Guiding Blind Transmitters: Degrees of Freedom Optimal Interference Alignment Using Relays

Channel state information (CSI) at the transmitters (CSIT) is of importance for interference alignment schemes to achieve the optimal degrees of freedom (DoF) for wireless networks. This paper investigates the impact of half-duplex relays on the degrees of freedom (DoF) of the X channel and the interference channel when the transmitters are blind in the sense that no ISIT is available. In particular, it is shown that adding relay nodes with global CSI to the communication model is sufficient to recover the DoF that is the optimal for these models with global CSI at the transmitters. The relay nodes in essence help steer the directions of the transmitted signals to facilitate interference alignment to achieve the optimal DoF with CSIT. The general MxN X channel with relays and the K-user interference channel are both investigated, and sufficient conditions on the number of antennas at the relays and the number of relays needed to achieve the optimal DoF with CSIT are established. Using relays, the optimal DoF can be achieved in finite channel uses. The DoF for the case when relays only have delayed CSI is also investigated, and it is shown that with delayed CSI at the relay the optimal DoF with full CSIT cannot be achieved. Special cases of the X channel and interference channel are investigated to obtain further design insights.