Abstract: The design of self-triggered radio arrays is one of the opportunities and challenges in the radio detection of cosmic ray air shower. For example, high amplitude transient noise from the background source can lead to false triggering of the radio array. And the array design needs to avoid false triggering caused by noise. The unique polarization characteristics of radio signals which generated by air shower provide a solution to problem of false triggering of the radio array, and the premise of the use of signal's polarization characteristics to solve false triggering of the radio array is to reconstruct the electric field of radio signals. Background noise is also coupled into the final observed data through the antenna response, posing a significant challenge to correctly reconstruct the electric field of the radio signal. Based on the prototype array GP300 (Grand-Proto 300) of GRAND (Giant Radio Array for Neutrino Detection), combined with the Simulation software ZHAireS's (ZHS AIR-shower Extended Simulations) simulation of radio signals generated by air shower, and coupled with the real response of the bow-tie antennas, the authors use the least square method to reconstruct the electric field and then study the polarization characteristics of the radio signals. Finally the authors calculate the trigger efficiency of antennas on polarization's basis.