We propose a system of detecting the position of a device embedded with an antenna by sensing the electrical power from a two-dimensional communication (2DC) sheet. The system obtains a characteristic power pattern at each position by sweeping the frequency of the microwave supplied to the 2DC sheet. Our system uses a machine learning technique to learn the accumulated power-pattern data to detect the position of a device. The position-detection accuracy of our system was 79.1% when the antenna was moved in 12 mm intervals. In addition to detecting the position of a device, we also estimated the direction.