In this paper, we propose a new MIMO communication system in a time-varying multipath environment, using a Khatri-Rao space-time (KRST) coding combined with a multiple Khatri-Rao product of symbol matrices (MKRSM). It is shown the signals received at the receiver form a tensor which satisfies a (M + 2)-order nested PARAFAC model, where (M − 1) denotes the number of symbol matrices considered for MKRSM coding. Such a generalization of the nested PARAFAC model to (M + N )-order tensors is first studied from a general point of view, with the discussion of some parameter estimation methods depending on the a priori knowledge on the model. Then, a semi-blind receiver composed of three stages, is de-
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