A Robust Sparse RLS-Volterra Nonlinear Equalizer Using ℓ₀-Regularization for 4 × 150 Gbit/s IMDD-Based Optical Interconnect

Abstract

Volterra equalizer (VE) is a well-known and effective algorithm to deal with the linear and nonlinear distortions in optical interconnect, but the high computational complexity hinders its practical application. Generally, sparse VEs based on ℓ 1-or ℓ 0-regularization are good ways to reduce the complexity by discarding some inessential taps. However, a tap threshold needs to be chosen in these sparse VEs like the threshold-based pruned retraining VE (TR-VE) to decide the discarded taps. And this tap threshold should be adjusted fine to balance the reduced complexity and equalization performance, especially when the testing environments alter. Thus, the reduced complexity in these sparse VEs may fluctuate. To address this issue, a robust and stable complexity reduced sparse VE using ℓ 0-regularization (ℓ 0-SR-VE) is proposed in this paper. The recursive least square (RLS) algorithm is used to replace the least mean square algorithm for the faster convergence speed and better equalization performance. The complexity of this equalizer depends on its parameters but not the tap threshold. Once the equalizer parameters are determined, the complexity would not change with the system characteristics, contributing to higher practicability. In our experiment, a 150 Gbit/s PAM8 signal transmission system based on intensity modulation and direct detection (IMDD) is achieved, and a dual-drive Mach-Zehnder modulator for optical single-sideband signal generation is used to mitigate the power fading effect. The experimental results show that with the help of ℓ 0-SR-VE, the reduced complexity percentage is stable at 66.18% compared with the RLS-based VE, even after 75 km standard single-mode fiber (SSMF) transmission. By using this equalizer, 4×150 Gbit/s PAM8 signals have also been successfully transmitted over 30 km SSMF at C-band. The reduced complexity variation of ℓ 0-TR-VE is >20%, but the reduced complexity of the proposed ℓ 0-SR-VE is stable at 60% even after 30 km SSMF for all four lanes. INDEX TERMS PAM8, IMDD system, data center interconnect (DCI), sparse Volterra equalizer (VE).

Nonlinear Signal Estimation Using Semi-Blind Mutually Referenced Equalizers in Convolutive Mixture

“…The authors in [5] present an adaptive least mean square using truncated Volterra series. In [6], the authors proposed a robust and stable sparse Volterra equalizer that addresses both linear and nonlinear distortions in optical interconnect while also attempting to reduce the Volterra equalizer's computational complexity. This equalizer uses l 0 regularization with a recursive least squares algorithm.…”

Simplified SVM Equalization Algorithm Based on Single Hyperplane Training Enabled 50Gb/s PAM-4/8 With 10-G Optics in NG-PON System

“…To resolve this problem mentioned above, some equalization schemes [9][10][11][12][13][14][15][16][17][18][19] based on digital signal processing (DSP) technology have been presented in high-speed limitedbandwidth NG-PON system. Owing to its simple implementation, strong adaptability, and significant performance improvement [14], the equalization schemes have become the mainstream ISI compensation methods.…”

“…Owing to its simple implementation, strong adaptability, and significant performance improvement [14], the equalization schemes have become the mainstream ISI compensation methods. Among these proposed researches, the commonly used are the feedforward equalizer (FFE) [15], decision feedback equalizer (DFE) [19], and Volterra filter [13], whose tap coefficients are updated through adaptive algorithms such as the least mean square (LMS) algorithm and the gradient least squares (RLS) algorithm [17]. Despite that, these common equalizers have unsatisfactory performances in severely distorted channel transmission systems.…”