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In this paper, a full-duplex (FD) amplify-andforward (AF) relay is designed to compensate for the duplexing loss of the half-duplex (HD) AF relay. In particular, when there is no direct link between a source and a destination, joint analog domain self-interference suppression and digital domain residual self-interference cancellation is considered with an FD-AF relay having single receive antenna but multiple transmit antennas. Unlike previous approaches, a nonconvex quadratically constrained quadratic programming problem is formulated to find the optimal solution. The end-to-end spectral efficiency or, equivalently, the end-to-end signal-to-interference-plus-noise ratio from the source to the destination is chosen as the objective function to be maximized subject to the average transmit power constraint at the relay. In addition, an average power constraint is imposed on the output of the relay's receive antenna to avoid the nonlinear distortion in the low noise amplifier and the excessive quantization noise in the analog-to-digital converter. Through the systematic reduction and the partitioning of the constraint set, the optimal solution is derived in a closed algorithmic expression and shows how it allocates the transmission power not only in the direction of maximal performance improvement but also in the orthogonal direction in order to balance the system performance and the amount of self interference. It is shown that the optimal FD-AF relay significantly outperforms the optimal HD-AF relay even with the hardware limitations in the RF chain of the relay's receiver being well taken into account.Index Terms-Full-duplex relay, amplify-and-forward relay, self-interference cancellation, nonconvex quadratically constrained quadratic programming.

In this paper, a joint analog and digital domain selfinterference 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.

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