Frequency offset estimation for nonlinear frequency division multiplexing with continuous spectrum modulation.

Carrier frequency offset (CFO) estimation is very important for the optical fiber communications and has been studied widely in linear coherent systems, while only a few works have been reported for nonlinear Fourier transform (NFT) based systems. In continuous spectrum (CS) modulation nonlinear frequency division multiplexing (CS-NFDM) systems, frequency offset (FO) has a great influence on its performance, requiring an improved frequency offset estimation (FOE) method. We found that the oversampling rate R adopted in NFDM to ensure the accuracy of the NFT and inverse NFT (INFT) calculations, would cause the estimation accuracy of the traditional FFT-FOE method to decrease by R times. Moreover, CS-NFDM signals with higher baud rate require more subcarriers and then result in an oversampling factor greater than 16. This makes the traditional FFT-FOE method be ineffective to use the common training sequence (TS) overhead to meet the FOE error requirement of CS-NFDM system. Therefore, a modified FOE method based on FFT assisted by TS and autocorrelation has been proposed. The theoretical analysis and simulation results show that the proposed method is applicable to CS-NFDM system, no matter what modulation format is used. For 512 subcarriers, with a high rate of 70GBaud and the TS length of 8192, the proposed method can obtain a minimum FO estimation error about 0.1 MHz, which is better than the other two typical FFT-FOE and Schmidl & Cox methods. In addition, the proposed method can save at least 87.5% and 50% overhead. Thus, the proposed method has obvious improvement for CS-NFDM system with requiring high oversampling rate.