A Method of Moments Estimator for Modulation Index of Continuous Phase Modulation

A novel non data-aided estimator based upon the method of moments is proposed for estimating the modulation index of continuous phase modulation (CPM) schemes. Analytical expressions are derived for the asymptotic (large data record N) mean and variance of the estimator using truncated Taylor series. It is shown that the estimator is asymptotically unbiased and has variance that depends upon the modulation index, which decreases as $O(N^{-1})$. Numerical simulations are performed to study the convergence of mean and variance of the estimator to their respective asymptotic values. The performance comparison establishes that the proposed estimator outperforms state-of-the-art estimators in the low signal-to-noise ratio regime.