Achieving the DoF limits of the SISO X channel with imperfect-quality CSIT

In the setting of the two-user single-input single-output X channel, recent works have explored the degrees-offreedom (DoF) limits in the presence of perfect channel state information at the transmitter (CSIT), as well as in the presence of perfect-quality delayed CSIT. Our work shows that the same DoF-optimal performance - previously associated to perfect-quality current CSIT - can in fact be achieved with current CSIT that is of imperfect quality. The work also shows that the DoF performance previously associated to perfect-quality delayed CSIT, can in fact be achieved in the presence of imperfect-quality delayed CSIT. These follow from the presented sum-DoF lower bound that bridges the gap - as a function of the quality of delayed CSIT - between the cases of having no feedback and having delayed feedback, and then another bound that bridges the DoF gap - as a function of the quality of current CSIT - between delayed and perfect current CSIT. The bounds are based on novel precoding schemes that are presented here and which employ imperfect-quality current and/or delayed feedback to align interference in space and in time.