In this paper, we present a novel nonlinear pre-distortion scheme enabled by indirect learning architecture and cross-correlation based behavioral modeling. 120-Gbps PAM-4 error free transmission is demonstrated using 30-GHz class VCSEL. © 2020 The Author(s)
IntroductionAs the society is stepping into the era of information, there emerges evolutionary development of new technologies, such as 5G, AR, VR and HD video. The urgent needs for high speed short-reach data transmission [1] have been the fuel for engine of the development of optical interconnects. As the required data rate for single lane approaching 100 Gbps and 200 Gbps to achieve aggregate 400G even towards 800G/1T transmission capacity, the impact of nonlinearities of optical and electrical devices would become a significant factor for the high speed signals. Thus, it is essential to characterize the nonlinearity of devices and mitigate the impacts of nonlinearities on the signal quality for high speed transmissions.There are many studies investigating methods to mitigate the nonlinearities of optical and electrical devices, such as receiver-side equalization using Volterra nonlinear equalizer (VNLE) and artificial neural network (ANN) [2][3][4] and transmitter-side pre-distortion [5]. As indicated in [6,7], the nonlinear pre-distortion scheme would be more attractive than the receiver-side nonlinear equalization for the following reasons: (1) The SNR at transmitter side is higher than that at receiver side, thus the coefficients estimation would be more accurate at the transmitter side; (2) nonlinear pre-distortion is capable of dealing with the nonlinear distortions before the signal is further distorted by other distortions in the transmission channel. In order to calculate the nonlinear pre-distortion coefficients, the indirect learning architecture (ILA) [8] is proposed for its convenience. In the ILA, in order to process the data offline to avoid real-time processing, the nonlinear characteristic of the devices emulated with Volterra series is proposed where the kernels are obtained using least square (LS) fitting method [5,9]. This fitting method would lead to numerical instability when identifying and extracting the Volterra kernels that describe the nonlinearity of devices [10]. It also requires high computational complexity since in the process of optimizing memory length for each order of kernels to fit the response of the system, each memory length will require a new training process. Kernel estimation based on behavioral modeling [11] using cross-correlation method [12] can directly obtain the kernel distribution for the nonlinear system without need of iterative training, therefore, it can eliminate the shortcomings of the LS fitting method when determine the kernels that emulate the nonlinear system. There also exists pre-distortion scheme using rate equation for vertical-cavity surface-emitting laser (VCSEL) [13] as well as micro-ring modulator (MRM) [14]. However, the rate-equation based pre-distortion scheme cannot compensate nonline...