On the DoF of X-Networks With Synergistic Alternating CSIT: A Step Towards Integrated Communication and Sensing

The coexistence of communication and sensing services in the next wireless communication systems, i.e., beyond 5G and 6G systems, revive the central role of interference management techniques such as interference alignment, coordinated multipoint transmission, and cell-free massive multiple-input–multiple-output (MIMO), in defeating interference and achieving the network capacity. In this article, we consider the <inline-formula> <tex-math notation="LaTeX">$K$ </tex-math></inline-formula>-user single-input–single-output (SISO) X-channel and its variants (<inline-formula> <tex-math notation="LaTeX">$2 \times K$ </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">$K \times 2$ </tex-math></inline-formula>) in fast-fading environments. This can theoretically model many practical use cases for beyond 5G and 6G networks. For instance, it can model the case of having <inline-formula> <tex-math notation="LaTeX">$K$ </tex-math></inline-formula> cars communicating with another <inline-formula> <tex-math notation="LaTeX">$K$ </tex-math></inline-formula> cars, while former cars are sensing environment using the latter ones (in a cooperative, bistatic, and active approach) over the same time and frequency resources. We assume that the transmitters have access to synergistic alternating channel state information at the transmitter (CSIT) where it alternates between three states: perfect (P), delayed (D), and no-CSIT (N), and these states are associated with fractions of time denoted by <inline-formula> <tex-math notation="LaTeX">$\lambda _{P}$ </tex-math></inline-formula>, <inline-formula> <tex-math notation="LaTeX">$\lambda _{D}$ </tex-math></inline-formula>, and <inline-formula> <tex-math notation="LaTeX">$\lambda _{N}$ </tex-math></inline-formula>, respectively. We develop novel degree-of-freedom (DoF) achievability schemes that exploit the synergy of the instantaneous CSIT and the delayed CSIT to retrospectively align interference in the subsequent channel uses. In particular, we show that the sum DoF of the <inline-formula> <tex-math notation="LaTeX">$K$ </tex-math></inline-formula>-user SISO X-channel is at least <inline-formula> <tex-math notation="LaTeX">${2K}/{K + 1}$ </tex-math></inline-formula>, using a two-phase transmission scheme over finite symbols channel extension and under a certain distribution of the CSIT availability of <inline-formula> <tex-math notation="LaTeX">$\Lambda (\lambda _{P}=({1}/{3}), \lambda _{D}= ({1}/{3}), \lambda _{N}=({1}/{3}))$ </tex-math></inline-formula>. This achievability result can be considered as a tight lower bound where it coincides with the best lower bound known for the same network but with partial output feedback instead of alternating CSIT. In addition, it shows that the role of synergistically alternating CSIT with distribution <inline-formula> <tex-math notation="LaTeX">$\Lambda ({1}/{3},{1}/{3},{1}/{3})$ </tex-math></inline-formula> is equivalent to the one of the partial output feedback. Moreover, we show the optimality of the proposed two-phase-based scheme using a simple combinatorial proof. This establishes a DoF lower bound, which is strictly better than the best lower bound known for the case of delayed CSI for all values of <inline-formula> <tex-math notation="LaTeX">$K$ </tex-math></inline-formula>. Thus, the proposed schemes offer higher DoF gain in comparison to delayed CSIT and no-CSIT.