Degrees of Freedom of Two-Hop MISO Broadcast Networks With Mixed CSIT

A downlink two-hop MISO broadcast network is considered, with a two-antenna source communicating to 2 single-antenna destinations, via multiple single-antenna relays in between. The sum degrees of freedom (DOF) of the network with mixed channel state information at the transmitter (CSIT) is investigated. The mixed CSIT consists of accurate delayed CSIT and inaccurate instantaneous CSIT, and its availability is limited within each hop, i.e., the source is oblivious to the channels of the second hop. Given a transmission power P and a real value α ∈ [0, 1], if the variance of the error for instantaneous CSIT decreases as O(P-α), it is shown that the sum optimal DOF of the considered network is d = 4+2α/3 when there exist at least 3 intermediate relays. The result can be extended to the MIMO and multiple-hop cases. The proposed achievable schemes essentially combine the concept of retrospective interference alignment based on delayed CSIT and linear beamforming based on inaccurate instantaneous CSIT into an integrated form. Our results show that, in multi-hop MISO broadcast networks, delayed CSIT and inaccurate instantaneous CSIT can be exploited simultaneously to benefit network DOF.