Performances of a non data aided estimator of the modulation index of continuous phase modulations

In this paper, a new non data aided estimator of the modulation index of a CPM signal is proposed. It is based on the observation that the inverse of the index is the smallest positive real number to which the CPM signal should be expanded in order to generate a sinusoid of frequency 1 over 2Ts. The asymptotic behavior of the estimate is studied. If N is the sample size, the estimate is shown to converge to a non Gaussian distribution at rate 1 over N. Simulations results sustain our theoretical claims.