Antenna diversity technique improves the instantaneous and average signal to noise ratio (SNR) by combining all the diversity branches. The channel noise and fading reduce the performance of any communication system through making loss of some information of the transmitted symbol. In this paper, we mathematically represented the effect of noise and multi-path fading on the transmitted signal. Then we performed a computer simulation study to show the BER performance of the fading channel and also showed how the BER performance of the fading channel could be improved by Antenna diversity technique.