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In this paper, we investigate the capacity of orthogonal space-time block coding (STBC) in Rayleigh fading, subject to different power and rate adaptation policies. These policies can be performed on a frame-by-frame basis provided that partial channel state information (CSI), consisting of the signal-to-noise ratio (SNR) level as estimated by the receiver, is fed back to the transmitter. This allows for adapting the transmit power and rate to the variations of the fading channel using different policies that provide for different compromises between the achievable capacity and the corresponding implementation complexity. In particular, we derive exact closed-form expressions for the Shannon capacity of three power and rate adaptation policies, namely, the optimal power and rate adaptation, the total channel inversion with fixed rate policy, and its variant, the so-called truncated channel inversion with fixed rate policy.