Degrees of Freedom of the Broadcast Channel with Hybrid CSI at Transmitter and Receivers

In general the different links of a broadcast channel may experience different fading dynamics and, potentially, unequal or hybrid channel state information (CSI) conditions. The faster the fading and the shorter the fading block length, the more often the link needs to be trained and estimated at the receiver, and the more likely that CSI is stale or unavailable at the transmitter. Disparity of link fading dynamics in the presence of CSI limitations can be modeled by a multi-user broadcast channel with both non-identical link fading block lengths as well as dissimilar link CSIR/CSIT conditions. This paper investigates a MISO broadcast channel where some receivers experience longer coherence intervals (static receivers) and have CSIR, while some other receivers experience shorter coherence intervals (dynamic receivers) and do not enjoy free CSIR. We consider a variety of CSIT conditions for the above mentioned model, including no CSIT, delayed CSIT, or hybrid CSIT. To investigate the degrees of freedom region, we employ interference alignment and beamforming along with a product superposition that allows simultaneous but non-contaminating transmission of pilots and data to different receivers. Outer bounds employ the extremal entropy inequality as well as a bounding of the performance of a discrete memoryless multiuser multilevel broadcast channel. For several cases, inner and outer bounds are established that either partially meet, or the gap diminishes with increasing coherence times. Index Terms Broadcast channel, Channel state information, Coherence time, Coherence diversity, Degrees of freedom, Fading channel, Multilevel broadcast channel, Product superposition. The authors are with the Department of Electrical Engineering, University of Texas at Dallas, Richardson, TX 750830688 USA, E-mail: [email protected];[email protected]. This work was presented in part at the IEEE International Symposium on Information Theory (ISIT), Germany, June 2017 [1]. September 12, 2017 DRAFT