In case of the limited communication capacities of the nodes in the realistic decentralized networks

a consensus-based auction approaches(CDACA)was proposed to achieve the optimal multi-assignment for multiple spectrum.Based on local information

each secondary user conducts an ascending-bid auction for a single channel in CDACA forward auction phase

and primary users with unassigned channels conduct descending-bid auction for their favorite secondary users in reverse auction phase;both secondary users and primary users use consensus routine based on local communication as the conflict resolution mechanism to achieve agreement on the winning bid values.Theory analysis proves CDACA always converges to an assignment that maximizes the total network benefits within finite number of iterations

even for nodes in realistic decentralized networks with limited communication and local outdated information;the algorithm convergence is also proved in dynamic decentralized networks.Under different network topologies in the simulation

CDACA is shown to be superior on convergence speed and spectrum efficiency.