  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.
