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We analyze the asymptotic error performance of different receiver schemes based on block space-time codes over a fully correlated Rician fading MIMO channel. The receivers differ in the way they obtain the channel state information at the receiver (CSIR) required to detect the transmitted signal. The baseline is a genie-aided receiver, which has perfect CSIR knowledge without any power or rate expenditure. Alternatively, a mismatched receiver extracts CSIR by pilot symbol insertion and uses it in the perfect CSIR decision metric. Finally, an optimum receiver, avoiding direct CSIR detection, estimates the transmitted data from the whole received sample and from the knowledge of pilot symbols. Key results are the receiver diversity and asymptotic power gain.