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This paper derives respective precise bit error probability (BEP) expressions for a two-user binary phase shift keying (BPSK) system in Rayleigh, Nakagami and Rician fading channels. Our expressions allow for different symbol rate and symbol timing asynchronism between the desired user and interfering user. We provide some theoretical results concerning the BEP performance with respect to the fading severity. Comprehensive simulation study and comparison of the BEP performance between the Gaussian and non-Gaussian interference models are also provided. The results show that the Gaussian interference model has limitation in predicting the exact BEP performance in fading channels. It fails in accurately tracking the variation of the BEP with respect to the signal-to-noise ratio (SNR), signal-to-interference ratio (SIR), symbol rate ratio and fading severity.