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The closed-form exact bit error rate (BER) expressions of generalized orthogonal space-time block codes (OSTBCs) are first derived for quadrature amplitude modulation (QAM) and phase shift keying (PSK) constellations in spatially white Rayleigh multiple input multiple output (MIMO) channels. Then this analysis is generalized to arbitrarily spatially correlated MIMO channels. Based on the BER analysis, the transmission power of the generalized OSTBCs is optimized such that the average BER is minimized. Furthermore, the optimum transmit power which maximizes the upper-bound of the capacity is derived in closed-form.