Optimal Backward Transmission of Reciprocal X Channels with Two Receivers via Cyclic Interference Alignment

For a given forward transmission scheme, the backward transmission in reverse direction is often wanted in practical communications. This letter proposes an optimal scheme for the backward transmission of the propagation-delay (PD) based general X channel with two receivers, which is reciprocal to forward transmission. With cyclic interference alignment, the desired messages are shown to be allocated at specified time-slots without interference, while other interfering messages are aligned in the remaining time-slots. Thus the backward transmission achieves the maximal degrees of freedom (DoF) with the reciprocal PD channel, which supports optimal bidirectional transmission of the X channel with two receivers.