Degrees of Freedom Regionof the MIMO X Channel

We provide achievability as well as converse results for the degrees of freedom region of a multiple-input multipleoutput (MIMO) X channel, i.e., a system with two transmitters, two receivers, each equipped with multiple antennas, where independent messages need to be conveyed over fixed channels from each transmitter to each receiver. The inner and outer bounds on the degrees of freedom region are tight whenever integer degrees of freedom are optimal for each message. WithM = 1 antennas at each node, we find that the total (sum rate) degrees of freedom are bounded above and below as 1 ? X 4 3 . If M > 1 and channel matrices are nondegenerate then the precise degrees of freedom ? X = 4 3 M . Thus, the MIMOX channel has noninteger degrees of freedom whenM is not a multiple of 3. Simple zero forcing without dirty paper encoding or successive decoding, suffices to achieve the