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In wireless systems, providing high data rate wireless services is a major challenge, particularly for mobile terminals (MTs) in multi-floor buildings. The system performance is impaired by co-channel interference due to the need to reuse the limited available spectrum. One way to achieve higher data rates and better signal quality in this environment, is to reduce the radio transmission distance between the transmitter and the receiver through the use of distributed antenna systems (DASs). DAS reduces the overall transmit power (and hence co-channel interference) while at the same time exploiting spatial diversity. This paper proposes and investigates the impacts of DAS for uplink transmission in high-rise buildings; where remote antenna units (RAUs) are deployed on each floor throughout the building and connected to a central unit (CU) where received signals are processed. The performance of the system is analysed in terms of achievable spectral efficiency for a variety of system parameters and deployment conditions using a propagation channel model derived from multi-floor in-building path loss values retrieved from measurement data. Numerical results obtained suggest that the proposed scheme can facilitate better use of the available radio spectrum and provide higher data rates for indoor MTs than the conventional macrocell system using centralised base station antennas.