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In this paper, we investigate a behavior of the cell average ergodic capacity for distributed antenna systems (DAS) in a composite fading channel model which contains small-scale and large-scale fadings. For small-scale Rayleigh fadings, based on the proof of asymptotic normality, the mean and the variance of the instantaneous capacity were recently presented as a closed form solution. However, this solution is too complicated to be applied directly for obtaining the average ergodic capacity over a cell. In this work, we derive a simple and accurate expression for the ergodic capacity by utilizing the high signal to noise ratio (SNR) analysis. Our simple solution provides meaningful insight on how the ergodic capacity is affected as SNR, pathloss and antenna configurations change. Also it is useful for capturing quantitative performance measures such as the multiplexing gain and the power offset. In addition, we analyze the cell average ergodic capacity by taking into account the shadowing effect and the pathloss on the basis of our results on the small-scale fadings. These expressions lead to some insights on the performance of DAS under practical environments. Finally, numerical results confirm the validity of our analytical results.