This paper presented a scheme of relayed cellular mobile telecommunication network, which only employs fixed digital relays and not more than two-hop relay routes. Power saving potential of the network is deeply studied under the assumption of not occupying additional frequency bands (i. e. relays share the same frequency bands as used by the base stations). Theoretical analysis and simulation results have both shown that, with the same radio coverage requirement, the necessary effective transmission powers in such a relayed network have greatly decreased compared to conventional cellular network.