ABSTRACT
The result was shown first by Jafar and Shamai [6-8] under the assumption that the channel coefficients are time varying. By using a combination of linear beamforming, symbol extensions and asymmetric complex signaling, Cadambe et al. showed that DoF are achievable on the ×2 2 X-channel even if the channels are held constant, for almost all values of channel coefficients. Motahari [9-10] et al. proposed the framework of rational dimensions which allows DoF to be achieved almost surely even if the channels is fixed and restricted to real values. Thus, regardless of whether the channels are time varying or constant and whether they can take complex or only real values, interference alignment through the X-channel approach allows the ×2 2 IC to achieve DoF for almost all channel coefficient values.
