On the Capacity of the Multiantenna Gaussian Cognitive Interference Channel

The capacity of the multiantenna Gaussian cognitive interference channel is studied. The cognitive interference channel is a variation of the classical two-users interference channel in which one of the transmitters, the cognitive transmitter, is also provided with the message of the second transmitter, the primary transmitter. We study the capacity of the multiple-input multiple-output Gaussian model, that is the channel in which the inputs are vectors and the outputs are obtained as linear combinations of the channel inputs plus an additive complex Gaussian noise. This channel models a wireless scenario in which transmitters and receivers have multiple antennas. For this channel, we derive capacity to within an additive gap, that is we show that inner and outer bounds to capacity lie to within a constant distance of each other. The gap between the inner and outer bounds depends on the number of antennas at the cognitive receiver and both bounds can be easily evaluated by considering jointly Gaussian inputs. We also derive capacity to within a constant multiplicative factor of two, that is we show that the ratio between inner and outer bound is at most two. The additive gap well-characterizes the capacity at high SNR, while the multiplicative gap is useful at low SNR. We also derive the exact capacity for a subset of the "strong interference" regime: in this subset, the primary transmitter can decode the cognitive message without loss of optimality. This new capacity result extends and generalizes previously known capacity results, in particular, the capacity in the "very strong interference" and the "primary decodes cognitive" regimes.