On the Degrees of Freedom of SISO X-Channel with Alternating CSIT

In this paper, we establish the degrees of freedom (DoF) of the two-user single input single output (SISO) X-channel with alternating channel state information at the transmitters (CSIT). Three cases are considered for the availability of CSIT; perfect, delayed and no-CSIT. Each state is associated with a fraction of time denoted by ${\lambda }_P,{\lambda }_D$ and ${\lambda }_N$, respectively. We provide new results for DoF of the two-user SISO X-channel when the available CSIT alternates between these three cases under a certain distribution $\mathrm{\Lambda }({\lambda }_P,{\lambda }_D,{\lambda }_N)$. Specifically, we show that the X-channel with alternating CSIT for $\mathrm{\Lambda }(1\mathrm{/}8,3\mathrm{/}8,1\mathrm{/}2)$ can achieve $5\mathrm{/}4$ DoF. The interesting thing about $5\mathrm{/}4$ is that it represents a position of compromise or a middle ground between the channel knowledge that transmitters need to steer interference and the degrees of freedom that the network can achieve. Moreover, $5\mathrm{/}4$ is strictly greater than $6\mathrm{/}5$ which is the upper bound for the X-channel with $\mathit{\text{fixed}}$ delayed CSIT.