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The smart antenna (SA) can adjust the direction pattern adaptively and reduce the interference signals using some adaptive interference ing algorithms, and thus enhances the performance of mobile telecommunication systems. It especially enlarges the user system capacity. The smart antenna system is mainly applied to the base station (BS) now, but in the next step, the smart antenna technology will be applied to mobile stations (MS), along with hardware and software in the MS becoming more powerful. This article provides a description and analysis of some basic adaptive algorithms and their modifications. The smart antenna system will be applied in both BS and MS in next generation mobile telecommunication systems.