CSIT Thresholds for Collapse of Degrees of Freedom in Wireless Networks

We study K-user Interference Channels (IC), K-user MIMO ICs and K-user MIMO Broadcast Channels (BC) with generic channel coefficients where, for some channel coefficients the channel state information at the transmitter(s) (CSIT) is perfect, while for the others the CSIT is available only to finite precision. By generalizing the Aligned Image Sets (AIS) bound we are able to characterize the necessary and sufficient condition for the collapse of sum degrees of freedom (DoF) to 1 in each case. For example, the K=3 user interference channel has sum DoF=1 if and only if the CSIT for at least one of the undesired channel coefficients is limited to finite precision.