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This article presents a novel procedure of implementing software defined radio modem using a graphics processing unit instead of conventional digital signal processors and/or field programmable gate arrays. Considering that modern GPU is suitable for parallel computing due to its numerous powerful arithmetic logic units, we suggest a proper architecture of hardware and software platform for the SDR modem to be implemented on GPU. Then, we show a design example of mobile WiMAX terminal implemented on the proposed GPU platform. In our experimental tests, we observed that the GPU-driven modem is nearly 90 times faster than the conventional 8-way Very Long Instruction Word architectured DSP-driven modem for the application of Viterbi decoder implementation of mobile WiMAX terminal.