Paranoid secondary: Waterfilling in a cognitive interference channel with partial knowledge

We study a two-user cognitive channel, where the primary flow is sporadic, cannot be re-designed and operating below its link capacity. To study the impact of primary traffic uncertainty, we propose a block activity model that captures the random on-off periods of primary's transmissions. Each block in the model can be split into parallel Gaussian-mixture channels, such that each channel resembles a multiple user channel (MAC) from the point of view of the secondary user. The secondary senses the current state of the primary at the start of each block. We show that the optimal power transmitted depends on the sensed state and the optimal power profile is paranoid, i.e. either growing or decaying in power as a function of time. We show that such a scheme achieves capacity when there is no noise in the sensing. The optimal transmission for the secondary performs rate splitting and follows a layered water-filling power allocation for each parallel channel to achieve capacity. The secondary rate approaches a genie-aided scheme for large block-lengths. Additionally, if the fraction of time primary uses the channel tends to one, the paranoid scheme and the genie-aided upper bound get arbitrarily close to a no-sensing scheme.