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The privacy risks for individuals are becoming more concrete in communication systems, and existing privacy protection methods may not be suitable in communication systems. Among existing privacy definitions, the utility privacy trade-off is proper evaluation model of privacy in communication systems due to its relation with information theory and rate distortion theory. In this paper, at first we theoretically investigate the utility privacy trade-off on noisy channels and derive the updated expressions for trade-off functions. Then, these functions are both simulated and tested with software defined radios (SDRs) for orthogonal frequency division multiplexing (OFDM) based wireless communication system.