Blind interference alignment for three-user multi-hop SISO interference channel

Interference Alignment (IA) is a rather new technique to achieve higher Degrees-of-Freedom (DoF) compared to traditional orthogonal naive methods, like, Time Division Multiple Access (TDMA). In many IA schemes, Instantaneous Channel State Information at Transmitter (CSIT) is mandatory. However, this requirement becomes an obstacle to implement those methods in practice. In some practical scenarios, it is not possible to provide instantaneous or even delayed CSIT. Recently, Blind Interference Alignment (BIA) has been introduced as a solution to align interference without CSIT. In spit of major advances in single-hop Interference Channels (ICs), few researches focused on multi-hop ICs. In this paper, we investigate the three-user multi-hop Single-Input Single-Ouput (SISO) IC. We present a BIA method to achieve the optimal DoF of this network without CSIT. Moreover, the relays do not have CSI and they using Amplify-and-Forward (AF) relaying strategy. Our method is based on using multi-mode antennas at the receivers. We also investigate a more practical case, in which the relays of an intermediate layer are equipped with multi-mode antennas and know global CSI, while the receivers use conventional antennas. In both cases, our methods achieve maximum achievable sum-DoF, equal to 6/5. Hence, our proposed methods are optimal in the sense of DoF.