To boost the performance of binary pulse amplitude modulation at low signal-to-noise ratio, the parameter-tuned stochastic resonance (SR) is introduced into digital communications system. In this study, an analytical framework is developed for evaluating the system performance by approximating the probability density function of the Ornstein–Uhlebeck noise based on the central limit theorem. Expression for the bit error rate of the bistable SR system with coherent receiver is derived. Theoretical and numerical results are presented to verify the analysis that the noise can improve the performance of the SR system with non-coherent receiver. Also, it is shown that the performance of the bistable SR system with coherent receiver is superior to that with non-coherent receiver, and the background noise is not favourable to signal processing in the coherent receiver.