In this paper, we examine the bit error rate (BER) performance of square orthogonal space-time block codes (OSTBCs) under arbitrarily correlated Rayleigh fading channels. We consider a mismatched maximum-likelihood receiver that obtains the channel state information through pilot-based linear minimum mean-square error channel estimation. For PAM and QAM constellations, a closed-form approximation of the BER is presented, which yields very accurate BER results over a wide range of signal-to-noise ratios.