New interference alignment schemes with full and half-duplex relays for the quasi-static X channel

In this study, two relay-aided interference alignment (IA) schemes are proposed for the quasi-static M × 2 X channel where M is the number of transmitters and two is the number of receivers, respectively. The first scheme utilises one full-duplex relay and the second one utilises two half-duplex relays. In the proposed schemes, the transmitters transmit signals in every time slot and the relays operate in the amplify-and-forward (AF) mode. By verifying the linear independence between the desired signals and the interference, it is shown that the proposed schemes can achieve 2M/(M + 1) degrees of freedom (DoF) which is the maximum DoF for the M × 2 X channel. It is also shown by using the concept of reciprocity that the proposed IA schemes are applicable to the 2 ×M X channel. Finally, through the numerical analysis, it is confirmed that the proposed IA schemes provide good alternatives to the previously known relay-aided IA scheme.