Degrees of Freedom for the MIMO Interference Channel

Abstract

In this correspondence, we show that the exact number of spatial degrees of freedom (DOF) for a two user nondegenerate (full rank channel matrices) multiple-input–multiple-output (MIMO) Gaussian interference channel with $M_{1}, M_{2}$ antennas at transmitters 1, 2 and $N_{1}, N_{2}$ antennas at the corresponding receivers, and perfect channel knowledge at all transmitters and receivers, is $min {M_{1}+M_{2},N_{1}+N_{2},max (M_{1},N_{2}),max (M_{2},N_{1})}$. A constructive achievability proof shows that zero forcing is sufficient to achieve all the available DOF on the two user MIMO interference channel. We also show through an example of a share-and-transmit scheme how the gains of transmitter cooperation may be entirely offset by the cost of enabling that cooperation so that the available DOF are not increased.