On the degrees of freedom of two-hop MISO broadcast networks with mixed CSIT

We consider a downlink two-hop MISO broadcast network with a 2-antenna source communicating to 2 single-antenna destinations, via 2 single-antenna relays. We investigate spectrally efficient transmission and the associated achievable sum degrees of freedom (DoF) with mixed channel state information at the transmitter (CSIT), which consists of perfect delayed CSIT and imperfect instantaneous CSIT. When the variance of the estimation error of the instantaneous CSIT lies on level of O(P^-α) for the transmission power P and some α ∈ [0, 1], we show that the sum DoF 4-2α/3-2α ∈ [4/3, 2] can be achieved by a novel interference alignment (IA) scheme. The result shows that rather than exploiting only delayed or imperfect instantaneous CSIT, the transmission design taking advantages of both can achieve higher sum DoF.