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The parametric estimation of Multiple-Input Multiple-Output (MIMO) channels is an important step towards the space-time characterization of the radio channel as well as for the design of efficient space-time signaling techniques. In this paper, we address the problem of multipath parameter estimation for frequency-selective block-fading MIMO channels by means of parallel factor (PARAFAC) analysis -. First, we present a fourth-order PARAFAC model for a specular MIMO radio channel, which jointly captures the space-time signature (angles of arrival, angles of departure and delays) and the time-varying fading amplitudes. Based on this model, an Alternating Least Squares (ALS) algorithm is used for estimating the multipath signals from a collection of received data blocks. After the multipath resolution stage, final estimates of the angles, delays and fading amplitudes are obtained by exploiting the knowledge of a multi-block training sequence. Numerical results are provided to illustrate the performance of this estimation approach.