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The passive RFID tag, which receives energy for its operation from electromagnetic waves radiated by RFID readers, changes the antenna impedance to modulate the back scattering waves caught by the reader. For this reason, during the back-scattering communication, the energy received by the RFID tag much reduces due to the impedance mismatch. To resolve this problem, the double antenna system which consists of receiving and sending antennas has been proposed. In this paper, the double antenna shapes are optimized on the basis of FDTD analysis and genetic algorithm to maximize the communication distance.