EM-Based Joint Channel Estimation and Detection for Frequency Selective Channels Using Gaussian Message Passing

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It has been recently shown that the expectation-maximization (EM) algorithm may be viewed as message passing in factor graphs, and in particular, for a linear Gaussian system (with unknown coefficients), the EM algorithm may be purely implemented with Gaussian message passing. In this work, with a Gaussian assumption of the data symbols and a Forney-style factor graph representation for single-carrier transmission over frequency selective channels, a Gaussian message passing EM approach for joint channel estimation and detection is developed. The complexity of the proposed approach grows logarithmically with the length of the observation vector, enabling an efficient handling of (quasi-static and time-varying) frequency selective channels with a large number of channel taps.