Interference Aligned Space-Time Transmission with Diversity for the $2 \times 2$ X-Network

The sum degrees of freedom (DoF) of the two-transmitter, two-receiver multiple-input multiple-output (MIMO) X-Network ($2 \times 2$ MIMO X-Network) with $M$ antennas at each node is known to be $\frac{4M}{3}$. Transmission schemes which couple local channel-state-information-at-the-transmitter (CSIT) based precoding with space-time block coding to achieve the sum-DoF of this network are known specifically for $M=2,4$. These schemes have been proven to guarantee a diversity gain of $M$ when a finite-sized input constellation is employed. In this paper, an explicit transmission scheme that achieves the $\frac{4M}{3}$ sum-DoF of the $2 \times 2$ X-Network for arbitrary $M$ is presented. The proposed scheme needs only local CSIT unlike the Jafar-Shamai scheme which requires the availability of global CSIT in order to achieve the $\frac{4M}{3}$ sum-DoF. Further, it is shown analytically that the proposed scheme guarantees a diversity gain of $M+1$ when finite-sized input constellations are employed.