An optimal design method of linear processors intended for a multi-input multi-output (MIMO) full-duplex (FD) amplify-and-forward (AF) relay network is presented under the condition of spatial-domain self-interference nulling. This method is designed to suit the availability of channel state information (CSI). If full CSI of source station (SS)-relay station (RS), RS-RS (self-interference channel), and RS-destination station (DS) links are available, the instantaneous end-to-end capacity is maximized. Otherwise, if CSI of the RS-DS link is either partially available (only covariance is known), or not available, while CSI of the other links is known, then the ergodic end-to-end capacity is maximized. Performance of the proposed FD-AF relay system is demonstrated through computer simulations, especially under various correlation conditions of the RS-DS link.