In traditional cognitive radio (CR) network,secondary users (SUs) are always assumed to obey the rule of “introducing no interference to the primary users (PUs) ”.However,this assumption may be not realistic as the CR devices becoming more and more intelligent nowadays.In this paper,with the concept of lighthanded CR,which is proposed to deal with the above mentioned problem by enforcing “punishment” to illegal CR transmissions,the action decisions of primary users (PUs) are modeled as a partially observable Markov decision process (POMDP),and the optimal spectrum allocation scheme with the objective of maximizing their reward is proposed,which is defined by the utility function.Furthermore,a reduced scheme with much smaller state space has been proposed in this paper for lower computational complexity.Extensive simulation results show that the proposed schemes improve the reward significantly compared to the existing scheme.