$K$-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 (MIMO) Interference Channel (IC) under the assumption that the channel state information at the transmitters (CSIT) 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 $\sim P$, while each undesired channel has strength $\sim P^\alpha$, 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 $\alpha$ 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.