Carrier Frequency Offset Estimation in Burst-Type CPM via the EM Algorithm

In this work, the continuous phase modulation (CPM) with short block lengths (up to 128 symbols) is considered as a waveform, which is used e.g. in tactical networks. In order to deploy an optimal coherent detector, among other parameters as e.g. carrier phase or symbol timing, the carrier frequency has to be estimated. It is proposed to use the expectation maximization algorithm (EM) for a maximum likelihood estimation. It is pointed out why finding a suitable starting value, so that the EM does not converge to a local maximum of the likelihood function, is non-trivial in this case. Based on the insights given on the likelihood function in this case, an algorithm to tackle that issue and to ensure convergence to the global maximum is formulated. The algorithm's performance is evaluated in terms of estimation error variance, including a comparison to the theoretical limit, and in terms of bit error rate, where it is compared to the perfectly synchronized receiver. The algorithm's robustness against unknown carrier phase is investigated and its computational complexity is reflected.