Interference alignment for two-user two-hop interference X-channel with delayed and No CSIT

Capacity approximation of multi-hop unicast and multi-hop multicast channels is one of unsolved problems in information theory. Recently some researches investigate Degrees of Freedom (DoF) characterization and Interference Alignment schemes for these channels. However most of them assumed perfect instantaneous Channel State Information (CSI) at the relays and the transmitters. Due to practical limitations, like the delay and the rate limitation in the feedback links and the fading channels, it is difficult to provide perfect instantaneous CSI at the transmitters and even the relays. Achievable DoF by the IA schemes collapses greatly with imperfect CSI. It has been shown that the delayed CSI at the Transmitter (CSIT) can help to achieve higher DoF. In this paper, we investigate the DoF in the two-user two-hop Interference X-channel (2×2×2-X) under two regimes of CSI availability: delayed CSIT and no CSIT. We present IA scenarios for each of these regimes which achieve the optimal Dof of 4/3. In no CSIT case, we apply suitable strategy at the relays, which have delayed CSI, to compensate the effect of CSI absence in the transmitters from DoF point of view.