A data processing system includes a display device, a proximity sensor, a wireless data processing apparatus, and an external antenna. The display device and the wireless data processing apparatus are connected. The display device is equipped with an internal antenna indirectly connected to a wireless communication module of the wireless data processing apparatus. The external antenna is electrically connected to the wireless communication module. A data processing circuit of the wireless data processing apparatus normally controls the wireless communication module to set signal transmission strengths of the antennas by using a first antenna control mode. When the proximity sensor detects an object located close to proximity sensor, the data processing circuit controls the wireless communication module to set the signal transmission strengths by using a second antenna control mode that includes at least decreasing the signal transmission strength of the internal antenna.