Fixed-point realization of fast nonlinear Fourier transform algorithm for FPGA implementation of optical data processing

Abstract

The nonlinear Fourier transform (NFT) based signal processing has attracted considerable attention as a promising tool for fibre nonlinearity mitigation in optical transmission. However, the mathematical complexity of NFT algorithms and the noticeable distinction of the latter from the "conventional" (Fourier-based) methods make it difficult to adapt this approach for practical applications. In our work, we demonstrate a hardware implementation of the fast direct NFT operation: it is used to map the optical signal onto its nonlinear Fourier spectrum, i.e. to demodulate the data. The main component of the algorithm is the matrix-multiplier unit, implemented on field-programmable gate arrays (FPGA) and used in our study for the estimation of required hardware resources. To design the best performing implementation in limited resources, we carry out the processing accuracy analysis to estimate the optimal bit width. The fast NFT algorithm that we analyse, is based on the FFT, which leads to the O(N log 2 2 N ) method's complexity for the signal consisting of N samples. Our analysis revealed the significant demand in DSP blocks on the used board, which is caused by the complex-valued matrix operations and FFTs. Nevertheless, it seems to be possible to utilise further the parallelisation of our NFT-processing implementation for the more efficient NFT hardware realisation.

Implementing Neural Network-Based Equalizers in a Coherent Optical Transmission System Using Field-Programmable Gate Arrays

“…In this article, we compare the performance of our NN-based equalizers when applying 3-, 5-, 7-, and 9-segment PWL approximations to both tanh and sigmoid. 9 The expressions for the PWL used in this article are included in Table III in Appendix B. The corresponding plots for the equations mentioned in Table III with 3 and 9 segments are depicted in Fig.…”

“…O VER the previous couple of decades, the race to find various compensation methods to mitigate the nonlinearities of the fiber and components has produced several noticeable high-performance solutions [1], [2], [3], [4], [5], [6], [7]. However, due to the high complexity of the proposed solutions, only a few published studies [8], [9], [10], [11] have been conducted to implement these solutions in hardware, e.g., in a field programmable gate array (FPGA) or application-specific integrated circuit (ASIC) Recently, machine learning (ML)-based techniques have started to penetrate more and more into different digital signal processing (DSP) applications. Therefore, it is natural now to consider how nonlinear equalizers may be designed, addressing NN-based setups while simultaneously taking into account the issues of flexibility and computational complexity.…”

“…[62] shows that the implementation of PWL can be further optimized to have zero multipliers by simplifying the shift and addition operations 9. Note that when the number of segments is lower than 3 segments that used to represent sigmoid or tanh in the biLSTM cell, the biLSTM model in our case is not able to learn to mitigate the approximation errors.…”

Serial and Parallel Convolutional Neural Network Designs for NFDM Signals

“…One aspect is the lack of hardware implementation of NFT. Only very recently, hardware implementation was conceptually proposed on an FPGA platform 8 . However, due to the complexity of NFT algorithms, implementing and optimizing the hardware can take years of effects before any products can be built for practical use.…”