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In a wide band and multipath rich environment, precise channel estimation allows authenticating the source and protecting the integrity of a message at the physical layer without the need of a pre-shared secret key. This allows also a reduction of the burden on the authentication protocols at higher layers. In this paper we develop an authentication scheme in the framework of hypothesis testing that suits a multiple wiretap channels environment with correlated fading, as is the case of multiple input multiple output (MIMO) systems and/or orthogonal frequency division multiplexing (OFDM) modulation. By allowing some degree of correlation among the channels, we formulate the optimal attack strategy for the cases of both single attempt and multiple repeated trials. For the latter scenario, due to the complexity of the optimal solution, we also develop a simpler suboptimal attack strategy. The performance of the proposed methods is evaluated in a MIMO/OFDM scenario and numerical results show the merits of the proposed approaches that can be adopted as a layer one authentication mechanism.