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Abstract
In this paper, we introduce an innovative post-equalization technique leveraging bidirectional reservoir computing (BiRC), and apply it to waveform-to-symbol level equalization for visible light laser communication for the first time. This strategy is more resistant to nonlinearities compared to traditional equalizers like least mean square (LMS) equalizer, while requiring less training time and fewer parameters than neural network (NN) -based equalizers. Through this approach, we successfully conduct a 100-meter transmission of a 32-amplitude phase shift keying (32APSK) signal using a green laser operating at a wavelength of 520 nm. Remarkably, our system achieves a high data rate of 11.2 Gbps, all while maintaining a satisfying bit error rate (BER) below the 7% hard decision forward error correction (HD-FEC) threshold of 3.8E-3.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
The sixth-generation mobile network (6 G) stands as a pivotal advancement in communication, boasting elevated transmission rates, capacity, and spectral efficiency compared to the fifth-generation mobile communication technology (5 G) [1]. This leap forward not only bridges the digital divide but also paves the way for global interconnectivity. Due to the depleting wireless spectrum, the need for new spectrum resources like terahertz and visible light has become increasingly urgent. The spectrum of visible light ranges from 400 THz to 800 THz, far away from the existing wireless communication bands, and utilizes unallocated frequency bands for transmission. This approach brings forth advantages including energy efficiency, remarkable speed, large capacity, ample bandwidth, and incorporable with daily lighting systems [2–4]. The architecture of visible light communication (VLC) encompasses a transmitter, channel, and receiver. Based on the light source employed, the VLC system can be categorized into light emitting diode (LED) based system and laser diode (LD) based system. These light sources differ fundamentally in their emission principles, with LEDs emitting through spontaneous radiation and LDs via stimulated radiation. Currently, LEDs, which are less costly and less hazardous to human eyes, have been used as emitters for VLC [5]. However, due to the advantages of LDs, such as high modulation bandwidth, beam concentration and narrow linewidth, the present emphasis on high-rate VLC has steered attention towards LDs [6,7]. Figure 1. shows the achievements in data rates and transmission distances for free-space VLC based on LEDs and LDs, and LD-based systems have the potential and trend to achieve higher bit-distance products [8–19].
However, due to a series of problems such as high complexity of actual communication systems, variable environment, limited device bandwidth, cross-talk and nonlinear distortion [20–22], traditional signal equalization algorithms such as LMS algorithms may not be able to resist the crosstalk and nonlinear distortion of the real VLC systems. Thanks to the universal approximation property of artificial intelligence, neural networks have outstanding advantages in dealing with the complex problems above. In 2014, Haigh et al. first demonstrated a neural network equalizer's effectiveness in transmitting 170 Mbps on-off keying signals in an LED-VLC system [23]. In 2019, Rajbhandari et al. proposed a NN-based joint spatial and temporal equalizer for LED-based multiple input multiple output VLC system [24]. And our team's research on the application of neural networks in visible light communication systems is progressing. In 2018, we introduced a Gaussian kernel-assisted deep neural network for post-equalization in a PAM-8 underwater VLC system, achieving 1.5 Gbps [25]. In 2020, we proposed TFDNet with joint temporal-frequency domain for post-equalization [26]. In 2021, we proposed a complex neural network-based algorithm to segment constellation points to address nonlinear impairments [27].
Nonetheless, it's worth noting that neural networks usually have a large number of parameters to be optimized, which extends the requisite training time. To address this, our focus shifts towards reservoir computing (RC) with simple structure [28]. However, the current applications of RC are mainly time series prediction and modulation format identification of communication systems [29,30]. The applications in signal equalization are predominantly reported in waveform-level or symbol-level equalization in fiber optic communication systems in the near-infrared band. In 2018, Apostolos Argyris et al. pioneered the application of RC to signal equalization in fiber optic communication systems [31]. Sarah Masaad et al. implemented RC-based waveform-level equalization for 64-level quadrature-amplitude modulation (64QAM) signals after the simulated fiber transmission [32].
In this paper, we apply RC to waveform-to-symbol level signal equalization for free-space visible light laser communication for the first time, and design a bidirectional data injection strategy during data pre-processing and reservoir input. With a 520 nm gallium nitride (GaN) based laser diode, we finally achieve a transmission rate of 11.2 Gbps for 32APSK signals over a distance of 100 meters. This rate outpaces the traditional equalization algorithms by 1.1 Gbps. To the best of our knowledge, this is currently the highest achievable bit-distance product and the first time exceeding a rate of 10 Gbps for free-space visible light laser communication.
2. Principle
Within this session, we will analysis the principle of the proposed approach. In this paper, we use 32APSK carrier-less amplitude-phase modulation (CAP) signals for transmission [33], which is the highest modulation order that can be transmitted within the signal-to-noise ratio (SNR) constrains of our 100-meter channel. The APSK signals are proposed by the Consultative Committee for Space Data Systems (CCSDS) standard [34], and are suitable for interstellar transmission.
As depicted in Fig. 2, our system consists of three key phases: signal generation, transmission and post-equalization at the receiver end. An arbitrary bit sequence is generated at the transmitter side for APSK mapping, CAP modulation, up-sampled by 4, and then transmitted by an arbitrary waveform generator (AWG). Through direct modulation, a green laser is driven and then generates an optical signal output. After channel transmission, the distorted signal is obtained for data pre-processing and post-equalization.
The traditional reservoir computing [35] consists of three layers, the input layer, the reservoir layer and the output layer. The input information is an m-length vector, denoted as ${\boldsymbol X} = {[{{x_1},{\; }{x_2}, \ldots ,{x_m}} ]^T}$, which is injected into the reservoir layer after multiplication by an input weight vector ${{\boldsymbol w}_{\boldsymbol{in}}}$ of equivalent length. In the reservoir layer, there are M nodes which can be denoted as $\{{{r_1},{r_2}, \ldots ,{r_M}} \}$, and they are connected to each other through an $M \times M$ dimensional weight matrix ${\boldsymbol w}$. The update of the nodes at time step i is depicted by Eq. (1), where $\gamma $ is the decay factor. The updated value of the nodes, denoted as ${{\boldsymbol r}^{{\boldsymbol i} + 1}}$, consist of two parts. The first part is the residual of the node state ${{\boldsymbol r}^{\boldsymbol i}}$ at the current time step, and the second part is the current state altered by the newly injected information, acting on the node through specific weights:
When employing reservoir computing for signal equalization, assuming that the waveform signal flow from the oscilloscope can be denoted as ${[{{x_1},{x_2}, \ldots ,{x_{4N}}} ]^T}$, where N is the number of transmitted symbols and 4 is the up-sampling rate. Considering the potential interference of preceding and subsequent signals with the current signal, first, the signal is sequentially slid from ${x_1}$ to obtain the input vector corresponding to symbols from the first to the ${N^{th}}$, where the sequential part for the ${k^{th}}$ symbol is denoted as ${\boldsymbol x}_{\boldsymbol{pre}}^{\boldsymbol k}$:
3. Experimental setup
During this session, we present the experimental setup of our system as shown in Fig. 3. At the transmitter side, the digital signal to be transmitted is obtained by 32APSK mapping of the random bit sequence and then CAP modulation. After that, the signal is fed to an AWG (Keysight M8190A, 12 GSa/s) for digital-to-analog conversion. An electrical amplifier (EA, ZFL-2500VH+) amplifies the electrical signal, with a bias-Tee (ZFBT-4R2GW-FT+) coupling the direct current (DC) signal to the amplified signal. Then the signal drives a green laser (OSRAM PL520) at a wavelength of 520 nm. The optical signal is transmitted to a reflector at a distance of 50 meters where it is reflected and then travels a distance of 50 meters to the receiver terminal. At the receiver side, the incident light is first converged by a lens and then converted into an electrical signal via an avalanche photodiode (APD). After amplification, the received electrical signal is sampled by an oscilloscope (OSC, MSO9404A, 20 GSa/s) and used for offline processing.
The received signal undergoes waveform-level equalization in the computer, followed by a BiRC-based waveform-to-symbol equalization, and the resulting 32APSK constellation points are then de-mapped for BER testing. Throughout this process, the digital signal processing and equalization at the transmitter and receiver ends are performed offline by a computer, which is implemented using MATLAB and the Python-based artificial neural network library Keras.
4. Experimental results and discussions
In this session, we will present the experimental results and provide corresponding performance analysis and complexity analysis of the equalization algorithms we use.
Firstly, we conduct a traversal to determine the optimal operating point of the system by varying the bias current ${I_b}$ (ranging from 200 mA to 250 mA in steps of 10 mA), and the peak-to-peak voltage (Vpp) of the AWG (ranging from 150 mV to 550 mV in steps of 100 mV). Figure 4 illustrates the variation in system BER with changes in bias current and voltage amplitude. When Vpp is held constant, with ${I_b}$ increasing, BER initially decreases and then rises. Similarly, with a fixed ${I_b}$, as the Vpp increases, the BER exhibits a trend of decreasing and then increasing. This behavior can be attributed to the impact of non-linear effects causing performance degradation at excessive Vpp or ${I_b}$ values. Conversely, excessively low Vpp or ${I_b}$ values submerge the signal within the noise, leading to a reduced signal-to-noise ratio at the receiver and subsequently an increase in BER. Consequently, the system exhibits an optimal operating point. Within the discrete values of ${I_b}$ and Vpp utilized in the experiment, the system achieves its peak performance at ${I_b} = 230mA$ and $Vpp = 350mV$. Furthermore, the transmission BER remains below the 7% HD-FEC threshold of 3.8E-3 between the boundaries indicated by the black lines in Fig. 4.
In the following sections, we employed the traditional LMS-Volterra + LMS scheme as a benchmark for waveform-level and symbol-level equalization. It is worth noting that since the correction of system nonlinear distortion is primarily achieved through waveform-level equalization, the nonlinearities to be addressed at the symbol level are minimal. Therefore, in symbol-level equalization, only the LMS algorithm is employed without additional Volterra equalization to avoid overfitting. Under the benchmark of LMS-Volterra + LMS equalization, we investigated the effectiveness of the BiRC equalizer and its performance as both a waveform-level and waveform-to-symbol equalizer. Thus, we adopted a controlled variable research method, replacing the waveform-level and symbol-level equalization of the benchmark scheme with BiRC to study the system's equalization performance.
4.1 BiRC-based waveform-to-waveform (W2W) equalization
We apply reservoir computing to waveform-to-waveform equalization like [30,31]. But we employ waveform-level equalization based on the proposed BiRC, using the ideal transmit waveforms as training labels. To prevent overfitting, we perform exhaustive optimization of the BiRC parameters at a suboptimal operating point (${I_b} = 230mA\; $and $Vpp = 450mV$) in terms of system performance. Furthermore, to ensure a fair comparison between different algorithms and parameter settings, we use the same random seed when generating random input connection weights ${{\boldsymbol w}_{\boldsymbol{in}}}$ and the reservoir adjacency matrix ${\boldsymbol w}$. Figure 5 illustrates the variation in BER as a function of the reservoir size (resSize, ranging from 20 to 160 in increments of 20) and the spectral radius (sr, ranging from 0.1 to 0.9 in increments of 0.2) of the reservoir adjacency matrix ${\boldsymbol w}$. The subplots display the absolute values of the matrix ${\boldsymbol w}$ for different spectral radius. The spectral radius refers to the maximum absolute value of the eigenvalues of a matrix and is commonly used to describe the stability of linear dynamic systems. When the spectral radius approaches 0, it indicates system stability because the absolute values of the eigenvalues are small, and the system response does not diverge. On the other hand, when the spectral radius approaches 1, it signifies that the system is in a critically stable state, and the system response may exhibit oscillations or slow divergence. In the context of RC, a smaller spectral radius implies lower connection strength between nodes, indicating diminished influence of nodes in the reservoir. From Fig. 5, it can be observed that when the spectral radius of BiRC or RC is set to 0.1 (red curves), the system performs best. But at this point, the reservoir does not operate in the theoretically optimal state. In other words, when BiRC (or RC) is applied to waveform-level equalization, it does not effectively maximize its performance. As the reservoir size increases, the information from the input vectors is unfolded into higher-dimensional feature spaces within the reservoir layer. With a larger reservoir size, BER decreases as the signal information is more fully extracted and utilized, leading to improved equalization performance. However, after increasing the BiRC (RC) reservoir size to 120(140), the BER no longer decreases but shows a slight tendency to increase. This is because the reservoir starts to capture some redundant information, and learning from this redundant information can lead to overfitting. Ultimately, we selected the parameters for the W2W BiRC equalizer with a spectral radius of 0.1, a reservoir size of 120, a decay factor of 0.9, and the parameters for W2W RC equalizer with a spectral radius of 0.1, a reservoir size of 140 and a decay factor of 0.9.
Fig. 5. The variation of the BER with respect to the number of reservoir nodes and the spectral radius of the reservoir adjacency matrix ${\boldsymbol w}$. Insets are the absolute values of ${\boldsymbol w}$ when (a) $sr = 0.1$, (b) $sr = 0.5$ and (c) $sr = 0.9$.
Under the chosen optimal parameters, we investigate the performance of waveform-level equalization using the traditional LMS-Volterra equalizer, the common RC equalizer and the proposed BiRC equalizer. Before the investigation, we first analyze the alignment between the training approach of RC and the characteristics of the actual experimental system. For a fitting problem, assuming the parameters to be fitted are represented as $\theta $, and the observed data is denoted as ${\boldsymbol Z}$, based on the maximum likelihood (ML) estimation criterion and assuming that each observation is independent of the others, we have:
Figure 6 presents the equalization performance of three waveform-level equalizers based on ridge regression. It can be observed that the outputs of BiRC and RC equalization both approximately follow a Gaussian distribution. Across different values of Vpp, the BER of BiRC is lower than that of RC. However, the performance of using BiRC for waveform-level equalization is not as effective as traditional equalizers. This may be attributed to the strong non-linear distortion in the system, and the reservoir's limited ability to correct non-linear distortions. In the following sections, we will keep waveform-level equalization fixed as the LMS-Volterra equalizer and investigate the effectiveness of BiRC for waveform-to-symbol level equalization.
Fig. 6. The BER performance of W2W equalization using the LMS-Volterra equalizer, the traditional RC equalizer and BiRC equalizers based on ridge regression. Insets are the constellation and their distribution of the output of (a) RC and (b) BiRC equalizers at the optimal operating point.
4.2 BiRC-based waveform-to-symbol (W2S) equalization
For waveform-to-symbol level equalization, we use ideal transmit constellation as training labels and perform parameter optimization for BiRC and traditional RC. Figure 7 illustrates the variations in BER under different conditions, considering reservoir size (ranging from 20 to 300 with increments of 40) and the spectral radius (ranging from 0.1 to 0.9 with increments of 0.2) of the reservoir adjacency matrix ${\boldsymbol w}$. Insets depict the absolute values of the matrix ${\boldsymbol w}$ for different spectral radius. The influence of the spectral radius on BER is similarly minimal, with 0.9 being an optional value for the spectral radius. The reservoir nodes are in a strong connectivity state at this spectral radius and function normally, preserving and utilizing signal characteristics more effectively. This can provide more information for the training of output weights. Additionally, BER exhibits a trend of decreasing and then increasing as the number of reservoir nodes increases. Ultimately, the selected parameters are a spectral radius of 0.9, a reservoir size of 220, and a decay factor of 0.7, and the same parameters for W2S RC equalizer.
Fig. 7. The variation of the BER with respect to the number of reservoir nodes and the spectral radius of the reservoir adjacency matrix ${\boldsymbol w}$. Insets are the absolute values of ${\boldsymbol w}$ when (a) $sr = 0.1$, (b) $sr = 0.5$ and (c) $sr = 0.9$.
Using the determined best parameters, a performance comparison between LMS equalizer, RC and BiRC W2S equalizers is conducted. The baseline is the traditional LMS-based symbol-level equalizer and the results are shown in Fig. 8. It is evident that the system performance with the W2S equalizers based on BiRC and RC are significantly improved compared to the traditional LMS equalizer, with an extended operating range of approximately 400 mV (BiRC) and 200 mV (RC). At the optimal operating point, the BER of the LMS equalizer is only 3.27E-3, whereas the BER of the RC and BiRC equalizers can be reduced to 2.39E-3 (RC) and 1.11E-3 (BiRC). The constellation diagrams and their distributions are shown in the insets on the right. It can be observed that the constellation points for the output of W2S BiRC are more concentrated, making the decision-making process more robust and accurate.
Fig. 8. The BER performance of symbol-level equalization using the LMS equalizer, traditional W2S RC equalizer and W2S BiRC equalizers based on ridge regression. Insets are the constellation and their distribution of the output of (a) RC and (b) BiRC equalizers at the optimal operating point.
To sum up, employing a waveform-level LMS-Volterra equalizer in conjunction with a waveform-to-symbol level ridge regression-based BiRC equalizer yields the optimal performance. The waveform-level LMS-Volterra equalizer can proactively correct nonlinear distortions and other impairments in received waveforms, while the waveform-to-symbol level BiRC can replace a series of complex digital signal processing operations such as matched filtering, down-sampling, and symbol-level equalization, achieving superior performance at lower complexity.
4.3 BiRC-based equalizer versus NN-based equalizer
Next, we demonstrate the advantages of BiRC compared to neural network-based equalizers. Firstly, we compare the performance of waveform-level equalization using LMS-Volterra, NN, and the proposed BiRC algorithm. Symbol-level equalization employs LMS algorithm with the same parameters. For waveform-level equalization, all the equalizers have 13 input nodes. The NN equalizer has 2 hidden layers, and utilizes rectified linear unit (ReLU) activation functions, Adam optimizer, and mean square error (MSE) loss function. Figure 9 depicts the variation of BER with Vpp under the influence of different waveform-level equalizers. Insets display the output spectra of the three equalizers at $Vpp = 350mV$ and $Vpp = 450mV$. When the BiRC is used for waveform-level equalization, its performance is worse than LMS-Volterra equalizer and the NN-based equalizer performs the best, achieving optimal system performance at $Vpp = 350mV$, where it reduces the BER from 3.27E-3 to 2.63E-3.
Fig. 9. BER performance of waveform-level equalization using LMS-Volterra, BiRC, and DNN. Insets are the spectra of the respective equalized output waveforms.
We compare the performance of waveform-to-symbol level equalization using LMS, NN, and BiRC algorithms. In this scenario, waveform-level equalization employs the LMS-Volterra algorithm with the same parameters, while the NN equalizer has 2 hidden layers. Figure 10 illustrates the corresponding BER and constellation diagrams for the three algorithms. When Vpp is small and the system is primarily affected by channel noise with less noticeable nonlinearity, BiRC yields the best equalization performance. In contrast, using NN may lead to overfitting as it tends to learn redundant information from the channel. However, when Vpp is large, and the system is predominantly influenced by nonlinearity, BiRC is slightly inferior to the NN equalizer.
Fig. 10. BER performance of W2S equalization using LMS, BiRC, and DNN. Insets are the constellation diagrams for the corresponding equalized outputs, with the black points representing misclassified points.
Although the NN equalizer exhibits strong nonlinearity resistance, practical considerations such as complexity and time cost must be taken into account. Table 1 presents the parameter quantities, Multiply-Accumulate Operations (MACC) [36], and training time requirements for BiRC and NN when used for waveform-level equalization and waveform-to-symbol level equalization. In terms of the required number of training parameters, BiRC needs to train parameters only for the output layer, which has a length equal to the sum of the input nodes, reservoir nodes, and an additional bias unit. In contrast, for the NN equalizer, weights in each layer need to be trained, resulting in a significantly higher parameter quantity compared to BiRC. Regarding computational complexity, it can be quantified using MACC. For a network layer with ${n_I}$ input nodes and ${n_O}$ output nodes, the MACC can be calculated as:
When using BiRC, the MACC for the input layer is equal to the number of input nodes. The MACC for the output layer is equal to the product of the number of output states and the number of reservoir nodes. And the MACC for the reservoir layer can be calculated similarly to an LSTM network layer, which is shown as follows (where M represents the number of reservoir nodes):
Table 1. The parameter quantities, MACC, and training times for different equalizers
The computational complexity of BiRC primarily lies in the interconnections between reservoir nodes, and this limitation may be addressed through hardware implementations based on single nonlinear nodes with time-delayed reservoirs.
Finally, we also gathered statistics on the training times required for BiRC and NN, as shown in Fig. 11. The training time for NN-based equalizers is approximately 10 seconds, whereas equalizers based on BiRC typically require less than 2 seconds to complete training. To sum up, the proposed BiRC equalizer exhibits a straightforward structural design with a limited number of trainable parameters, leveraging spatial complexity to trade for performance gains. This approach significantly reduces the training time and minimizes the required latency for obtaining effective signals.
4.4 Exploring the maximum data rate
Finally, we compare the achievable rates of three low-complexity equalization algorithms: LMS-Volterra + LMS, BiRC + LMS, and LMS-Volterra + BiRC. By varying the sampling rate of the AWG, we measure the BER as a function of the transmission rate, as shown in Fig. 12. The insets on the right display the training results of the reservoir. The orange region corresponds to the weights connecting input signals to the output (equivalent to the linear part), while the green region corresponds to the weights of the reservoir nodes (equivalent to the nonlinear part). During W2W equalization, stronger nonlinear corrections are required, limiting the performance of BiRC. However, in W2S equalization, where weaker nonlinear distortions need correction, the use of the simpler BiRC results in better performance.
Fig. 12. The achievable rates with different equalization algorithms. Insets are the corresponding output weight matrices ${{\boldsymbol W}_{\boldsymbol{out}}}$ obtained through reservoir training.
As the transmission rate increases, the required bandwidth increases. However, the systems use bandwidth-limited devices, and the rise in transmission rate exacerbates inter-symbol interference (ISI). Additionally, due to the severe high-frequency attenuation in visible light communication systems, increasing the transmission bandwidth leads to greater signal attenuation, causing a decrease in signal quality and an increase in BER. When the bit error rate is below the 7% HD-FEC limit of 3.8E-3, using LMS-Volterra + LMS for equalization achieves a baud rate of 2.02GBaud, while employing the proposed bidirectional reservoir computing for waveform-to-symbol equalization, i.e., using LMS-Volterra + BiRC equalization strategy, results in a baud rate of 2.24GBaud. Since the signal is modulated into 32APSK signal, the achievable data rate after the LMS-Volterra + LMS equalizer is 10.1Gbps and the highest data rate after the LMS-Volterra + BiRC equalizer is 11.2Gbps. This represents a 1.1Gbps improvement over the traditional LMS-Volterra + LMS approach.
5. Conclusion
In this paper, we introduced the bidirectional reservoir computing algorithm for post-equalization in visible light laser communication systems. Through experiments conducted in a 100-meter free-space communication scenario, we transmitted 32APSK signals and applied different strategies for post-equalization of the received signals. We innovatively applied BiRC for waveform-to-symbol equalization, revealing a significant improvement in performance compared to waveform-level equalization. Particularly, when the system exhibits low nonlinearity, BiRC outperforms NN-based equalizers. Furthermore, evaluating training time and number of participants, BiRC proves to be more computationally efficient than NNs. Employing LMS-Volterra + BiRC for post-equalization enables a transmission rate of 11.2Gbps, achieving, for the first time, a rate exceeding 10Gbps in a 100-meter free-space visible light laser communication system.
Funding
National Key Research and Development Program of China (2022YFB2802803); National Natural Science Foundation of China (61925104, 62031011, 62201157); Office of Global Partnerships (Key Projects Development Fund).
Acknowledgments
This research was funded by the National Key Research and Development Program of China (2022YFB2802803), the Natural Science Foundation of China Project (No. 61925104, No. 62031011, No. 62201157) and the Office of Global Partnerships (Key Projects Development Fund).
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. P. Yang, Y. Xiao, M. Xiao, et al., “6 G Wireless Communications: Vision and Potential Techniques,” IEEE Network 33(4), 70–75 (2019). [CrossRef]
2. H. Kaushal and G. Kaddoum, “Underwater Optical Wireless Communication,” IEEE Access 4, 1518–1547 (2016). [CrossRef]
3. N. Chi, H. Haas, M. Kavehrad, et al., “Visible light communications: demand factors, benefits and opportunities,” IEEE Wireless Communications 22(2), 5–7 (2015). [CrossRef]
4. N. Chi, Y. Zhou, Y. Wei, et al., “Visible Light Communication in 6G: Advances, Challenges, and Prospects,” IEEE Vehicular Technology Magazine 15(4), 93–102 (2020). [CrossRef]
5. Z. Xu, W. Niu, Y. Liu, et al., “31.38 Gb/s GaN-based LED array visible light communication system enhanced with V-pit and sidewall quantum well structure,” Opto-Electron Sci. 2(5), 230005 (2023). [CrossRef]
6. C. Shen, O. Alkhazragi, X. Sun, et al., “Laser-based visible light communications and underwater wireless optical communications: a device perspective,” Proc. SPIE 10939, Novel In-Plane Semiconductor Lasers XVIII, 109390E (2019).
7. F. Zafar, M. Bakaul, and R. Parthiban, “Laser-Diode-Based Visible Light Communication: Toward Gigabit Class Communication,” IEEE Commun. Mag. 55(2), 144–151 (2017). [CrossRef]
8. H. L. Minh, D. O’Brien, G. Faulkner, et al., “High-Speed Visible Light Communications Using Multiple-Resonant Equalization,” IEEE Photonics Technol. Lett. 20(14), 1243–1245 (2008). [CrossRef]
9. J. F. C. Carreira, E. Xie, R. Bian, et al., “On-chip GaN-based dual-color micro-LED arrays and their application in visible light communication,” Opt. Express 27(20), A1517–A1528 (2019). [CrossRef]
10. M. A. Umair, M. Seminara, M. Meucci, et al., “Long-Range Optical Wireless Communication System Based on a Large-Area, Q-Dots Fluorescent Antenna,” Laser Photonics Rev. 17(2), 2200575 (2023). [CrossRef]
11. S. Zhu, P. Qiu, X. Shan, et al., “High-speed long-distance visible light communication based on multicolor series connection micro-LEDs and wavelength division multiplexing,” Photonics Res. 10(8), 1892–1899 (2022). [CrossRef]
12. W. Niu, Z. Xu, Y. Liu, et al., “Key Technologies for High-Speed Si-Substrate LED Based Visible Light Communication,” J. Lightwave Technol. 41(11), 3316–3331 (2023). [CrossRef]
13. Y. F. Huang, Y. C. Chi, H. Y. Kao, et al., “Blue Laser Diode Based Free-space Optical Data Transmission elevated to 18 Gbps over 16 m,” Sci. Rep. 7(1), 10478 (2017). [CrossRef]
14. L. Y. Wei, C. W. Hsu, C. W. Chow, et al., “40-Gbit/s Visible Light Communication using Polarization-Multiplexed R/G/B Laser Diodes with 2-m Free-Space Transmission,” 2019 Optical Fiber Communications Conference and Exhibition (OFC) (IEEE, 2019), 1–3.
15. H. Chun, A. Gomez, C. Quintana, et al., “A Wide-Area Coverage 35 Gbps Visible Light Communications Link for Indoor Wireless Applications,” Sci. Rep. 9(1), 4952 (2019). [CrossRef]
16. C. Lu, J. Wang, S. Li, et al., “60 m/2.5Gbps Underwater Optical Wireless Communication with NRZ-OOK Modulation and Digital Nonlinear Equalization,” 2019 Conference on Lasers and Electro-Optics (CLEO) (IEEE, 2019), 1–2.
17. G. Qin, Q. Biau, W. Niu, et al., “100 m Free-space Visible Light Communication at 6 Gbps GS-APSK Modulation Utilizing a GaN Blue LD,” 2021 Asia Communications and Photonics Conference (ACP) (IEEE, 2021), 1–3.
18. J. Hu, F. Hu, J. Jia, et al., “46.4 Gbps visible light communication system utilizing a compact tricolor laser transmitter,” Opt. Express 30(3), 4365–4373 (2022). [CrossRef]
19. H. Pahuja, S. Sachdeva, and M. Sindhwani, “Capacity enhancement of WDM visible light communication system employing 3-SOPs/channel/LD color,” Journal of Optical Communications, (2022). [CrossRef]
20. I. Neokosmidis, T. Kamalakis, J. W. Walewski, et al., “Impact of Nonlinear LED Transfer Function on Discrete Multitone Modulation: Analytical Approach,” J. Lightwave Technol. 27(22), 4970–4978 (2009). [CrossRef]
21. K. Ying, Z. Yu, R. J. Baxley, et al., “Nonlinear distortion mitigation in visible light communications,” IEEE Wireless Commun. 22(2), 36–45 (2015). [CrossRef]
22. B. Inan, S. C. J. Lee, S. Randel, et al., “Impact of LED Nonlinearity on Discrete Multitone Modulation,” J. Opt. Commun. Netw. 1(5), 439–451 (2009). [CrossRef]
23. P. A. Haigh, Z. Ghassemlooy, S. Rajbhandari, et al., “Visible Light Communications: 170 Mb/s Using an Artificial Neural Network Equalizer in a Low Bandwidth White Light Configuration,” J. Lightwave Technol. 32(9), 1807–1813 (2014). [CrossRef]
24. S. Rajbhandari, H. Chun, G. Faulkner, et al., “Neural Network-Based Joint Spatial and Temporal Equalization for MIMO-VLC System,” IEEE Photonics Technol. Lett. 31(11), 821–824 (2019). [CrossRef]
25. N. Chi, Y. Zhao, M. Shi, et al., “Gaussian kernel-aided deep neural network equalizer utilized in underwater PAM8 visible light communication system,” Opt. Express 26(20), 26700–26712 (2018). [CrossRef]
26. H. Chen, Y. Zhao, F. Hu, et al., “Nonlinear Resilient Learning Method Based on Joint Time-Frequency Image Analysis in Underwater Visible Light Communication,” IEEE Photonics J. 12(6), 1–13 (2020). [CrossRef]
27. H. Chen, W. Niu, Y. Zhao, et al., “Adaptive deep-learning equalizer based on constellation partitioning scheme with reduced computational complexity in UVLC system,” Opt. Express 29(14), 21773–21782 (2021). [CrossRef]
28. Y. Paquot, F. Duport, A. Smerieri, et al., “Optoelectronic Reservoir Computing,” Sci. Rep. 2(1), 287 (2012). [CrossRef]
29. Q. Cai, Y. Guo, P. Li, et al., “Modulation format identification in fiber communications using single dynamical node-based photonic reservoir computing,” Photonics Res. 9(1), B1–B8 (2021). [CrossRef]
30. Y. Hou, G. Xia, W. Yang, et al., “Prediction performance of reservoir computing system based on a semiconductor laser subject to double optical feedback and optical injection,” Opt. Express 26(8), 10211–10219 (2018). [CrossRef]
31. A. Argyris, J. Bueno, and I. Fischer, “Photonic machine learning implementation for signal recovery in optical communications,” Sci. Rep. 8(1), 8487 (2018). [CrossRef]
32. M. Sarah, G. Emmanuel, S. Stijn, et al., “Photonic reservoir computing for nonlinear equalization of 64-QAM signals with a Kramers–Kronig receiver,” Nanophotonics 12(5), 925–935 (2023). [CrossRef]
33. N. Chi, Y. Zhou, S. Liang, et al., “Enabling Technologies for High-Speed Visible Light Communication Employing CAP Modulation,” J. Lightwave Technol. 36(2), 510–518 (2018). [CrossRef]
34. BOOK, DRAFT RED, “Flexible Advanced Coding and Modulation Scheme for High Rate Telemetry Applications,” (CCSDS Washington, 2012), Chap. 5.
35. D. J. Gauthier, E. Bollt, A. Griffith, et al., “Next generation reservoir computing,” Nat. Commun. 12(1), 5564 (2021). [CrossRef]
36. C. Wang, K. Wang, Y. Tan, et al., “Low Complexity Joint Neural Network Equalizer in a 248 Gbit/s VSB PS-PAM8 IM/DD Transmission System,” European Conference on Optical Communication (ECOC) (Optica Publishing Group, 2022), paper Tu5.28.
