Nowadays, the Unmanned Aerial Vehicle (UAV) become more and more popular in aerial photography, especially in mini and micro size UAV. The UAV used for aerial photography usually use a high power video transfer communication block to send the real time video signal to the ground station, which is high power consuming. It is important to increase the power efficiency of on-board communication system for improving the endurance of small-scale UAVs. The power amplifier (PA) is the most power consuming component among all the units in communication system. Given the nature feature of the PA, it tends to be either linear response or higher power efficiency, but rarely both. The PA with high power efficiency always has a horrible non-linear distortion performance that discards its use. There are several available linearization methods to compensate the non-linear behavior of PA. Among them the digital predistortion (DPD) method is widely used with the development of digital electronic technology. However, the design cost of DPD block itself should be taken into consideration. The DPD linearizer requires a feedback path to monitor the PA behavior and the analog to digital convertor (ADC) is a critical component from the cost and efficiency point of view. The price of ADC makes a prominently contribution to the total cost of DPD linearizer. The price of the ADC is usually proportional to the sampling frequency, which, according to the Nyquist-Shannon sampling theorem, should be higher than twice the bandwidth of the communication's signal. In this thesis, we will present an under sampling method and its supporting algorithm aimed to decrease the frequency rate requirements of the ADC to perform the DPD linearization. In this way, ADC with lower sampling frequency is able to be used in the DPD feedback loop and thus decrease the total cost without compromising the linearization performance. The theoretical analysis will be first presented in this thesis and then experimental results showing the performance of the DPD with under-sampling method will be shown and discussed.