Computational Complexity Optimization of Neural Network-Based Equalizers in Digital Signal Processing: A Comprehensive Approach

Experimental results based on offline processing reported at optical conferences increasingly rely on neural network-based equalizers for accurate data recovery. However, achieving low-complexity implementations that are efficient for real-time digital signal processing remains a challenge. This paper addresses this critical need by proposing a systematic approach to designing and evaluating low-complexity neural network equalizers. Our approach focuses on three key phases: training, inference, and hardware synthesis. We provide a comprehensive review of existing methods for reducing complexity in each phase, enabling informed choices during design. For the training and inference phases, we introduce a novel methodology for quantifying complexity. This includes new metrics that bridge software-to-hardware considerations, revealing the relationship between complexity and specific neural network architectures and hyperparameters. We guide the calculation of these metrics for both feed-forward and recurrent layers, highlighting the appropriate choice depending on the application's focus (software or hardware). Finally, to demonstrate the practical benefits of our approach, we showcase how the computational complexity of neural network equalizers can be significantly reduced and measured for both teacher (biLSTM+CNN) and student (1D-CNN) architectures in different scenarios. This work aims to standardize the estimation and optimization of computational complexity for neural networks applied to real-time digital signal processing, paving the way for more efficient and deployable optical communication systems.