Abstract—In cognitive mobile multihop relay (CMMR) network, the mobile user as the primary user is allocated with the channel for transmitting data. Relay station as the secondary user can help primary user to relay transmitted data while in return primary user grants channel access to secondary user. In this paper, credit-based spectrum sharing for primary and secondary user in CMMR network is proposed. With this sharing scheme, the credit is given to the secondary user when primary user requests relay transmission. Primary user can then later allow secondary user to access the allocated channel in return given available credit. An optimization model based on Markov decision process is formulated and solved to obtain optimal policy for primary user in this credit-based spectrum sharing. Knowing that the primary user will adopt optimal policy to grant channel access, the secondary user can optimize the relay transmit power such that the cost is minimized. The performance evaluation s...