Detection of a random amplitude modulation in polynomial phase signals

We consider the problem of detecting the presence of a random amplitude modulation in polynomial phase signals embedded in additive white Gaussian noise. The presence of a random amplitude can be determined by testing the hypothesis that the modulating process has zero variance against the one-sided alternative. Under the assumption that the modulating sequence is Gaussian a likelihood ratio test is derived. A test which uses cyclic moments-based estimators is also proposed. Under the Gaussian assumption and for large sample lengths the cyclic moments-based test has performance equivalent to the likelihood ratio test but requires much less computation. The cyclic moments-based test may still be applied when the modulating sequence is non-Gaussian. Simulation results are presented which indicate the utility of the cyclic moments-based test.