Power and transmission duration control in un-slotted cognitive radio networks

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 degree of protection and 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.