  In a cognitive radio setting, secondary users opportunistically access the
spectrum allocated to primary users. Finding the optimal sensing and
transmission durations for the secondary users becomes crucial in order to
maximize the secondary throughput while protecting the primary users from
interference and service disruption. In this paper an adaptive sensing and
transmission scheme for cognitive radios is proposed. We consider a channel
allocated to a primary user which operates in an unslotted manner switching
activity at random times. A secondary transmitter adapts its sensing and
transmission durations according to its belief regarding the primary user state
of activity. The objective is to maximize a secondary utility function. This
function has a penalty term for collisions with primary transmission. It
accounts for the reliability-throughput tradeoff by explicitly incorporating
the impact of sensing duration on secondary throughput and primary activity
detection reliability. It also accounts for throughput reduction that results
from data overhead. Numerical simulations of the system performance demonstrate
the effectiveness of adaptive sensing and transmission scheme over non-adaptive
approach in increasing the secondary user utility.
