Comments on Degrees of freedom region for $K$-user interference channel with $M$ antennas

For a $K$-user interference channel with $M$ antenna at each transmitter and each receiver, the maximum total DoF of this channel has been previously determined to be $\max \sum_{k=1}^K d_k = MK/2$. However, the DoF region remains to be unknown. In this short note, through a simple time-sharing argument, we obtain the degrees of freedom (DoF) region of this channel.