Optimal beamforming in MISO cognitive channels with degraded message sets

In this paper we consider the coexistence of a single-input single-output (SISO) primary link with a multiple-input single-output (MISO) secondary user pair that has non-causal knowledge of the primary message. We study an achievable rate region that exploits this knowledge by combining selfless relaying to maintain the rate supported by the primary link with dirty paper coding to pre-cancel the interference at the secondary receiver. We find the optimal choice of power allocation between these operating modes at the secondary transmitter as well as the optimal beamforming vectors. Moreover, we address the robustness of the solution to uncertainties in the channel knowledge. Finally, we show by numerical evaluation the gains obtained due to the additional knowledge of the primary message.