A simultaneous-alternate relaying scheme for the two-cell two-hop MIMO X channel with shared relays

We consider a two-cell two-hop X channel, where each of the two base stations sends an independent message to each of the two mobile stations via two half-duplex relays. It is assumed that each of the base stations and mobile stations has M antennas while each relay is equipped with N antennas. In this channel, the previously known upper bounds on the degrees of freedom (DoF) are characterized based on the alternate relaying and simultaneous relaying, respectively. In this paper, we establish a new DoF upper bound based on the simultaneous-alternate relaying, which provides superior DoF gain over the derived upper bounds of the alternate relaying and simultaneous relaying for the case of 3/2 < N/M < 8/3. Furthermore, an achievable scheme is provided to reach the DoF upper bound of the simultaneous-alternate relaying.