Distributed learning under imperfect sensing in cognitive radio networks

We consider a cognitive radio network, where M distributed secondary users search for spectrum opportunities among N independent channels without information exchange. The occupancy of each channel by the primary network is modeled as a Bernoulli process with unknown mean which represents the unknown traffic load of the primary network. In each slot, a secondary transmitter chooses one channel to sense and subsequently transmit if the channel is sensed as idle. Sensing is considered to be imperfect, i.e., an idle channel can be sensed as busy and vice versa. Users transmitting on the same channel collide and none of them can transmit successfully. The objective is to maximize the system throughput under the collision constraint imposed by the primary network while ensuring synchronized channel selection between each secondary transmitter and its receiver. The performance of a channel selection policy is measured by the system regret, defined as the expected total performance loss with respect to the optimal performance under the ideal scenario where all channel means are known to all users and collisions among users are eliminated throughput perfect scheduling. We show that the optimal system regret has the same logarithmic order as the centralized counterpart with perfect sensing. An order-optimal decentralized policy is constructed to achieve the logarithmic order of the system regret while ensuring fairness among all users.