Degrees of Freedom of Multi-Hop MIMO Broadcast Networks with Delayed CSIT

We study the sum degrees of freedom (DoF) of a class of multi-layer relay-aided MIMO broadcast networks with delayed channel state information at transmitters (CSIT). In the assumed network a K-antenna source intends to communicate to K single-antenna destinations, with the help of N-2 layers of K full-duplex single-antenna relays. We assume identical and independent fading channels on every hop. Two practical delayed CSIT feedback scenarios are studied. If the source can obtain the CSI feedback signals from all layers, we prove the optimal sum DoF of the network to be K/1+1/2+...+1/K. If the CSI feedback is only within each hop, we show that when K=2 the optimal sum DoF is 4/3, and when K ≥ 3 the sum DoF 3/2 is achieved asymptotically.