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CPM modulation index estimation using LS and BLUE methods

In this paper, we propose two methods for blind estimation of modulation index of full‐response binary continuous phase modulation (CPM) scheme. Most of previous works assume that there is a single sample for each symbol; thus, they cannot improve their performance when sampling rate is bigger than symbol rate. In our proposed methods, modulation index is estimated using samples of autocorrelation function of the received signal, which is a nonlinear function of modulation index. We propose Taylor expansion for approximating this nonlinear function by a linear function. Then, by choosing some samples of the autocorrelation function, we estimate the modulation index with the least square (LS) estimator. For decreasing estimation errors, in the second proposed method, we apply the statistical properties of the autocorrelation function estimation errors, to design the best linear unbiased estimation (BLUE) estimator. The numerical performance analysis in terms of mean‐squared error (MSE) and bit error rate (BER) shows that the proposed methods outperform the reference methods in accurate estimation of the modulation index.