###### Abstract  
Modulation format identification (MFI) is one of the most critical functions embedded in digital coherent receivers in elastic optical networks (EONs). In view of inherent amplitude and phase characteristics of received signals, different modulation formats exhibit a set of notable features in the polar coordinate system, based on which an MFI scheme incorporating the Gaussian weighted k-nearest neighbors (KNN) algorithm was proposed to identify polarization division multiplexed (PDM)-QPSK/-16 QAM/-32 QAM/-64 QAM/-128 QAM signals. The performance of the proposed scheme was numerically verified in 28 GBaud coherent optical communication systems. The numerical simulation results show that, to achieve 100% correct identification rates for all of the five modulation formats, the required minimum optical signal-to-noise ratios (OSNRs) were less than their relevant thresholds corresponding to the 20% forward error correction (FEC). The tolerable ranges of the residual chromatic dispersion (CD) for QPSK, 16 QAM, 32 QAM, 64 QAM, and 128 QAM were \(-\)1920 ps/nm\(-\)1920 ps/nm, \(-\)720 ps/nm\(-\)360 ps/nm, \(-\)1200 ps/nm\(-\)1680 ps/nm, \(-\)600 ps/nm\(-\)360 ps/nm, and \(-\)600 ps/nm\(-\)480 ps/nm, respectively. Meanwhile, the results demonstrate the maximum tolerable differential-group delay (DGD) for the QPSK, 16 QAM, 32 QAM, 64 QAM, and 128 QAM signals were 34 ps, 16 ps, 20 ps, 6 ps, and 1.2 ps, respectively. In addition, the simulated results also show that the proposed MFI scheme is robust against the fiber nonlinearities, even if the launch power is increased to 4 dBm. m _et al._Article  
15 January  
the operation of its embedded digital signal processing (DSP) modules and demodulation of received signals, as such without the assistance from a corresponding supervisory control layer. Previously reported modulation format identification (MFI) schemes for the digital coherent receivers can be generally classified into the following two categories: (1) Schemes based on Stokes space [5, 6, 7, 8, 9, 10, 11, 12, 13]. These schemes are not sensitive to carrier phase noise, frequency offset, and polarization mixing. However, it is difficult for these schemes to identify high-order modulation formats that have a large number of clusters. (2) Schemes based on signal characteristics obtained after the constant modulus algorithm (CMA) equalization [14, 15, 16, 17, 18, 19, 20, 21, 22]. The CMA is capable of compensating for the residual chromatic dispersion (CD) and polarization mode dispersion (PMD) effects, thus resulting in the enhanced MFI performance tolerance against residual CD and PMD. However, as the CMA equalization is placed in the middle of DSP chain where phase noise is not eliminated yet by the carrier phase recovery algorithm, only amplitude information can therefore be identified in these schemes [14, 15, 16, 17, 18, 19, 20, 21, 22]. To minimize the influence of phase noise, some approaches including differential-phase [23], fractal dimension (FD) and gray-level co-occurrence matrix (GLCM) [24], principal component analysis (PCA), and singular value decomposition (SVD) [25] can be employed in the MFI schemes. Meanwhile, in order to utilize detailed phase information, a blind phase search strategy of 4 QAM (4 QAM-BPS) can also be introduced to roughly recover the phase of the CMA-equalized signals before the MFI operation [26]. Nevertheless, in addition to complicated feature-extraction [24], these schemes [23, 25, 26] can just identify the highest order modulation format of up to 64 QAM. In this paper, an MFI scheme using features in the polar coordinate system is proposed for digital coherent receivers. Firstly, the phase of a CMA-equalized signal was roughly recovered by using 4 QAM-BPS, as the phase pre-compensation does not require any modulation format information. The signal was then converted into the polar coordinate system to better characterize the notable features of a modulation format [27].