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This thesis discuss on new technique called space time block coding (especially Alamouti‟s code) which is used to increase capacity and reliability of data transmission over time varying multi-path fading channel. The over all work of the thesis included in the following four chapters. In chapter-1 we are going to cover some theoretical part which is useful to understand thesis work and in chapter-2 we will discuss the comparison between simple space time block code (Alamouti‟s code) and MRRC (Maximum Ratio Receiver Combining) which is receiver diversity and then in chapter-3 we will see the channel capacity & probability error performance for 2x2 Alamouti code over Rayleigh and Rice fading channel.Finally the conclusion and further work included in chapter-4