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Interference alignment is known to achieve the maximum sum DoF of$\frac{4M}{3}$ in the $2 \times 2$ $X$-Network (i.e., two-transmitter (Tx)two-receiver (Rx) $X$-Network) with $M$ antennas at each node, as demonstratedby Jafar and Shamai. Recently, an Alamouti code based transmission scheme,which we call the Li-Jafarkhani-Jafar (LJJ) scheme, was proposed for the $2\times 2$ $X$-Network with two antennas at each node. This scheme achieves asum degrees of freedom (DoF) of $\frac{8}{3}$ and also a diversity gain of twowhen fixed finite constellations are employed at each Tx. In the LJJ scheme,each Tx required the knowledge of only its own channel unlike the Jafar-Shamaischeme which required global CSIT to achieve the maximum possible sum DoF of$\frac{8}{3}$. Bit error rate (BER) is an important performance metric when thecoding length is finite. This work first proposes a new STBC for a threetransmit antenna single user MIMO system. Building on this STBC, we extend theLJJ scheme to the $2 \times 2$ $X$-Network with three antennas at each node.Local channel knowledge is assumed at each Tx. It is shown that the proposedscheme achieves the maximum possible sum DoF of 4. A diversity gain of 3 isalso guaranteed when fixed finite constellation inputs are used.

Interference Alignment with Diversity for the $2 \times 2$ $X$-Network with three antennas