Chromatic dispersion (CD) dynamic monitoring and compensation technique by using peak to average power ratio (PAPR) to as a feedback is used in coherent communication system , and this method is insensitive for pattern, polarization mode dispersion and polarization dependent loss. Because the smallest PAPR typically corresponds to the CD that results in the best performance, PAPR is used as feedback signal. We search PAPR minimum through direct search and two step search algorithms in frequency compensation. CD compensation value is the accumulated value in the link. The average errors of two methods to monitor CD are 312 ps/nm and 226 ps/nm. Therefore two search algorithm has lower complexity, and higher sensitivity.