An upsurge of interest in relay-augmented infrastructure-based networks has appeared in recent years.Radio resource management in such relay systems has great influence on the system performance. How to utilize the limited frequency resources efficiently in the system is a hot research topic. In this paper, performance of frequency reuse schemes has been studied in fixed relay systems. A novel scheme is achieved by modifying an existing one. Theoretical model is proposed for the performance analysis of two schemes. Both the theoretical analysis and simulation results show that the modified scheme outperforms the existing one not only in power consumption of mobile stations but also in cell carrier-to-interference ratio coverage.