Capacity Bounds for a Cognitive MIMO Gaussian Z-Interference Channel

In this paper, we compute an achievable rate of a multiple-input-multiple-output (MIMO) Gaussian Z-interference channel (ZIC), as shown in Fig. 1, when transmit node C has imperfect cognitive knowledge of the signal sent by transmit node A. First, we compute the capacity of this channel, assuming noncausal but noisy knowledge at node C of node A's signal. We then compute the achievable rate for a causal cognitive strategy: This achievable rate is derived using a two-phase transmission scheme, in which node C uses a combination of a linear MMSE (LMMSE) estimator and a dirty-paper code, and node D employs a combination of an LMMSE estimator and a partial interference canceler. The achievable rate is studied in two different cases: 1) Node C operates in full-duplex mode, and 2) node C operates in half-duplex mode. To quantify the performance of the proposed strategy, we compute simple lower and upper bounds on the capacity of this channel. Similar to an interference channel, the achievable rate of the cognitive ZIC nonmonotonically varies with the interference. Specifically, the achievable rate first decreases with the channel gain between nodes A and D and then begins to increase beyond a certain threshold. The difference in the achievable rate between full-and half-duplex transmissions is also numerically evaluated.