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We consider the problem of channel estimation in a multiple-input-multiple-output (MIMO) full-duplex (FD) wireless communication system assisted by a reconfigurable intelligent surface (RIS) with hardware impairments (HI) occurring at the transceivers and RIS elements. We propose an unbiased channel estimator that requires knowledge of only the first and second order statistics of the HI, for which we derive closed form expressions. The proposed estimator reduces to the maximum likelihood estimator in the case of ideal hardware. We also describe a FD pilot scheme that significantly reduces the computational complexity of obtaining this channel estimate. We verify the performance of the estimator under varying conditions of transceiver and RIS HI via numerical simulations.

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