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In this paper, we propose a new method to analyze the performance of distributed antenna systems (DAS), which can overcome the repeated-root problem existing during deriving the probability density function (PDF) of signal-to-interference plus-noise ratio (SINR). In addition, a novel single transmission selection scheme (STSS) based on maximum SINR criterion is put forward. Assuming channels suffer from independent identical Rayleigh fading together with propagation pathloss, we derive the closed-form expressions for the ergodic capacity as well as outage probability of DAS. Extensive simulations are carried out to validate the theoretical analysis. Numerical results show that the proposed STSS not only is superior to the STSS by criterion of minimizing propagation pathloss but also outperforms blanket transmission scheme (BTS) that all distributed antennas (DAs) in the cell broadcast data.