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In wireless systems, coverage and capacity is a major challenge especially in high buildings. The system performance is impaired by co-channel interference due to the need to reuse the limited available spectrum in neighbouring floors. In this environment, distributed antenna systems (DASs) can provide adequate coverage and high speed data services in the presence of multipath fading and co-channel interference by optimally combining the same signal from several antennas. This paper proposes a DAS for uplink transmission in high-rise buildings; where remote antenna units (RAUs) are deployed on each floor so as to reduce the access distance while at the same time exploiting spatial diversity. The RAUs are connected to a central unit (CU) where received signals are processed. To analyse the bit error rate (BER) performance of the system with diversity reception, Nakagami/Rayleigh fading channel is assumed for different building geometries and a propagation channel model for in-building propagation is developed based on multiple floor in-building path loss values retrieved from measurement data. This model accounts for the propagation between different floors and ceilings and includes possible reflections from surrounding buildings. The effects of different numbers of receive antennas per floor and deployment conditions are investigated. Numerical results indicate that the proposed scheme provides improved BER performance, leading to many more simultaneous users being supported on the same frequency in high buildings when compared with a system with a single antenna per floor.