Coherent Optical Orthogonal Frequency Division Multiplexing (CO-OFDM) system with Pilot-free phase noise compensator was introduced in order to accomplish the need of high spectral efficiency in the optical communication. In CO-OFDM system Discrete wavelet packet transforms (DWPTs) in place of Fast Fourier Transforms (FFTs) had attracted more attention since it has removed the need of cyclic prefix used to compensate fiber dispersion. In this paper, a DWPT based CO-OFDM system with Wilcoxon Robust Extreme Learning Machine based pilot-free phase noise compensator using multi-level QPSK partitioning of 16-QAM has been proposed. From the results of this work it has been seen that the percentage improvement in performance (in terms of Q-Factor) and spectral efficiency over traditional pilot-aided techniques is approximately 6 and 21 respectively. Moreover, this proposed work will comparatively reduce the overall system complexity.