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

This work is inspired by the question "Can 100 speakers talk for 30 minutes each in one room within one hour and with zero interference to each other's audience?" posed by Cadambe and Jafar at the 45th Allerton conference 2007. We consider the problem of how many transmitter-receiver pairs can be placed such that each desired link may use half of the channel time free of interference from unintended transmissions. The answer is given in the title: at least n pairs, i.e., 2n stations can be positioned in the (n-1)-dimensional Euclidean space such that complete interference alignment in time is achieved. Regular patterns with equal distances between receivers and transmitters, respectively, are the solution. The basic methodology for achieving this result is borrowed from the field of distance geometry.