In this paper, we investigate the outage and ergodic capacity of downlink distributed antenna systems (DAS) where each distributed antenna unit (DAU) has multiple antennas with per-DAU power constraint. We first derive the optimal beamforming vector in a closed form by applying a matrix minor condition to relax the positive semi-definite constraint. We observe that our derived solution has a form of maximum ratio transmission per each DAU with full power. Based on the derived optimal beamforming, the outage and ergodic capacity under Rayleigh fading channels are analyzed. To this end, we show that a distribution of the received signal-to-noise ratio is characterized as a Gamma distribution by approximating a sum of non-identical independent Nakagami-m random variables as a single Nakagami-m random variable based on the moment matching method. Then, we present an accurate formula of the outage and ergodic capacity in a closed form which matches well with the simulation results. Furthermore, we derive an upper bound of an achievable average rate of DAS with limited feedback. We then propose a new feedback bit allocation algorithm to maximize the derived metric. Simulation results confirm the accuracy of the derived outage and ergodic capacity expressions and the efficiency of the proposed bit allocation method.