In this paper, a joint analog and digital domain self-interference cancellation is considered for the full-duplex (FD) amplify-and-forward (AF) relay with a single receive antenna but multiple transmit antennas. Under the assumption that there is no direct link between a source and a destination, the end-to-end spectral efficiency is maximized subject to the average transmit power constraint at the relay. Unlike previous approaches, an average power constraint is imposed also on the output of the relay's receive antenna to take into account the hardware limitations in the RF chain of the relay's receiver. A nonconvex quadratically constrained quadratic programming problem is formulated and the optimal beamforming vector is derived in a closed algorithmic expression through the systematic reduction and the partitioning of the constraint set. It is shown that the FD-AF relay significantly outperforms the half-duplex (HD) AF relay by properly compensating for the duplexing loss of the HD-AF relay.