###### Abstract  
Nonlinear impairment is one of the critical limits to enhancing the performance of high-speed communication systems. Traditional digital signal processing (DSP)-based nonlinear channel equalization schemes are influenced by limited bandwidth, high power consumption, and high processing latency. Optoelectronic reservoir computing (RC) is considered a promising optical signal processing (OSP) technique with merits such as large bandwidth, high power efficiency, and low training complexity. In this paper, optoelectronic RC was employed to solve the nonlinear channel equalization problem. A parallel optoelectronic RC scheme with a dual-polarization Mach-Zehnder modulator (DPol-MZM) is proposed and demonstrated numerically. The nonlinear channel equalization performance was greatly enhanced compared with the traditional optoelectronic RC and the Volterra-based nonlinear DSP schemes. In addition, the system efficiency was improved with a single DPol-MZM. reservoir computing; nonlinear channel equalization; optoelectronic; communication +
Footnote †: journal: _Photonics_  
Reservoir computing (RC) brings a drastic simplification of the system design to the feedback ANNs in an easily trainable manner. Compared with conventional feedback ANNs, RC only needs to train the output connection weight matrix, and the other connection matrices are randomly generated. The principle of RC dramatically reduces the computational complexity of feedback ANNs, and it also overcomes the problem of fading memory. The coefficients of the readout layer can be computed by solving linear equations. Therefore, RC is a promising method to solve the nonlinear channel equalization problem in communication systems. The hardware implementation of RC can be realized with pure electrical methods [8], optoelectronic methods [9], and all-optical methods [10; 11; 12]. The main difference among these methods lies in the categories of the components that make up the RC. The pure electrical method is designed with pure electrical devices [8] in which the bandwidth is limited and the power consumption is high. Comparatively, optical signal processing (OSP) methods provide new insight into the design of RC schemes. The optoelectronic and all-optical RC schemes are favored thanks to their higher bandwidth, faster processing speed, and lower power consumption than pure electrical methods [11]. In [10], the all-optical RC is realized with a simple optical delay feedback loop, using semiconductor optical amplifiers to provide a nonlinear transformation function. Still, its performance might be influenced by its internal noise. In [12], the delay RC system based on a semiconductor laser was studied using the phase response of the laser. The RC with a parallel processing scheme is also an important developing trend in nonlinear signal processing [13; 14; 15; 16]. In [13], an on-chip architecture for parallel photonic RC is proposed employing multiple electronically tunable delay lines with an electronically tuned switch. In [14], a new hidden layer is introduced to form an RC structure with two different feedback delay loops and dual nonlinear nodes. However, the rich parallelism of optics is not utilized in these schemes, and multiple discrete components are required in the parallel RC systems to act as the nonlinear activation units, which will deteriorate the systems' efficiency and performance. Moreover, the optimization of parallel RC in terms of nonlinear channel equalization has not been analyzed in detail. In this paper, we innovatively explore the potential of the optics parallelism in parallel RC, propose to utilize the optical polarization multiplexing scheme to enhance the RC system's efficiency and performance, supported by a novel double-loop scheme with a dual-polarization Mach-Zehnder modulator (DPol-MZM). Therefore, only one modulator is required to perform as the nonlinear activation unit for the parallel RC loops. We compared the internal dynamics of this novel RC structure with the typical single-loop RC through a numerical study.