# Design and Research of Photonic Reservoir Computing for Optical Channel Equalization
## 1 Introduction  
The increasing communication signal speed in optical fiber communication links rapidly intensifies signal distortion over the same transmission distance, significantly increasing the difficulty of equalization, which obstructs the upgrade and expansion of traditional intensity modulation direct detection (IMDD) communication systems [1, 2]. In optical channels, signals are subject to linear noise, such as dispersion, nonlinear noise, such as self-phase modulation (SPM) noise, and noise generated by imperfections in amplifiers, such as amplified spontaneous emission (ASE) noise [3]. To mitigate the impact of noise on signals, the mainstream channel noise equalization scheme is based on digital signal processing (DSP) technology using electronic chips [4, 5, 6, 7]. However, due to the gradual failure of Moore's Law, equalization schemes based on DSP chips have difficulty supporting the continued development of signal rates. And it requires a trade-off between power consumption due to computational complexity and equalization performance [8, 9]. Artificial neural networks (ANNs) possess the advantages of strong flexibility and high universality [10]. Compared to DSP technology, ANNs have a simpler training principle and require fewer hyperparameters to adjust [11]. Therefore, the use of ANNs for distortion equalization has been widely discussed, especially recurrent neural networks (RNNs) [12, 13] with recurrent memory characteristics. Reservoir computing (RC) is a form of RNN characterized only by the need to train the weights of the readout layer, while other weights are randomly generated and kept fixed [14, 15, 16]. As a result, the trainingdifficulty of RC is much lower than that of other types of RNN, significantly reducing computational complexity and power consumption. However, RC based on electronic chips [17] still suffers from the separation of storage and computation latency inherent in the von Neumann architecture. And its computing speed is limited by advancements in the fabrication process of transistors. In addition, electronic chips also lose some phase information of optical signals due to the influence of the square-law relationship between optical intensity and current in photoelectric conversion. The photonic reservoir computing (PhRC) chip can directly input optical signals, thereby increasing the bandwidth of signal processing and reducing latency [18; 19; 20; 21]. Currently, the mainstream photonic reservoir computing schemes are classified into two types: virtual node-based and spatial node-based [22; 23; 24; 25]. The virtual node-based scheme employs a loop as the primary structure, using the concept of time-division multiplexing to realize the functionality of the reservoir [26]. However, its nodes have highly fixed connectivity, limiting their parallelism and flexibility. On the other hand, the spatial node-based scheme utilizes discrete devices to represent each node, which form a complex nonlinear dynamical system in physical space [27]. The selection of node devices in this type is highly flexible, such as directional couplers (DCs), multimode interferometers (MMIs), and micro-ring resonators (MRRs). Furthermore, the connections between the nodes of a spatial node-based scheme can have more variety, enabling more complex designs and subsequently enhancing the equalization performance of reservoir channels. When the input and readout layers are positioned outside the reservoir, it facilitates easier design. In spatial-node-based PhRC, which employs internal nodes for both input and output purposes, the input and output waveguides create crossings as they traverse waveguide delay lines. Furthermore, if internal nodes are used only as input nodes and not as output nodes, this results in unused output ports, ultimately causing power loss. In this paper, we propose four rectangular reservoir structures with varying numbers of nodes for channel equalization in IMDD systems.