Relay-aided interference alignment for the quasi-static X channel

In this paper, we first introduce a simple procedure for aligning interference directions in an M×N user MIMO X channel. The scheme is then modified for an M×2 user X channel in which each user is equipped with M + 1 antennas. Next we investigate the degrees of freedom (DOF) for a single antenna X channel in slow fading environments with the help of a simple relay. The relay stores all the received signals and sends their linear combination in subsequent transmissions. Using this scheme, it is shown that adding a relay can help the system to achieve all the available DOF. It is also proved that if the relay´s output power scales with P/(log P)^s, there is no loss in the achieved DOF as long as s > 0. In other words, in a network with quasi-static channels, it is possible to achieve a higher DOF through the use of randomizing relays whose powers grow at a much slower rate than the main transmitters. Similarly, when there are stricter constraints on the output power scaling of the transmitters, all the DOF can still be utilized, if the relay power can grow with P/(log P)^t for any t > 0. These results suggest that adding relays to a network can be beneficial in terms of simultaneously acquiring higher DOF.