On the Sum-Rate of the Gaussian MIMO Z Channel and the Gaussian MIMO X Channel

In this paper, we study the Gaussian MIMO Z channel and the Gaussian MIMO X channel. The MIMO X channel (XC) consists of two multiple antenna transmit-receive pairs, where each transmitter communicates with both receivers. The MIMO Z channel (ZC) is obtained from the MIMO X channel by eliminating one of the links and its corresponding message. First, we derive a sum-rate upper bound for the MIMO Z channel and compare it with an existing bound in literature. Next, we consider the MIMO X channel and propose a new sum-rate upper bound by utilizing the sum-rate upper bound for the MIMO ZC. Subsequently, we derive another upper bound for the MIMO XC by assuming receiver cooperation and deriving the worst noise covariance matrix for the resulting two-user MAC. We compare the above two upper bounds for the MIMO XC with the MaddahAli-Motahari-Khandani (MMK) scheme. Then, we consider some consequences of the above results for the MIMO interference channel. Finally, we present some numerical results. The numerical results suggest that the proposed sum-rate capacity upper bounds are tighter than existing bounds.