  A cognitive radio can operate as a secondary system in a given spectrum. This
operation should use limited power in order not to disturb the communication by
primary spectrum user. Under such conditions, in this paper we investigate how
to maximize the spectral efficiency in the secondary system. A secondary
receiver observes a multiple access channel of two users, the secondary and the
primary transmitter, respectively. We show that, for spectrally-efficient
operation, the secondary system should apply Opportunistic Interference
Cancellation (OIC). With OIC, the secondary system decodes the primary signal
when such an opportunity is created by the primary rate and the power received
from the primary system. For such an operation, we derive the achievable data
rate in the secondary system. When the primary signal is decodable, we devise a
method, based on superposition coding, by which the secondary system can
achieve the maximal possible rate. Finally, we investigate the power allocation
in the secondary system when multiple channels are used. We show that the
optimal power allocation with OIC can be achieved through intercepted
water-filling instead of the conventional water-filling. The results show a
significant gain for the rate achieved through an opportunistic interference
cancellation.
