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This paper applies large deviations theory (LDT) to the design of efficient importance sampling (IS) simulation of M-ary digital phase detectors subject to random carrier phase drift within symbol interval. Phase tracking is accomplished by extended Kalman-Bucy filters or dedicated stochastic nonlinear filters. The LDT approach relies essentially on the properties of the receiver's error sets, which present unique topological features in an N-dimensional space. We show how to derive the referred topological properties for the particular phase modulating sequences and receiver solutions adopted. The proposed methodologies lead to very high simulation gains both for the assessment of the error floors induced by the random phase drift and for the scenarios where simultaneous random phase and channel noise preclude the derivation of the error regions.