  We consider an unslotted primary channel with alternating on/off activity and
provide a solution to the problem of finding the optimal secondary transmission
power and duration given some sensing outcome. The goal is to maximize a
weighted sum of the primary and secondary throughput where the weight is
determined by the minimum rate required by the primary terminals. The primary
transmitter sends at a fixed power and a fixed rate. Its on/off durations
follow an exponential distribution. Two sensing schemes are considered: perfect
sensing in which the actual state of the primary channel is revealed, and soft
sensing in which the secondary transmission power and time are determined based
on the sensing metric directly. We use an upperbound for the secondary
throughput assuming that the secondary receiver tracks the instantaneous
secondary channel state information. The objective function is non-convex and,
hence, the optimal solution is obtained via exhaustive search. Our results show
that an increase in the overall weighted throughput can be obtained by allowing
the secondary to transmit even when the channel is found to be busy. For the
examined system parameter values, the throughput gain from soft sensing is
marginal. Further investigation is needed for assessing the potential of soft
sensing.
