Super-imposed training can be used as an alternative solution to estimating the channel state information (CSI). Since pilots are sent together with the data symbols, superimposed training improves the bandwidth efficiency. In this paper, we study the effects of the channel estimation errors on binary phase shift keying (BPSK) systems using superimposed pilots. Specifically, we derive an approximate bit error rate (BER) expression in low signal-to-noise ratio (SNR) region while in high SNR region, we derive the lower bound of the BER. Simulation results are then provided to corroborate the proposed studies.