Abstract
Linear minimum mean square error (LMMSE) is by definition the optimal channel estimator in the sense of mean square error criterion, but its practical application is limited by its high complexity. Furthermore, the LMMSE estimation method requires the knowledge of both the channel and the noise statistics, which are a priori unknown at the receiver. A wide range of techniques are proposed in the literature in order to overcome these two drawbacks. In this study, the authors give an overview of the LMMSE-based channel estimation in an orthogonal frequency division multiplexing (OFDM) context. A didactic reminder concerning the basics of LMMSE estimation and its performance is provided, and a survey of techniques of the literature, which enable the practical application of LMMSE and the reduction of its complexity, is presented in both single-input single-output and multiple-input multiple-output contexts. Finally, some perspectives are provided, in particular the application of the LMMSE estimator to flexible waveforms beyond OFDM.
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