How to Position n Transmitter-Receiver Pairs in n-1 Dimensions Such That Each Can Use Half of the Channel with Zero Interference from the Others

Cyclic Interference Alignment by propagation delay

“…A corresponding node placement for this special case of delay matrix D is investigated in [5], [9]. However, a general solution for node placement of K users with any valid delay matrix D exceeds the scope of the present paper.…”

“…This assumption also occurs in [5], [9], [10]. We neglect further wireless effects as, e. g., multi-path propagation, path loss and fading and consider a line-of-sight environment.…”

“…, 4, and obtain: Node placement terms a procedure of how to place usernodes in Euclidean space enabling (Cyclic) IA by propagation delay. Here, we consider the problem as an Euclidean embedding of the dissimilarity matrix ∆ according to [9], [10] with fixed entries in the matrix C and variable entries a, b ∈ R + in B, A, respectively. To derive the sought distances b and a, the receivers j and k, j ≠ k ∈ {3, 4}, must be positioned s. t. all the given distances in C are fulfilled.…”

“…Our main goal is to formally generalize IA by propagation delay on delay-based interference channels as treated in [1], [4], [5], [9], [10]. We intend to keep an intuitive representation of the considered model as in the original examples.…”

“…In [5], [9]- [11], the authors further assume that propagation delay is proportional to the Euclidean distance between transmitters and receivers and derive node placement schemes, i. e., to answer the question of how to position transmitters and receivers in spatial dimensions to achieve IA by propagation delay.…”