UC Irvine

© 2014 IEEE. Seeking fundamental insights into multi-hop multi-flow networks we study the simplest non-trivial setting, a 2 × 2 × 2 MIMO interference network comprised of two sources, two relays and two destinations, wherein all nodes have M antennas, all first-hop channels are of rank D1, and all second hop channels are of rank D2. For this setting, we show that the optimal sum DoF is min(4D1, 4D2, 2M - |D1 - D2|). While 4D1, 4D2 are the obvious min-cut bottlenecks that are active when either hop is severely rank-deficient, what is remarkable is that under moderate rank-deficiencies the DoF are limited not by the higher or the lower of the two ranks D1, D2, but only by the difference of the two ranks |D1 - D2|. This suggests an interesting 'rank-matching' design principle for multi-hop networks, reminiscent of 'impedance matching', wherein the goal is not necessarily to increase or decrease the rank of each hop, but rather to use linear processing at intermediate hops to create effectively a two-hop setting with matching ranks.