In this paper, based on the theory of finite projective plane (FPP), a novel channel assignment is proposed with Markov chain modeling of N channels and N users, especially when the channel resources are often idle due to inefficient uses. The arrangements of intermixed grouping of channels based on FPP mechanism relate Markov chain modeling with our proposed punch through ratio (PTR) formulations successfully provide fairness among users as well. The defined throughput is obviously enhanced from simulation results with the proposed FPP scheme, especially when the traffic load is light. Nevertheless, if the proposed scheme is combined with successive interference cancellation (SIC) techniques, much better throughput for heavy traffic load is also predicted.