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Resolving hidden terminal problem is one of the major responsibilities in designing MAC protocols for wireless ad hoc networks. The paper proposes a fragmentation-based MAC protocol with power control, named F-RCRC MAC protocol, to avoid the LIRC (large interference range collision) problem, a kind of hidden terminal problem, for wireless ad hoc networks. F-RCRC designs a new interframe space, named FIFS, to reduce the overhead caused by the fragmentation scheme. With the fragmentation, the design of FIFS can effectively avoid the hidden STAs interfering with the receivers' receiving. Moreover, a dynamic transmission power scheme is devised to actively and timely warn the hidden STAs such that the possible collision is avoided. Thus, the LIRC problem can be solved and the network throughput is increased accordingly. In addition, F-RCRC can reduce the energy consumption and increase the spatial reuse due to the controlled transmission power. Simulation results show that F-RCRC performs much better than the related work in terms of network throughput as well as the power throughput.