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We propose an accurate and low-complexity blind adaptive algorithm for chromatic dispersion (CD) compensation and estimation in coherent optical systems. The method is based on a Frequency Domain Equalizer (FDE), a low complexity Time Domain Equalizer arranged in a butterfly structure (B-TDE) and an Optical Performance Monitoring (OPM) block in a loop configuration. The loop is such that, at each iteration, the CD value compensated by the B-TDE and estimated by the OPM is given to the FDE; according to this estimation, in the subsequent iteration, the FDE compensates also this quantity. The procedure is repeated until the majority of CD is compensated by the FDE and a small residual quantity is compensated by a low complexity B-TDE with a small number of taps. The method is extended to long haul uncompensated links exploiting the information on the mean square error (MSE) provided by the B-TDE. The proposed algorithm is then experimentally validated for a polarization multiplexed quadrature phase shift keying (PM-QPSK) signal at 112 Gbit/s propagating along 1000 km of uncompensated Z PLUS® optical fiber. A statistical analysis of the performance of the proposed solution, in terms of mean value and standard deviation of the CD estimation error, is carried out, running a set of simulations including different impairments, such as noise, polarization dependent loss, polarization mode dispersion and self-phase modulation in a line of 1000 km of uncompensated G.652 optical fiber. Our method could be used to compensate and estimate any CD quantity without increasing the number of taps in the B-TDE and exploiting devices already included in the system (TDE, FDE and OPM) arranged in a loop.