MISO Networks with Imperfect CSIT: A Topological Rate-Splitting Approach
  Recently, the Degrees-of-Freedom (DoF) region of multiple-input-single-output (MISO) networks with imperfect channel state information at the transmitter (CSIT) has attracted significant attentions. An achievable scheme is known as rate-splitting (RS) that integrates common-message-multicasting and private-message-unicasting. In this paper, focusing on the general $K$-cell MISO IC where the CSIT of each interference link has an arbitrary quality of imperfectness, we firstly identify the DoF region achieved by RS. Secondly, we introduce a novel scheme, so called Topological RS (TRS), whose novelties compared to RS lie in a multi-layer structure and transmitting multiple common messages to be decoded by groups of users rather than all users. The design of TRS is motivated by a novel interpretation of the $K$-cell IC with imperfect CSIT as a weighted-sum of a series of partially connected networks. We show that the DoF region achieved by TRS covers that achieved by RS. Also, we find the maximal sum DoF achieved by TRS via hypergraph fractional packing, which yields the best sum DoF so far. Lastly, for a realistic scenario where each user is connected to three dominant transmitters, we identify the sufficient condition where TRS strictly outperforms conventional schemes. 
Chenxi Hao and Bruno Clerckx
cs.IT math.IT