Interference Alignment for the K-user Interference Channel with Imperfect CSI

In this paper we explore the information-theoretic aspects of interference alignment and its relation to channel state information (CSI). For the $K-$user interference channel using different changing patterns between different users, we propose several methods to align some parts of interferences and to increase what is achieved by time sharing method. For more practical case when all the channel links connected to the same destination have the same changing pattern, we find an upper-bound and analyze it for the large interference channel network. This result shows that when the size of the network increases, the upper-bound value goes to $\frac{\sqrt{K}}{2}$. For the fast fading channel when all the channels have the same changing pattern, we show that when the direct links have different characteristic functions (channel permutation or memory), in the absence of half part of CSI (cross links) at both transmitters and receivers, one can achieve $K/2$ degrees-of-freedom (DoF). Also by the converse proof we show that this is the minimum channel information to achieve maximum DoF of $\frac{K}{2}$. Throughout this work, this fact has been pinpointed to prove statements about more general partial state CSI and achievable DoF. In other words, for the 3-user fully connected interference channel we find out while $\frac{3}{2}$ lies in achievable DoF, we don't need to know half part of the CSI. Also, the result has been extended to a more general form for $K-$user interference channel and through the converse proof, its functionality on channel state is proved to be optimum.