# Integrated Photonic Neural Networks for Equalizing Optical Communication Signals: A Review
## 5 Applications of Photonic Neural Networks for Equalizing Optical Communication Signals
published results of a small optical perceptron composed of four waveguides to compensate for chromatic dispersion in fiber-optic links [80]. The photonic device was designed, fabricated, and subsequently tested experimentally with optical signals at a rate of 10 Gb/s after propagation through distances of up to 125 km of optical fiber. During the learning phase, a separation loss function was optimized to separate the transmitted levels of 0s from 1s as much as possible, which automatically implies an optimization in the BER. The tests performed with this photonic neural network revealed that the excessive losses introduced by the device (greater than 6 dB) were compensated by the gain in the equalization of the transmitted signal for transmission distances of more than 100 km [80]. Furthermore, the measured data were reproduced by a simulation model that simultaneously considered the optical transmission medium and the photonic device. This allowed for simulating of the performance of the photonic neural network for data rates higher than 10 Gb/s, where the device presented improvements concerning the current state of the art [80]. For example, one of the experimental results obtained in this work is illustrated in Figure 11.  
Looking to extend the applicability of the integrated photonic neural networks for equalizing optical communication signals, [PERSON] et al. demonstrated a photonic neural network with eight waveguides for chromatic dispersion compensation of a pulse-amplitude modulation 4-level (PAM4) signal propagating in a 50 km optical fiber [78]. With a greater number of delay lines, the processing capacity of the photonic neural network increases; however, this comes at the cost of increased insertion loss of the device. To date, OOK, PAM2, and PAM4 signals have been equalized by photonic neural networks. In this regard, seeking to explore the optical correction of signals with other modulation formats in addition to those already investigated to expand the applicability of photonic neural networks, [PERSON] et al. [81], experimentally demonstrated the recovery of an orthogonal frequency-division multiplexing (OFDM) signal propagating over 125 km of optical fiber employing a photonic neural network. Ongoing studies have already revealed that this approach allows corrections to be performed on the distorted OFDM signal directly in the optical domain, pre-equalizing it by the photonic device, as illustrated in Figure 12.  
Figure 10: BER as a function of the target symbol for the binary pattern recognition task. Different colored bars refer to different bit rates. Transparent bars refer to a BER value equal to the statistical limit. Reproduced without modification from [PERSON]. [PERSON] et al. [76], © 2022, licensed under a Creative Commons Attribution International License 4.0 (CC BY 4.0). Furthermore, to demonstrate the robust performance of photonic neural networks for equalizing optical signals, [PERSON] et al. [81] evaluated constellation diagrams of an OFDM signal after propagation over 125 km of standard single-mode fiber with and without the photonic neural network device. This analysis is presented in Figure 13. Specifically, Figure 13a exhibits the significant impact of chromatic dispersion on the transmitted signal when no equalization techniques are applied. Even in this worst-case scenario, the distorted ODFM signal is adequately restored after using the photonic neural network, delivering a well-defined constellation diagram, as illustrated in Figure 13b [81]. Also, [PERSON] et al. demonstrated a multi-wavelength photonic recurrent neural network for channel distortion compensations in a 56 Gbaud WDM PAM4 communication system [77]. Simulations have shown that this photonic recurrent neural network can outperform the digital maximum likelihood sequence estimation and the feedforward neural network equalizer in optimum Q-factor and launch power metrics [77].