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The paper proposes a multi-rate supported power control, named MRPC, MAC protocol to avoid the LIRC (Large Interference Range Collision) problem for wireless ad hoc networks. The main concept of the MRPC protocol is to protect the current reception by means of the carrier-sensing range of the previous transmission to cover the induced interference range of the current reception. Based on the concept, MRPC formulates the requirements of a successful transmission and figures out the appropriate power strength for transmissions. Furthermore, since the threshold values of SNR and receiver sensitivity values are changed with the data transfer rates, MRPC also takes the different threshold values in multi-rate environments into consideration in formulating these requirements. MRPC can reduce the energy consumption and increase the spatial reuse due to the controlled transmission power. It is further shown that MRPC can also work correctly in multi-rate environments. Simulation results show that MRPC performs much better than the related work in terms of network throughput as well as the energy efficiency.