Performance degradation of digital modulation schemes caused by random-walk phase noise

Real oscillators experience spectral broadening due to internal noise processes. The key function of the carrier phase tracker in a data receiver is to track out these noise perturbations while rejecting additive white Gaussian noise introduced by the channel. This disturbance is modeled as random-walk phase noise, and optimal estimation theory is applied to establish a lower bound on the phase error variance and obtain its probability density function. Combining this with the modified Euclidean distance, the union bound technique is used to obtain irreducible bit error rates for common digital modulation schemes with oscillator phase noise variance as a parameter. Comparing these results with phase trackers currently in use establishes the potential gains still available. bit-error-rate performance using the analog phase lock loop did not deviate significantly from that of the optimum zero-lag phase tracker