# Integrated Photonic Neural Networks for Equalizing Optical Communication Signals: A Review
## 1 Introduction
To overcome the current limitations of classical neural networks operating in the electronic domain, a groundbreaking era of artificial intelligence governed by integrated photonic neural networks has received much attention in recent years [58; 59; 60; 61; 62; 63; 64; 65]. Exceptionally, photonic neural networks can operate in the optical domain, being energy-efficient, noise-resilient, and working at high speed [66; 67; 68], opening possibilities for real-time applications, even in the most critical scenarios [69]. At the same time, their integration on a chip paves the way for a cost-effective manufacturing process [60]. In terms of applications, photonic neural networks have recently been applied for image classification [70], pattern recognition [71], and image detection [72]. Currently, photonic neural networks have also been successfully employed in optical communications to compensate for distortions in signals transmitted through optical fiber links. These investigations include signals with different modulation formats, with data rates ranging from 10 Gb/s to 40 Gb/s over transmission distances ranging from 15 km to 125 km [73; 74; 75; 76; 77; 78; 79; 80; 81]. The main neural network architectures employed to date for equalizing optical communication signals are reservoir computing and perceptron. The main difference between perceptron and reservoir photonic neural networks is their architectural design, which directly affects their ability to handle specific signal equalization tasks. Specifically, all weights in the perceptron neural network structure are adjusted during the training phase. On the other hand, in photonic reservoir computing neural networks, only the output layer weights are adjusted, which can be achieved through a simple linear regression, making the training process fast and simple. In this way, the perceptron architecture is more controllable, with targeted weights learned for specific tasks, than reservoir computing photonic architectures. Regarding training, the ridge regression algorithm, the particle swarm optimizer, and the Adam optimizer are the most widely used training algorithms for photonic neural networks for equalizing optical communication signals, delivering bit error rates (BERs) ranging from \(1\times 10^{-3}\) to \(1\times 10^{-7}\)[73; 74; 75; 76; 77; 78; 79; 80; 81]. A detailed discussion of these works is given later in Section 5 of this review paper. In this scenario, this paper discusses the emergence of photonic neural networks as a promising alternative for equalizing optical communication signals distorted by the complex dynamics of the transmission channel. Thus, the remainder of this paper is systematized as follows to present this discussion: Section 2 introduces the principles and main architectures of the photonic neural networks employed as equalizers. Section 3 addresses the training algorithms of the photonic neural networks for equalizing optical communication signals. Section 4 explains the main building blocks of photonic neural networks. Section 5 presents the photonic neural networks recently built for equalizing optical signals and summarizes their main features for this application. The concluding remarks are made in Section 6.