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In order to combat high peak-to-average power ratio and poor power efficiency, drain modulated polar transmitter architectures have been proposed for orthogonal frequency-division multiplexing (OFDM) systems. However, this type of power amplifier architecture suffers from poor linearity in the low amplitude region, which often causes significant distortion to the system. In this paper, we propose a novel technique to introduce a vector hole into the constellation diagram of the OFDM signal, called vector hole punching, so that the envelope of the signal will avoid the origin region, thereby preventing the amplitude of the signal approaching zero, which dramatically improves the linearity of the system. This is achieved through a technique based on a combination of direct clipping, circle-tangent shifting, and the use of unused tones. Test results show a clear vector hole can be created by employing this technique that only slightly broadens the original spectrum and maintains a very low error vector magnitude.