The diversity-multiplexing tradeoff of the MIMO Z interference channel

The fundamental diversity-multiplexing tradeoff (DMT) of the quasi-static fading, MIMO Z interference channel (ZIC), with M1 and M2 antennas at the transmitters and N1 and N2 antennas at the corresponding receivers, respectively, is derived. Channel state information at the transmitters (CSIT) and a short-term average power constraint is assumed. The achievability of the DMT is proved by showing that a simple Gaussian superposition coding scheme can achieve a rate region which is within a constant (independent of signal-to-noise ratio (SNR)) number of bits from an upper bound to the capacity region of the ZIC. We also characterize an achievable DMT of the ZIC with No-CSIT and show that in a small region of multiplexing gains (MG), the full CSIT DMT of the ZIC can be achieved with no CSIT at all. The size of this MG region depends on the system parameters such as the number of antennas at the four nodes (referred to hereafter as "antenna configuration"), SNRs and interference-to-noise ratio (INR) of the direct and cross links. Interestingly, for some antenna configurations this MG region covers the entire MG region of the ZIC. Thus, under these circumstances, the optimal DMT of the MIMO ZIC with F-CSIT is same as that of a corresponding ZIC with No-CSIT and availability of CSIT can not further improve the DMT. Finally, we identify a class of ZICs with M1 = M2 = M ≤ N1 over 2, N1 ≤ N2 and SNR ≤ INR where the achievable DMT with No-CSIT coincides with the optimal DMT with F-CSIT.