Sum Degrees of Freedom of the $K$-user Interference Channel with Blind CSI

Abstract

In this paper, we consider the problem of the interference alignment for the $K$-user SISO interference channel (IC) with blind channel state information (CSI) at transmitters. Our achievement in contrast to the traditional $K-$user interference alignment (IA) scheme has more practical notions. In this case, every receiver is equipped with one reconfigurable antenna which tries to place its desired signal in a subspace which is linearly independent of interference signals. We show that if the channel values are known to the receivers only, the sum degrees-of-freedom (DoF) of the linear blind IA (BIA) with reconfigurable antenna is $\frac{Kr}{r^2-r+K}$, where $r = \left \lceil{\frac{\sqrt{1+4K}-1}{2}} \right \rceil$. The result indicates that the optimum sum DoF for the $K-$user IC is to achieve the sum DoF of $\lim_{K \rightarrow \infty} {\frac{Kr}{r^2-r+K}}=\frac{\sqrt{K}}{2}$ for an asymptotically large interference network. Thus, the DoF of the $K$-user IC using reconfigurable antenna grows sublinearly with the number of the users, whereas it grows linearly in the case where transmitters access to the CSI. In addition, we propose both achievability and converse proof so as to show that this is the sum DoF of linear BIA with the reconfigurable antenna.