Feature Issue on Optical Performance Monitoring (OPM). A new technique for monitoring the signal-to-noise ratio (SNR) of a randomly modulated optical data signal is proposed and demonstrated. The signal is detected and then subjected to a narrowband rf demodulation at precisely half the data clock frequency. Because of symmetries present in the modulation spectrum at the half-clock frequency, the demodulated signal is confined to a single dimension in the recovered phase space. In contrast, the noise power is distributed isotropically within the phase space, and the SNR is measured by taking the ratio of the power recovered along the signal dimension to the power recovered along the orthogonal dimension. The narrowband nature of the measurement makes it highly sensitive. The technique is demonstrated for return-to-zero modulated data at 10 Gbits/s, where it accurately tracks OSNR variations from 10 to 26 dB with only -24 dBm of optical input. The measurement is also shown to be sensitive to chromatic dispersion and can be made to track OSNR variations in the presence of large amounts of chromatic dispersion with vestigial sideband optical filtering. These properties make this technique an ideal candidate for optical performance monitoring in transparent optical networks, where a sensitive, low-cost monitoring solution is needed for effective fault localization.