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As optical networks continue to grow towards high capacity and high flexibility, new transmission technologies are being introduced. In order to maintain the quality of signal and control over network in the transparent domains, optical performance monitoring (OPM) systems are becoming a necessity. Phase modulation formats emerge as the solution of choice in transparent domains because of their sensitivity, spectral efficiency, and resilience to optical impairments. In this paper, we demonstrate a flexible OPM method for phase-modulated signals using asynchronous amplitude histogram analysis. We show numerically and experimentally the monitoring of optical signal-to-noise ratio (OSNR), chromatic dispersion (CD), and polarization-mode dispersion (PMD) for differential phase-shift keying (DPSK) and differential quadrature phase-shift keying (DQPSK) signals. The OSNR can be measured within range of 20-35 dB and accumulated chromatic dispersion between 600 and 600 ps/nm. The asynchronous amplitude histogram monitoring method is proved to be a precise and versatile monitoring tool for high-capacity optical networks.