<inline-formula> <tex-math notation="LaTeX">$K$ </tex-math> </inline-formula>-User Symmetric <inline-formula> <tex-math notation="LaTeX">$M\times N$ </tex-math> </inline-formula> MIMO Interference Channel Under Finite Precision CSIT: A GDoF Perspective

Abstract

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 $\sim P$ , 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.