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We derive the ergodic capacity of discrete-time fading channel with additive Gaussian noise subject to both peak and average power constraint. The average power can be interpreted as the cost that we incur to achieve a certain rate. On the other hand, the motivation of this analysis comes from the fuel that there is also a peak power limitation in practical communication system. It is been shown that the optimal power adaption is no longer water-filling or constant power adaption which is the case where there is no limitation on the peak power. The numerical results show that the importance of peak power constraint becomes negligible for relatively low available average power, while it is limiting the capacity to be finite even as the available average power goes to infinity.