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/-16QAM/-32QAM/-64QAM/-128QAM signals. The performance of the proposed scheme was numerically verified in 28GBaud 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, 16QAM, 32QAM, 64QAM, and 128QAM 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, 16QAM, 32QAM, 64QAM, and 128QAM 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