# Design and Research of Photonic Reservoir Computing for Optical Channel Equalization
## 3 Results and Discussion
### Equalization Performance for Different Types of Noise  
In optical communication systems, dispersion generated by optical fibers and ASE noise caused by amplifiers are the main types of noise. To thoroughly verify the impact of single-type noise on the equalization performance of different reservoir layouts, the distorted signals are discussed under the condition of considering only dispersion noise and ASE noise. When generating single-type noise signals, an ideal signal generation system is used. The degree of noise is controlled through simulation parameters during transmission. Dispersion noise is obtained by transmitting through a special fiber model that only has dispersion parameters over distances of 10 km, 15 km, 20 km, and 25 km. ASE noise is simulated using Gaussian white noise and obtained under optical signal-to-noise ratio (OSNR) conditions of 0 dB, 5 dB, 10 dB, and 15 dB. When verifying the equalization performance, the reservoir parameters of each layout are adjusted to their optimal values. The equalization results of dispersion noise are shown in Figure 7a. When dealing with 10 km of fiber dispersion noise, the 24-node layout achieves the best equalization performance with a BER of 1.416 \(\times\) 10\({}^{-14}\), which is followed by the 12-node layout, then the 48-node layout, and finally the 36-node layout. The worst performance has a BER of 7.449 \(\times\) 10\({}^{-9}\). Under these conditions, the extreme difference in the equalized signal's BER between the four layouts exceeds five orders of magnitude. According to mathematical principles, PhRCs with more nodes should possess greater capability and thus achieve better equalization performance. However, the simulation results show an opposite trend, when the transmission distance is less than 15 km. The reason for this phenomenon is that the BER of the distorted signal of 15 km is 2.043 \(\times\) 10\({}^{-3}\), suggesting that the distortion is not significantly severe. Layouts with fewer nodes are fully capable of handling this level of distortion. Additionally, layouts with a greater number of nodes suffer from higher insertion losses, which reduces the power of the equalized signal. As a result, layouts with more nodes exhibit inferior equalization performance in this scenario. However, when the transmission task exceeds 20 km, the equalization performance improves with an increase in the number of nodes. This is because the BER of the distorted signal reaches as high as 1.549 \(\times\) 10\({}^{-1}\) at 25 km, making the computational capability of reservoir structures with fewer nodes insufficient. In this scenario, the 48-node layout, which has the largest number of nodes, demonstrates a clear advantage with a BER of 1.373 \(\times\) 10\({}^{-4}\), representing a three-orders-of-magnitude reduction compared to the distorted signal. Therefore, it is necessary to comprehensively consider the computational complexity of the problem and the number of reservoir nodes in PhRC when solving problems of varying complexity to achieve the highest cost-effectiveness. The equalization results of PhRC with only ASE noise in the channel is shown in Figure 7b. As the OSNR increases from 0 dB to 15 dB, there is a downward trend in the equalized signal's BER from four layouts. PhRC has limited equalization performance at high OSNR. When OSNR at 0 dB, the BER of equalized signals from all architectures fails to achieve more than a one-order-of-magnitude reduction compared to the distorted signals. When the OSNR rises to 5 dB, the BER of the distorted signal is 1.506 \(\times\) 10\({}^{-1}\). The equalized signal's BER of the best-performing 48-node layout is 1.465 \(\times\) 10\({}^{-2}\), representing a one-order-of-magnitude decrease. At OSNR values of 10 dB and 15 dB, the optimal layout is the 48-node one, which reduces the BER of the distorted signals by one and three orders of magnitude, respectively. These results indicate that as the impact of ASE noise reduces and OSNR improves, the equalization capability of PhRC becomes stronger.