SINR Maximizing Beamforming Schemes for the Full Duplex Amplify-and-Forward Relay Channel

We propose signal-to-interference-plus-noise power ratio (SINR) maximizing rank one beamforming schemes for the full-duplex (FD) relay systems. The non-regenerative amplify and forward (AaF) relay is considered with multiple transmit antennas and multiple receive antennas. The residual selfinterference (SI) after analogue domain processing is to be suppressed by the proposed schemes so that the spectral efficiency of FD can be improved. We first analyze the correlation matrix of SI in a matrix power series and derive a convergent form of the correlation matrix so that the SINR expressions can be identified. Leveraging the structure of the SINR function on the beamformer (BF) vectors and power control parameter, two of the proposed schemes try to maximize SINR by optimizing a BF vector through iterative updates exploiting a bisection type search with the other BF vector being fixed. The third proposed scheme alternates over these two schemes to further enhance them by widening the search space that the BF vectors span. We compare the SINR of the proposed schemes with some reference schemes based on zero forcing approaches, maximum ratio reception, and maximum ratio transmission to characterize the performance improvement of the proposed schemes.