The generalized multiplexing gain region (GMGR) of the slow-fading MIMO interference channel is obtained under the assumption of perfect channel state information at the transmitters (CSIT) in the general case where there are an arbitrary number of antennas at each of the four nodes. It is shown that a simple Han-Kobayashi (HK) linear Gaussian superposition coding scheme with a public/private message split at each transmitter can achieve the GMGR of the channel if the covariance matrices associated with the private and public sub-message codewords at each transmitter are certain functions of the null-space of the respective cross-link channel matrix. Moreover, in such a coding scheme, the multiplexing gains of the sub-messages can be chosen without any CSIT. Building on this result, and with M i  and N i  denoting the numbers of transmit and receive antennas at the i th  transmitter and receiver, respectively, it is shown that at transmitter i an approximate version of the associated null-space expressed in terms of N j (M i -N j ) +  log(INR ij ) bits per channel realization is sufficient to achieve the perfect CSIT GMGR of the channel, where INR ij  is the interference-to-noise ratio at receiver j. Furthermore, under the assumption of no CSIT, the GMGR is characterized for two sub-classes of MIMO ICs.
['Sanjay Karmakar', 'Mahesh K. Varanasi']
The generalized multiplexing gain region of the slow fading MIMO interference channel and its achievability with limited feedback