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Abstract
Deep neural networks (DNNs) have been applied to recover signals in optical communication systems and have shown competence of mitigating linear and nonlinear distortions. However, as the data throughput increases, the heavy computational cost of DNNs impedes them from rapid and power-efficient processing. In this paper, we propose an optical communication signal recovery technology based on a photonic convolutional processor, which is realized by dispersion delay unit and wavelength division multiplexing. Based on the photonic convolutional processor, we implement an optoelectronic convolutional neural network (OECNN) for signal post-equalization and experimentally demonstrate on 16QAM and 32QAM of an optical wireless communication system. With system parameters optimization, we verify that the OECNN can achieve accurate signal recovery where the bit error ratio (BER) is below the 7% forward error correction threshold of 3.8×10−3 at 2Gbps. With adding the OECNN-based nonlinear compensation, compared with only linear compensation, we improve the quality (Q) factor by 3.35 dB at 16QAM and 3.30 dB at 32QAM, which is comparable to that of an electronic neural network. This work proves that the photonic implementation of DNN is promising to provide a fast and power-efficient solution for optical communication signal processing.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
In the era of explosive information growth, the communication network is confronted with an extremely high demand for capacity. Optical communication technology, including optical fiber communication [1] and optical wireless communication [2,3], provides an ultra-high transmission rate and is expected to be the ultimate solution to the future network and data center. However, the nonlinear distortions in optical communication systems will strongly increase the error rate at high-order modulation, thus putting a limit to the increase of data rate [3–6]. Researchers developed various channel equalization approaches to recover the received signal, including linear algorithms such as Least Mean Square (LMS) and Recursive Least Square (RLS) [7,8], and Volterra and Look-up Table predistortion algorithms that handle nonlinearity distortion [9,10]. In recent years, neural networks have been proved to successfully recover signals with linear and high-order nonlinear distortion by determining a complex mapping model of the transmission channel [6,11–17]. In 2014, Haigh et al. for the first time demonstrated the neural network post-equalizer in the optical wireless communication system [11], and achieved significantly better BER than using linear equalizers. A recent work [17] proposed to apply fully-connected layer based signal processing to the Fourier spectrum domain and achieved about one order of magnitude improvement in BER. Convolutional neural networks (CNNs) of advanced architecture are also applied to signal recovery in optical communication. In [18], a hybrid frequency temporal convolutional neural network is proposed to compensate for the strong nonlinear distortion in the underwater optical communication system.
As the computation demand grows, application-specific integrated circuit (ASIC) for the neural network has been designed, such as the Google vector processing unit. However, the development of electronic chips is approaching the limit of Moore's law. Great attention has been directed toward developing efficient neuromorphic computing architectures. Photonic neural networks (PNNs) emerge as promising implementation, given their potential for ultrafast computing speed, energy efficiency, and parallel computing ability [19–26]. A two-dimensional photonic computing neural network chip based on diffractive optics was developed by Lin et al. [20] and applied for image recognitions [20,21]. The diffractive neural networks allow massive computing nodes in parallel, however the fabrication is still challenging to prevent working in the visible and NIR spectrum. With the development of integrated silicon photonics, on-chip neuromorphic computing has made progress. Shen et al. [22] for the first time proposed and demonstrated a fully optical Mach Zehnder interferometer network to realize the matrix multiplication. The PNN device can support neural network forward operations 100 times more than state-of-art electronic computing hardware. Feldmann et al. [23]designed a synapse-like photonic unit using the phase-change materials with nonlinear light absorption, and further integrated optical frequency comb into the in-memory computing network to achieve parallelized data processing [24]. Up to date, Xu et al. [25] proposed a time-wavelength multiplexing photonic convolutional neural network architecture. Through large-scale multiplexing of wavelengths, the photonic accelerator reaches 11 tera operations per second (TOPS), which is the highest speed ever reported. To conclude, photonic neural networks exhibit great potential for fast and efficient computing in data-heavy applications.
In the field of optical communication, signal processing with PNNs has also attracted growing attention. Opto-electronic and fully optical systems that implement reservoir computing have been reported [27–32]. Sackesyn et al. [30] used waveguide-based photonic reservoir computing chip to alleviate fiber nonlinear distortion, and experimented on a 32Gbps OOK system with real-time processing ability. Cai et al. [31] realized modulation format recognition in optical fiber communication systems by using a single node delay reservoir computing network based on a semiconductor laser. Nevertheless, the reservoir networks can only handle modest nonlinearity, hence the applications are often confined to either low-order signal modulations (e.g., OOK or QPSK) or simple classification tasks. Lately, Huang et al. [32] proposed a reconfigurable integrated silicon photonic neural network platform, on which they demonstrated a fully connected neural network for nonlinear compensation of 16QAM signals received through a submarine long-distance optical fiber. The big success of the photonic implementation of advanced neural networks in processing optical communication signals offers a promising alternative to traditional digital signal processing circuits with enhanced processing speed and power efficiency.
In this paper, the photonic convolutional processor based on time wavelength multiplexing architecture [25] is introduced into the field of post-equalization of optical wireless communication for the first time. In the photonic processor, the convolutional weights are parallelly encoded to the optical power of the wavelength channels. Each channel is temporally modulated by input signals, and interleaved channels via a dispersion delay device are summed to yield a convolution. Unlike computer vision tasks such as image classification, signal recovery task in communication scenario requires bit-level accuracy, therefore is sensitive to the precision of photonic calculation. We characterize the photonic computing system to obtain optimized photonic convolution performance. With a proof-of-concept setup, we experimentally demonstrate OECNN for the recovery of 16QAM and 32QAM optical communication signals at 1.8Gbps and 2Gbps respectively and achieve accurate performance with the BER below the 7% forward error correction (FEC) threshold of 3.8×10−3. The photonic signal recovery network achieves an improvement on Q-factor by more than 3.3 dB compared with using only LMS equalizer, and the improvement is comparable to that of a neural network implemented on an electronic computer. The experimental results indicate that the photonic implementation of the advanced convolutional neural network is promising for the efficient recovery of strongly distorted signals and will break the transmission speed limit for future optical communication.
2. Principle of photonic convolutional processor
In a standard optical communication system (Fig. 1(a)), the original data, i.e., a sequence of 0/1 bit signals, is modulated and loaded on the light source by rapidly changing the light intensity. At the receiving end, a photodetector (PD) records the optical signal and converts it into electrical signal. Then, a post-processing procedure is carried out to demodulate and recover the data. Given the fact that the constellation of the signal will be distorted during transmission due to the nonlinear response of the communication channel, the signature cannot be distinguished correctly. Moreover, due to the inadequate bandwidth of electric devices, the high-frequency part of the signal spectrum will be attenuated, which will exacerbate the linear distortion. We can express the forward model of signal transmission in an optical communication system as follows:
where $\boldsymbol{s}$ is the original signal sequence, $\boldsymbol{x} = ({{x_1}, \ldots ,{x_j}, \ldots ,{x_m}} )$ is the received signal sequence, $h(. )$ denotes the response of the transmission system, and ${N_0}$ is the additive Gaussian white noise (AWGN).
Fig. 1. Optoelectronic convolutional neural network for transmission signal recovery. (a) Schematic diagram of using neural network to compensate nonlinear distortion and recover signal in optical communication system. (b) Photonic implementation of convolutional processor. TLS, tunable laser source; WSS, wavelength selective switch; MZM, Mach Zehnder modulator; SSMF, standard single mode fiber; EDFA, erbium-doped fiber amplifier; PD, photodetector; OSC, oscilloscope.
While the nonlinear distortion poses a challenge to identifying the signals, we can use the CNN algorithm to compensate for the nonlinearity at the receiving end and restore the signal spectrum and constellation as close to its original state as possible. The goal of the CNN signal compensation algorithm is to find the function ${h^{ - 1}}(. )$, which best maps the received data to the original data. The recovered signal $\tilde{\boldsymbol{s}}$ is expressed as
To allow fast and low power-consumption computing, we implement optoelectronic convolutional neural network for signal recovery. In Fig. 1(b), we depict the principle and hardware implementation of the time-wavelength multiplexing photonic convolutional processor. A tunable laser source (TLS) produces multi-wavelength lasers with the same wavelength spacing, and are coupled into a waveform selection switch (WSS) to individually adjust the laser power for each wavelength. The power of the lasers corresponds to the weights of the convolution kernel $\boldsymbol{w} = ({{w_1}, \ldots ,{w_i}, \ldots ,{w_n}} )$ that has been trained. The electrical input signal of the photonic convolutional processor represents the received signal $\boldsymbol{x}$ of the communication system. The input signal is generated by a high bandwidth arbitrary waveform generator (AWG), and multicast to each laser channel by modulating the laser power with a Mach Zehnder modulator (MZM). This way, the laser of each wavelength carries the signal $\boldsymbol{x}$ with different weight amplitudes. The output laser power after the MZM is the product of $\boldsymbol{w}$ and $\boldsymbol{x}$:
The multi-channel laser source propagates through a standard single-mode fiber (SSMF) of length L, resulting in different time delays due to dispersion. The time delay between adjacent wavelengths is exactly the duration of one symbol ${x_j}$. To achieve this, the following formula needs to be matched
Here, $\tau $ represents the time delay of adjacent wavelengths, B is the baud rate of the input signal, D is the dispersion index of the optical fiber, and $\mathrm{\Delta }\lambda $ is the laser wavelength spacing. The wavelength dispersive laser output from the SSMF can be expressed as
Finally, multiple wavelengths carrying signal $\boldsymbol{x}$ multiplied by different weights with stepped time delays are superimposed onto the PD. The incoherent intensity superposition is the summation of ${X_{MLS\_DL}}$ by column (as shown in the two orange circles at the bottom of Fig. 1(b)), which is also equivalent to the convolutional result of $\boldsymbol{w}$ and $\boldsymbol{x}$. The convolution output waveform is sampled and digitized by the oscilloscope, and then synchronized with the local convolved sequence. Here, we trim the convolutional output signal to the length of $m - n + 1$:
3. OECNN for communication signal recovery
To demonstrate the optoelectronic convolutional neural network for signal recovery, we build up a OECNN with the photonic convolutional processor and leverage it as the post-equalizer in an optical wireless communication system. As shown in Fig. 2(a), the optical communication system consists of three parts: the pre-processor, the data-transmission channel, and the post-processor. At the pre-processing, the original bit sequence is subjected to quadrature amplitude modulation (QAM) mapping, up-sampling, and carrier-less amplitude modulation (CAP) [33]. The normalized sequence is then loaded into an AWG for digital-to-analog conversion and the electric signal passes through a pre-equalization circuit and an electric amplifier, and is finally coupled with the DC from the bias tee to drive the LED. The emitted light carrying information is focused through a lens and transmitted 1.2m in free space. At the receiver, a collective lens focuses the light onto the PD, which converts the optical signal into electrical signal. A trans-impedance amplifier (TIA) amplifies the received electrical signal, and a digital storage oscilloscope (OSC) samples the signals and sends it for post-processing. For the post-processing part, the signals pass through the OECNN post-equalization, matching filterer, down-sampling, LMS post-equalization, and QAM de-mapping. The distortion in the system mainly comes from the nonlinear response of the LED, PD, and amplification circuits. To tackle it, here we adopt a two-stage signal recovery algorithm: the CNN equalizer compensates nonlinearity with original waveform signals as the target, where the computational cost is huge; while the LMS equalizer handles residual linear distortion after down-sampling by applying on QAM signals.
Fig. 2. Schematic of signal recovery with OECNN. (a) Optical transmission system and the pipeline of digital signal processing. (b) The network structure of OECNN post-equalization. The notation $M \times N \times C$ of kernel layers represents C kernels of length M and depth N. (c) LMS post-equalization.
At the first-stage equalization, OECNN is used to compensate for the linear and nonlinear distortions of the channel by recovering the received waveform signals. The structure of the CNN used in the experiment is shown in Fig. 2(b). The network is composed of one input layer of ${N_{CNN}}$ neurons, one output layer of one neuron, and three convolutional hidden layers. The number of input taps is optimized to be 23 by trial, and the numbers of hidden neurons are set to be 66, 17, and 1, respectively. We choose Rectified Linear Unit (ReLU) as the activation function. The network optimization algorithm is Adam, and the loss function is the mean squared error (MSE) between the feature set and the tag set. The original transmission signal is regarded as the tag set, while the output signal of OSC is regarded as the feature set for the training of network parameters. We leverage the back-propagation to train the CNN on an electronic computer and then apply the optimized kernel weights to the photonic hardware. Once the training is finished, we can apply the kernel weights to the photonic convolutional processor to conduct prediction. The convolutional layer with kernels of size $M \times N \times C$ is decomposed into $N \times C$ one-dimensional convolution kernels of size $M \times 1$, which can be performed by photonic convolutional processor. After all convolutions of the kernel layer are completed, $N \times C$ convolution results are superimposed by the depth N on the computer. A ReLU function is followed to achieve nonlinearity. The layer output can be fed into the photonic convolutional processor as the input to emulate the next convolutional layer. The whole network calculation can be done by repeating the procedure.
The LMS algorithm is used to solve part of the linear distortion at the symbol level after signal down-sampling. The received serial signals are divided into subsets of size ${N_{LMS}}$ in a sliding window manner and parallelly sent to the LMS equalizer. As the diagram in Fig. 2(c) shows, the product is performed between the parallel signal and the tap vector $\boldsymbol{v} = ({{v_0}, \ldots ,{v_{{N_{LMS}} - 1}}} )$ :
To optimize the equalization performance, we update the tap vector in the gradient descent method by computing the distance between $y(n )$ and QAM data at the sender and feeding the error back.
4. Experiments and results
Having established the OECNN, we next evaluate its applicability on experimental data. The powerful nonlinear estimation ability of CNN enables us to tackle with difficult tasks, for example, recovering signals at high-order modulation. To prove this, we first experiment on the 16QAM signals. A large set of bit sequences are modulated and sent to the optical wireless communication system in Fig. 2(a) to transmit signals with a bandwidth of 366MHz. The received waveforms consisting of 76800 sample points at each Vpp are divided into two groups, including 50% of training set and 50% testing set. Network parameters are trained at each Vpp with the batch size of 256 for 30 epochs. The network structure and parameters of OECNN and CNN are completely consistent. In the testing stage of OECNN, the received signals from the testing set are loaded into the MZM, while the trained weights at the corresponding Vpp are loaded to the WSS to control laser power of each channel. As a proof-of-concept demonstration, we implement the last convolutional layer with the photonic convolutional processor of kernel size $6 \times 1$. The first several convolution layers of OECNN are executed on the computer. After the computer executes, a one-dimensional sequence is obtained. The sequence enters the photonic processor system through MZM and convolutes with the corresponding kernel weight. Then the OECNN equalization is completed.
We evaluate the distorted signal recovery performance of OECNN as presented in Fig. 3. To test the robustness of OECNN under different levels of nonlinear distortion, we traverse the Vpps of the input signal from 0.2V to 1V in optical wireless communication system, and measure the BER with and without OECNN. The increase of Vpp, i.e., using higher signal optical power, can improve the optical signal-to-noise ratio (OSNR). Meanwhile, the increase of optical power will introduce increased nonlinear distortion to the signal. The $3.8 \times {10^{ - 3}}$ with 7% forward error correction (FEC) is considered as a BER threshold and error free recovery can be carried out through the forward error correction mechanism. From Fig. 3(a), we see that for the 16QAM signal, without CNN equalization, the LMS linear recovery algorithm can only reach a minimum BER of 0.0075, far higher than the BER threshold of 0.0038. As a comparison, by combining OECNN equalization with LMS equalization, the BER can be controlled below the threshold within the Vpp range of 0.2V to 0.9V. When Vpp = 0.6V, OECNN equalization reduces the BER by 37-fold, equivalent to a Q-factor increment of 3.35 dB (We use the standard relation between Q and BER: $Q = 20log10\left[ {\sqrt 2 \cdot erfcinv({2 \cdot BER} )} \right]$, where $erfcinv$ is the inverse of the complementary error function.). We also compare the calculation results with that of using an electric computer, denoted as CNN, which works as a baseline calculation approach. We see that the performance of OECNN and CNN are very close, and the BER difference is less than 5×10−4 in the range of Vpp = 0.4 ∼ 0.8V, verifying the high accuracy of OECNN. In addition, we illustrate the signal constellations obtained by three equalization methods at Vpp = 0.6V. Although the signals are fuzzily distributed via LMS-only equalization, the OECNN effectively realizes the segmentation of 16 QAM signals.
Fig. 3. OECNN for 16QAM signal recovery (a) BER versus signal Vpp of communication system. (b) BER versus transmission data-rates at Vpp = 0.6 V. (c) Comparison of experimental OECNN (black) and computer-based CNN output (green) at Vpp = 0.6 V.
With the increase of data rate, narrower signal pulses will lead to more serious inter-symbol interference (ISI). Considering that the system response is attenuated at high-frequency, the distortion of signals will be more affected due to the increase of signal bandwidth. The increased ISI makes the signal post equalization problem more difficult to solve. To further test that the proposed OECNN can adapt to higher data rates, we fix Vpp = 0.6V and gradually increase the data rates (Fig. 3(b)). Without nonlinear correction, the BER of using LMS-only equalization grows rapidly with the increase of bit rate. Whereas, the OECNN can preserve BER below the threshold at bit rate up to 1.8 Gbps, revealing high robustness to the increase of system ISI. We note that the slight deterioration of OECNN to its all-electric counterpart mainly comes from the system noise of the photonic processor. We compare the waveforms of photonic convolution output and the simulation output of 16QAM at Vpp = 0.6V (see Fig. 3(c)). The mean squared error (MSE) between the 38400 samples of the experimentally obtained waveforms and their expected counterparts is 0.0085.
Under the same signal bandwidth, the communication system at higher-order modulations can support higher data rates. Meanwhile, the accuracy of signal transmission will be more sensitive to the system noise. To further explore the applicability of OECNN on higher order signals, we carry out the same experiment on 32QAM signal with a bandwidth of 366MHz. The BER of using OECNN for 32QAM signal under different Vpps has the same trend as that of 16QAM signal (Fig. 4(a)). With only LMS linear recovery algorithm, the BER is still far above the threshold within the whole Vpp range. As a comparison, OECNN equalization largely reduces the BER by over 14-fold (Q-factor increased by 3.3 dB) when Vpp is 0.6V. Compared with 16QAM signal, the Euclidean distance of 32QAM constellation points is closer, hence it will be more sensitive to the equalization error. As a result, the Vpp range where the BER is below the threshold of OECNN is reduced to between 0.3V and 0.8V. When the Vpp is below 0.3V, the low SNR of the system cannot support the identification of 32QAM signal. When Vpp is higher than 0.8V, the increased nonlinear distortion of the signal cannot be fully compensated by the neural network. Under the similar test of increasing data rate (Fig. 4(b)), OECNN can maintain BER below the threshold within 2 Gbps. This result demonstrates that using OECNN for signal equalization enables the communication system to transmit signals at high-order modulation and increase the data rate. Figure 4(c) shows the comparison between optical calculation and electrical calculation of convolved spectrum when Vpp = 0.6V with an MSE of 0.0089. Although the convolutional calculation error is similar to that of 16QAM case, the BER gap between CNN and OECNN for 32QAM grows larger due to its reduced Euclidean distance.
Fig. 4. OECNN for 32QAM signal recovery (a) BER versus signal Vpp of 32QAM. (b) BER versus data-rates of 32QAM at Vpp = 0.6 V. (c) Comparison of experimental OECNN output (black) and computer-based CNN output (green).
Through the above experiments, we know that the signal recovery technology based on OECNN is greatly affected by the accuracy of photonic convolution calculation. Therefore, the above good post equalization effect is obtained by optimizing the system parameters in the experiment. Next, we show the process of investigating how various parameters influence the performance of the photonic convolutional processor.
An important factor affecting the accuracy of photonic convolution is the deviation of input signal values. Therefore, it is necessary to ensure that the MZM used to perform photoelectric intensity modulation works at the appropriate working condition. In the proposed photonic convolutional processor system, the transfer function of MZM is expressed as $f(x )= si{n^2}(x )$. Given its nonlinear response, the bias voltage and input signal Vpp of MZM need to be carefully adjusted to keep the response in the linear region as much as possible. This also avoids the unbalanced influence of MZM on the positive and negative parts of the signal. As a quantitative analysis, we first fix the Vpp of MZM and adjust its DC bias voltage. As shown in Fig. 5(a), the BER of OECNN combined with LMS algorithm reaches the minimum when the bias voltage of MZM is 4.4V. As the bias voltage deviates from 4.4V, the BER gradually increases from 1.4×10−3 to over 2.0×10−3, and the constellation signals are getting fuzzier. Next, we characterize the Vpp of MZM. The purpose is to make the photonic convolutional processor system tradeoff between OSNR and signal clipping distortion. As shown in Fig. 5(b), the BER after OECNN and LMS equalization first rapidly decreases with the increase of Vpp, then remains stable when Vpp is greater than 0.5V, resulting in a BER around 1.4×10−3. The reason is that when Vpp is lower, the input signal is buried with relatively stronger noise, hence cannot be accurately identified through the photonic convolutional processor. For the sake of optical power conservation, we choose Vpp of 0.5V in the experiments.
Fig. 5. OECNN performance to inaccurate input signal values (a) OECNN post equalization performance of different MZM bias voltages. (b) OECNN post equalization performance of different MZM input signal Vpp.
Another critical factor affecting the system precision is the temporal alignment of the multi-band delayed signals. According to Eq. (4), we know that the time slot alignment of delayed signals requires the baud rate, fiber length, dispersion index of fiber, and the wavelength spacing to be matched with each other. However, in practice, there often exists a deviation between the actual value of the dispersion index and the nominal value. Therefore, other parameters in Eq. (4) need to be adjusted to ensure a strict matching. Among them, the length of the optical fiber is usually fixed and difficult to adjust; and the baud rates of the input signal are determined by the AWG and signal up-sampling ratio. Hence, it is more convenient to adjust the wavelength spacing of the laser by changing the frequency spacing of TSL. In the experiment, the baud rate $\boldsymbol{B}$ of the photonic convolution calculation system is 10 GBaud, and the fiber length $\boldsymbol{L}$ is 10 km. Given the nominal dispersion index $\boldsymbol{D}$ of SSMF to be 16 ps/nm/km, the wavelength spacing $\boldsymbol{\varDelta \lambda }$ of the laser is calculated to be 0.625 nm, equaling to a frequency spacing of 78 GHz. After fine-tuning the experimental device, we found that 75 GHz is the best frequency spacing of the system, at which point the best photonic convolution calculation accuracy can be achieved. Therefore, the actual dispersion index of the fiber is deduced to be 16.6 GHz. The parameters are summarized in Tab. 1.
Table 1. Comparison of theoretical and experimental parameters of photonic convolutional processor
To evaluate the influence of misaligned spectral multiplexing, we numerically analyze the calculation accuracy of photonic convolution at different frequency spacings. Simulations are carried out with the received optical power of 3 dBm. The simulation parameters of data rate, fiber length, and fiber dispersion index are the same as the experimental system parameters in Tab. 1. We traverse the frequency spacing of $75 \pm 4$ GHz at a step of 2 GHz and compare the MSE of the convolution results simulated by photonics with the ground truth value. As shown in Fig. 6, the MSE reaches the minimum at the frequency spacing of 75 GHz, and the frequency shifting causes the MSE to grow. The MSE of 78 GHz frequency spacing is more than 15% larger than that of 75 GHz frequency spacing. From the plotted convolution spectrum, we also see that the calculated values at mismatched conditions are more fluctuated from the simulated values than in the strictly aligned case. This result inspires us that optimizing the frequency spacing to ensure strict temporal alignment is crucial for accurate photonic convolution.
Fig. 6. Accuracy analysis of photonic convolution with temporal misalignment. The mean square error of photonic convolution at different laser frequency intervals is presented. Convolution output waveform of photonic simulation(black) and expected ground truth (green) with frequency intervals of (i) 75 GHz and (ii) 79 GHz are presented.
Except for precisely setting the input signal, the accuracy of kernel weight parameters should also be considered to keep the photonic convolutional processor working in the best state. In the proposed system, kernel weights are applied by attenuating the laser power with the WSS. We calibrate the output laser power according to the attenuation coefficient of WSS for each wavelength channel, and present the response curves in Fig. 7. For example, if the same kernel weight is set, there is a maximum difference of 2.68dB in the attenuation coefficient on the 193.025GHz channel and 193.25GHz channel. We see that the power of the attenuated laser decreases almost linearly with the increase of the WSS attenuation coefficient, and each channel has a slightly different scaling factor and range. To precisely approximate the intensity modulation, we fit each response curve with a nonlinear function in the form of
where $\alpha ,\; \beta ,$ and ${a_k}$ are the parameters to fit. In the experiments, actual attenuation coefficients of WSS for the desired laser power can be computed via the above nonlinear mapping.Fig. 7. Characterization of laser power adjustment. The nonlinear responses of photonic convolutional processor at different wavelength channels are calibrated and fitted.
5. Conclusion
In this paper, we propose a simple waveform level optical communication CNN post-equalization technique by using a photonic convolutional processor. The optoelectronic convolutional neural network based on time wavelength multiplexing architecture is introduced into the field of post equalization of optical wireless communication for the first time and verified by experiments. We achieve signal recovery of 16QAM and 32QAM using OECNN. Compared with only linear equalization approach, the OECNN equalizer compensates the nonlinear distortion and improves the Q-factor by 3.35 dB for 16QAM and 3.3 dB for 32QAM signal. Processing on higher-order modulated signal is more vulnerable to the system noise, hence the photonic convolutional processor should be carefully optimized to achieve accurate performance.
There are two potential advantages to OECNN. (1) High speed. Photon computing can expand the computing speed through wavelength division multiplexing technology. The mainstream telecommunication frequency band includes C-band and L-band, and the frequency range can be up to 10THz. And the photodetector can detect at a rate of more than 100 GHz. (2) Low energy consumption. According to Ref. [25], the potential energy efficiency of integrated photon CNN is equivalent to the most advanced electronic technology. We further discuss the energy efficiency of the OECNN. The photonic convolutional processor demonstrated in the experiments operates at 0.12TOPS, and the power consumption of each laser is 14.5dBm (equivalent to 28.2mw). Therefore, the operation per energy consumption for the optical computing can be estimated as 0.12/0.0282/6 = 0.71TOPS/W, which is higher than the traditional electrical computing. The photonic implementation of CNN reveals great potential for a fast and power-efficient alternative to traditional signal processing on electronic computers.
Compared with the electric computing, there exists a small gap in BER of proposed OECNN, especially for the high-order signal experiments. The reasons for this gap include: the internal limitation of the AWG will lead to the deterioration of input waveform, the spontaneous emission noise introduced by the EDFA, and the quantization error of the sampling oscilloscope. Refining the network design scheme to better adapt to the noisy photonic system will obtain higher accuracy. In this proof-of-concept demonstration, we build up the OECNN system with commercially-available telecommunication components. With the development of photonic integration technology, we plan to further study the integrated implementation of the photonic convolutional processor to obtain more accurate and stable photonic computing. The photonic neural network with advantages of low power-consumption and high processing speed, will facilitate future large-scale optical communication and data switching.
Funding
National Key Research and Development Program of China (No.2021YFB2801804); Shanghai Municipal Science and Technology Major Project (2021SHZDZX0103); Peng Cheng Laboratory project (No. PCL2021A14); National Natural Science Foundation of China (No.61925104, No.62031011).
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.
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