs is a more accurate estimation of the real received spectrum. However, the differences between different spectra cannot be visually observed. Therefore, the absolute mismatch between each emulated spectrum and the received spectrum is calculated as follow,
Fig. 4 (a) Comparison among of received spectrum, Max-Abs based emulated spectrum, Max-Min normalization based emulated spectrum and Z-Score normalization based emulated spectrum. (b) Corresponding spectrum mismatch between emulated spectrums and received spectrum.
which is shown in Fig. 4(b). In the frequency domain, the mismatch between signals predicted by Max-Abs based neural network emulator and the real received signals is much smaller than other emulators. The average mismatch of Max-Abs, Max-Min and Z-Score are 0.83, 1.90 and 0.95, respectively. Therefore, Max-Abs is chosen as the normalization algorithm in our neural network UVLC channel emulator.
Figure 5(a) provides the structural designing process of our proposed TTHnet. Firstly, we design a linear convolution network that is the 1st tributary of TTHnet to emulate inner band distortion. The 1st tributary of TTHnet could be expressed as,
Fig. 5 (a) Comparison among received spectrum, spectrum emulated by 1st tributary based channel emulator, spectrum emulated by TTHnet based channel emulator without hollow layer and spectrum emulated by TTHnet based channel emulator. (b) The corresponding mismatch between emulated spectrums and received spectrum.
In comparison with the black curve and the red curve in Fig. 5(a), the 1st tributary of TTHnet can precisely emulate the spectrum response of inner band signals. However, the 1st tributary of TTHnet does not have the ability to emulate the out-of-band channel. Therefore, we added an MLP based tributary as the 2nd tributary, which could equip our network with the ability to emulate the out-of-band channel. The TTHnet without hollow layer could be expressed as,
According to the blue curve in Fig. 5(a), although the TTHnet without hollow layer can probably emulate the out-of-band noise of the received signal, the emulated spectrum is very different from the spectrum response of the real channel. Since the 1st tributary of TTHnet without hollow layer can emulate inner band channel spectrum response of the signal, and the 2nd tributary of TTHnet without hollow layer can emulate both inner band and out-of-band channel spectrum response, the function of the two tributaries overlaps in the estimation of inner band channel spectrum response. Consequently, it is possible for the 2nd tributary of TTHnet without hollow layer to waste resources (trainable parameters) on the estimating inner channel spectrum response rather than focusing on the estimating out-of-band channel spectrum response. Therefore, we added a hollow layer to the second tributary. The hollow layer ensures that the 2nd tributary ignores the center signal (the 96th feature in our case) during the forward propagation process, which will greatly reduce the ability of the 2nd tributary to emulate the inner band channel spectrum response of the UVLC channel. Therefore, 2nd tributary will pay more attention to estimating the out-of-band channel spectrum response of the UVLC channel.
According to the experimental results in Fig. 5(a), the frequency response of the signal emulated by TTHnet is closer to the real received signal. According to the spectrum mismatch curve in Fig. 5(b), the average mismatch of the 1st tributary of TTHnet, the TTHnet without hollow layer and the TTHnet are 25.03, 2.02 and 0.77, respectively. The hollow layer can reduce the spectrum mismatch of the TTHnet channel emulator without hollow layer by 62%. At this point, we have completed the design and optimization of the TTHnet channel emulator.
Sufficient training allows the neural network based channel emulators to converge, resulting in an optimal and stable performance of the neural network model. Therefore, it is necessary to determine the minimum epochs needed to make the proposed TTHnet converge. Figure 6 shows the mismatch between the BER and spectrum of the signals emulated by the three neural network based channel emulators and the BER and spectrum of practically received signals. The BER mismatch could be expressed as,
Fig. 6 BER mismatch and Spectrum mismatch of different neural network channel emulators on the validation set after 30-epochs training. (a) BER mismatch on CAP modulated signals. (b) Spectrum mismatch on CAP modulated signals. (c) BER mismatch on DMT modulated signals. (d) Spectrum mismatch on DMT modulated signals.
It can be seen that during the training process, whether it is a CAP modulation system or a DMT modulation system, the rate of convergence of TTHnet is slower than that of MLP and CNN. However, the performance of TTHnet after convergence is much better than MLP and CNN. In terms of CAP64 UVLC system, the BER mismatch of TTHnet based channel emulator is only 13% of MLP based channel emulator and 17% of CNN based channel emulator. After 30-epochs training, the average spectrum mismatch of MLP, CNN and TTHnet are 2.35, 1.92 and 0.85, respectively. In terms of DMT64 UVLC system, the BER mismatch of TTHnet based channel emulator is only 13% of MLP based channel emulator and 1% of CNN based channel emulator. After 30-epochs training, the average spectrum mismatch of MLP, CNN and TTHnet are 4.48, 1.40 and 0.74, respectively. Based on the analysis above, whether for single carrier or multi-carrier modulated UVLC system, the BER and spectrum of received signals emulated by THHnet based channel emulator are closest to the real received signals.
In order to verify the universality of the TTHnet emulator for UVLC channels in different states, we experimentally compared the BER performance between CAP64 transmit signal and DMT64 transmit signal after real UVLC channel and TTHnet estimation UVLC channel under different bias currents in Fig. 7(a). In Fig. 3, bias currents (DC) acts as the carrier for the transmitted signal and drives the LED, which is one of the key factor leading to nonlinear distortion at the transmitter end. In terms of CAP64, the predicted signal has a maximum difference of BER from the true received signal by 0.5 dB. When the modulation format of the transmitted signal is DMT64, the maximum error of BER on different bias currents is 0.35dB. Furthermore, when the bias current changes, the emulated signal has the same trend as the BER of the real received signal. Since the BER of the signals emulated by TTHnet channel emulator is not much different from the BER of the real received signal, and they have the same trend as the current changes, TTHnet channel emulator is universally applicable to changes in bias current.
Fig. 7 (a) Comparison of BER between CAP64 transmit signal and DMT64 transmit signal after real UVLC channel and TTHnet emulated UVLC channel under different bias currents. (b) Comparison of BER between CAP64 transmit signal and DMT64 transmit signal after real UVLC channel and TTHnet estimation UVLC channel under different Vpp.
Another important factor that causes nonlinear distortion in the UVLC channel is Vpp. In Fig. 7(b), experiments are performed by replacing various bias currents with various Vpp. With different Vpp, the maximum difference of BER for CAP64 and DMT 64 modulated signals are 0.29dB and 0.17dB on the validation set, respectively. Therefore, whether it is a bias current changing or a Vpp-changing UVLC channel, the signal distortion caused by TTHnet channel emulator is similar to the real UVLC channel.
Generally, as the communication rate increases, the ISI and nonlinear distortion of the UVLC system will also increase. To verify the universality of TTHnet channel emulator for UVLC channels at various bitrates, BER-Bitrate curves are measured in Fig. 8. In terms of CAP modulated UVLC system, TTHnet channel emulator trained with CAP modulated training set could accurately emulate the received CAP modulated signals, which is described in emulated CAP UVLC curve. In the DMT modulated UVLC system the performance of TTHnet channel emulator is the same as in the CAP modulated UVLC system.
Fig. 8 Comparison of the BER of the actual received signal with the bit error rate of the TTHnet emulated signal at different bitrates.
5. Conclusion
In this paper, we propose a novel deep learning algorithm named TTHnet for UVLC channel estimation. TTHnet based channel emulator has lower complexity and better performance than traditional neural networks based channel emulators, such as MLP and CNN. Meanwhile, we proved that Max-Abs is a proper algorithm to normalize signals before signals are input to artificial neural network based channel emulator. In comparison with TTHnet without hollow layer, the proposed hollow layer could reduce the spectrum mismatch of predicted signals by 62%. Compared with MLP and CNN based channel emulator, the TTHnet based channel emulator has much better performance in terms of BER and spectrum mismatch.Meanwhile, TTHnet based channel emulator with 1932 trainable parameters has only 0.85dB average spectrum mismatch, which is only 36% of MLP based channel emulator with 251,491 parameters and 44% of CNN based channel emulator with 194,945 parameters. The experimental results demonstrate the universality of TTHnet based channel emulator for UVLC channels with varying bias current, varying Vpp, and varying bitrate. Finally, the results of the experiments prove that the proposed TTHnet is a potential channel emulator for UVLC channel emulation.
Funding
National Natural Science Foundation of China (NSFC) (61571133); National Key Research and Development Program of China (2017YFB0403603).
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