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In this paper we present an analytical model to assess the blocking capacity of multi-service CDMA systems. Our model can include smart antenna systems and we show, how the capacity of CDMA systems can improve if smart antennas are employed at the base stations. Applying smart antennas can actually transform CDMA systems from being interference limited into being channel/code limited. To investigate this effect, we extend our model to include the limitation of channelization codes in CDMA based UMTS systems. From the point of view of the CAC in a smart antenna CDMA system, we can either accept the capacity loss due to code limitation, or we can additionally apply SDMA techniques to re-use channelization codes and thus re-approach the capacity which is obtained if no code limitation is considered.