In this paper, the achievable rate of distributed antenna systems (DASs) in high buildings is investigated for indoor downlink high data rate wireless transmission. A DAS, where radio transmission/reception within one or several neighbouring floors is controlled by a central unit (CU) exploiting the entire system bandwidth is considered. The same frequency channels are reused by all the CUs, co-channel interference is caused. A mathematical channel model for transmission to one user per floor including direct signal propagation between floors within the building and reflection from a nearby building is built based on practical measurements. Using the model, it is shown that the indoor path loss exponent and the Nakagami channel fading parameter have a significant effect on the achievable rate performance.