Broadcast channel under unequal coherence intervals

In practical multiuser wireless networks, different links often experience unequal coherence lengths due to differences in mobility as well as scattering environment, a common scenario that has largely been neglected in the fundamental studies of the wireless channel. A key feature of unequal coherence lengths is that the per-transmission cost of acquiring CSI and its effect on achievable rates may vary significantly among the nodes, thus pre-existing receive CSI on a typical node should not be assumed as it will hide this key feature of the problem. In this paper, the method of product superposition is employed to find the achievable degrees of freedom region of multiuser broadcast channel where the users coherence lengths have arbitrary integer ratios. The achievable degrees of freedom region meets the outer bound when the transmitter has fewer antennas than the receivers, or when all receivers have the same number of antennas, hence for this class of antenna configurations the optimal degrees of freedom is now known.