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Doubly-Selective Channel Estimation for Continuous Phase Modulation

In this paper, we present two Data-Aided channel estimators for Continuous Phase Modulation (CPM) in the case of transmissions over doubly -selective channels. They both capitalize on the Basis Expansion Model (BEM), widely used for OFDM systems and for Single Carrier transmission with linear modulation. However, in the case of CPM signals, we need to work on a over-sampled received signal (fractionally-spaced representation) as the equalization techniques are also working on the over-sampled received signal. The first one is a classical Least Squares (LS) estimation of the BEM parameters whereas the second channel estimator introduces first a parametric dependence on the paths delays. Indeed, in the case where those delays are known (by estimation or by geometrical consideration as for the aeronautical channel by satellite), the second LS estimation on the BEM parameters is improved and less computationally demanding. Simulations results are provided and show good performance of our parametric LS estimation.