Blind joint estimation of the technical parameters of continuous phase modulated signals

In this paper, a new non data aided estimator of the technical parameters of Continuous Phase Modulated (CPM) signals is proposed. It consists in estimating jointly the modulation index, the symbol period and the frequency offset. It is based on the following observations. Firstly, the inverse of the index is the smallest positive real number a CPM signal should be raised to in order to generate a deterministic harmonic signal; secondly, the frequencies of the harmonic signal are simply related to the symbol period and the carrier frequency. The asymptotic behavior of the estimation error is studied. If N is the number of signaling intervals, the estimate of the modulation index is shown to converge to a non Gaussian distribution at rate 1/N, while the estimate of the frequency offset and the estimate of the symbol period converge at rate 1/N^3/2. Simulations results sustain our theoretical claims.