Recently, Professor Lilin Yi's research group (LIFE, Laboratory of intelligent fiber ecosystem) from the Department of Electronic Engineering of Shanghai Jiao Tong University constructed a white-box machine learning algorithm based on the traditional physical model - Volterra-inspired neural network equalizer (Volterra-inspired neural network equalizer) network equalizer, VINN), using the convenient data preprocessing function of neural network (NN), combined with the powerful polynomial term of VNLE (Volterra nonlinear equalizer, VNLE), reduces the complexity of the equalizer and simplifies the optimization process. Realize 30.5dB power budget in 100G PON system. The relevant results were published in the international optical journal "Optics Letters" in October 2022 under the title "Low-complexity Volterra-inspired neural network equalizer in 100-G band-limited IMDD PON system". Doctoral student Huang Luyao is the first author, and Professor Lilin Yi is the corresponding author.

Research Background

As the global data traffic continues to increase, the rate of the passive optical network (PON) has increased significantly, from GPON to 10GPON to 50GPON to 100GPON. The access network is called the "last mile", which is close to the user side and is very sensitive to cost. Therefore, a low-cost power domain equalization algorithm is a good choice. NN and VNLE are effective equalizers. The neural network equalizer has a flexible structure, simple data preprocessing, and is easy to construct various nonlinear functions, while VNLE has concise polynomial terms and a direct optimization process.

However, both equalizers have disadvantages. NN uses fixed activation functions, such as Relu and sigmoid: a large number of redundant nonlinear terms are generated in the process of fitting nonlinear functions, resulting in a waste of computing resources. At the same time, due to its black box characteristics, interpretability is required to apply the key decision-making, such as disease prediction and judicial decisions. The complexity of VNLEs grows power-law with order and memory length: this high complexity makes them difficult to deploy in real-time receivers. Therefore, there is a need for a white-box equalizer model that maintains low complexity while maintaining performance.

Equalizer model

Figure 1 (a) VINN structure; (b) cosine annealing learning rate curve with hot restart; (c) loss curve

The structure of the proposed equalizer is shown in Fig. 1(a). It is divided into three fixed layers: input layer, hidden layer and output layer. The number of hidden layer nodes corresponds to the order of VNLE, thus avoiding almost endless structural optimization like NN. VINN utilizes the classic operations of NN, first performing a linear weighted summation, and then performing a non-linear activation function. Different from the traditional NN, it uses a custom activation function to construct the cross-beat term, which increases the granularity of the solution space while saving computational resources.

During training, if the learning rate is fixed, the performance of VINN is mediocre. The large granularity of the solution space makes it easy to fall into a local optimal solution. Therefore, the learning rate of cosine annealing with hot restart is used to speed up the training process and help the network jump out of the local optimal solution. The learning rate curves and corresponding loss curves are given in Fig. 1(b) and Fig. 1(c), respectively.

Figure 2 (a) Experimental setup of 100Gbps IMDD PON system; (b) Frequency response of back-to-back system; (c ) The eye diagram of the received signal before equalization; (d) The eye diagram of the received signal after equalization

The performance of the proposed VINN equalizer is evaluated in an O-band IMDD PON system as shown in Fig. 2. The transmitted signal is a 50GBaud PAM4 signal, using 10GHz MZM, and the system 3dB bandwidth is 6.11GHz. The digital signal is input into the equalizer after being synchronized, resampled, equalized, judged and decoded. The main impairments of the system are band limitation and device nonlinearity, which need to be compensated by the electric domain equalization algorithm.

Figure 3  12dBm transmit power 100Gbps O-band PAM4 signal sensitivity curve

Test the sensitivity performance of the VINN equalizer in the 100Gbps wire-speed O-band system, and the results are shown in Figure 3. To demonstrate the properties of reducing the complexity of the equalizer and simplifying the optimization process, two cases were tested. One is equalizer performance under constrained complexity, constrained to 50, 100, and 200 MACs; the other is optimal performance of VNLE without MACS constraints and performance of VINN equalizer, exploiting structural hyperparameters of VNLE, including order and memory length.

For the first case, VINN equalizer outperforms VNLE at the same low complexity level. VINN complexity is reduced by 50.5%, and a 1.5-dB sensitivity improvement is achieved. This is because the cross-beat frequency term of VNLE occupies most of the resources, which limits the choice of the number of second-order and third-order inputs. For the VINN equalizer, the second-order and third-order equalizers consume relatively few resources, and can strike a balance between the number of inputs and the cross-beat term.

For the second case, as mentioned earlier, the hyperparameter set (265 25 17) is optimized based on the greedy algorithm, and the structure of the VINN equalizer is also set to (265 25 17). The curves show that they perform identically, both with a sensitivity of -18.5 dBm. In this case, the VINN equalizer has a complexity of 313 MACs, while the VNLE has a complexity of 3822 MACs. The VINN equalizer achieves the same 30.5dB power budget as the VNLE with less complexity.

In this work, we propose an efficient white-box low-complexity VINN equalizer by incorporating the physics of VNLE into NN. The effectiveness of the equalizer is verified in the 100Gb/s rate band-limited IMDD PON system. When the computational complexity is limited to the same level, the performance of VINN equalizer is better than that of VNLE; optimizing VINN based on the order and memory length of VNLE can achieve similar performance to VNLE under the condition of lower complexity. With 313 MACs, a power budget of 30.5 dB is obtained. In the future, the equalizer will be further deployed in the FPGA to verify the reliability and efficiency of VINN in real time, and save hardware computing resources while maintaining the high performance of the high-speed communication system.

The LIFE research group has been committed to the algorithm design, system architecture design, and intelligent development of optical fiber communication systems. At present, the research group conducts in-depth research on channel equalization in the optical access network, automatic optimization of the equalizer by reinforcement learning, global optimization of end-to-end performance, new P2MP architecture based on coherent detection, and FPGA implementation and deployment, contributing to the sustainable development of the optical access field . The work in this direction is supported by the Outstanding Youth Fund of the National Natural Science Foundation of China (62025503), the Key Research and Development Program of the Ministry of Science and Technology (2019YFB1803803), and the Shanghai Jiaotong University-Huawei Advanced Optical Technology Joint Laboratory.
For the implementation details of the equalizer and detailed result analysis, please refer to the original text
The full text of the paper: https://doi.org/10.1364/OL.474900