In-band (cochannel) full-duplex multiple-Input multiple-output (MIMO) radios employ independent transmit and receive antenna arrays to enable simultaneous transmission and reception. One of the most significant challenges is the mitigation of the radio's self-interference. While there are numerous issues, such as dynamic range, that limit the ability of the radio to mitigate the interference, in this paper effects associated with self-interference channel estimation are considered. In this paper, adaptive transmit processing is used to protect the radio's receive antenna array from self-interference. We develop bounds on post-mitigation self-interference residual to provide guidance on the amount of training required to effectively remove channel estimation as a limiting concern. To allow extending the system dynamic range beyond the dynamic range of the receiver, we consider using a training signal that is lower in transmit power than the data signal. As a specific example, the three-node relay problem is explored. Simulation results are presented to demonstrate the validity of the bound.