$K$ -User Symmetric $M\times N$ MIMO Interference Channel Under Finite Precision CSIT: A GDoF Perspective

Generalized degrees of freedom (GDoF) are characterized for the symmetric K-user multiple-input multiple-output interference channel under the assumption that the channel-state information at the transmitters (CSITs) is limited to finite precision. In this symmetric setting, each transmitter is equipped with M antennas, each receiver is equipped with N antennas, each desired channel (i.e., a channel between a transmit antenna and a receive antenna belonging to the same user) has strength ~P, while each undesired channel has strength ~P
^α
, where P is a nominal SNR parameter. The result generalizes a previous GDoF characterization for the SISO setting (M = N = 1) and is enabled by a significant extension of the aligned image sets bound that is broadly useful. GDoF per user take the form of a W-curve with respect to α for fixed values of M and N. Under finite precision CSIT, in spite of the presence of multiple antennas, all the benefits of interference alignment are lost.