Cyclic Interference Alignment by propagation delay

In the present paper, Interference Alignment by propagation delay is applied to a delay-based X-channel and a delay-based K- user interference channel. The key ingredient in our approach is the cyclic permutation property of the delay-based channel model that uses cyclic right-shifts in polynomials. Based on this cyclic channel model, we derive necessary conditions on the propagation delay matrix between users and provide Cyclic Interference Alignment schemes achieving the upper bounds on X - networks as given by Cadambe et al. By further assuming that the propagation delays are proportional to the Euclidean distances, a delay matrix with integer-valued propagation delays can be derived. It enables us to investigate the placement of user-nodes in Euclidean space such that Cyclic Interference Alignment is achieved in two dimensions.