Degrees of freedom region of the MIMO two-transmit, two-receive network with General message sets

We establish the degrees of freedom (DoF) region for the multiple-input multiple-output (MIMO) two-transmit, two-receive network which has an arbitrary number of antennas at each of its four terminals. General message sets are considered, from which all possible communication scenarios based on two-transmit, two-receive network can be regarded as special cases. An outer bound is given first and then it is shown to be tight. In particular, we propose a linear precoding scheme that can achieve all the DoF tuples in the region. Time extension and asymmetric complex signaling are utilized when necessary. The scheme works for both constant channel as well as time/frequency varying channel scenarios. From our general result, one can obtain the degrees of freedom region and the corresponding DoF-optimal precoding scheme for the two-transmit, two-receive network with any subset of all possible messages. Some of these DoF regions have been found before, but many are new. Our work sheds light on the optimal message sets design that could take the most advantage of channel resources in a flexible and efficient manner.