On spatial patterns of transmitter-receiver pairs that allow for interference alignment by delay

As a theoretical concept, and a means to understand the potential of interference alignment, in this paper we investigate possibilities to place n transmitter-receiver pairs in n - 1 dimensions such that the interference from unintended transmissions is aligned at each receiving node. By such an arrangement each link has half of the capacity available, at least in theory. Regular patterns of stations are considered. It is shown that placing transmitters ldquooutsiderdquo a regular arrangement of receivers provides solutions in any dimension, while placing transmitters ldquooppositerdquo to intended receivers only yields a solution in dimension one and two. Methodologically we borrow from the field of distance geometry.