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This paper investigates orthogonal space-time block-coded (OSTBC) transmission for a multiple-input multiple-output (MIMO) channel with noncoherent amplify-and-forward (AF) relaying in a situation where the source-relay and relay-destination channels undergo Rayleigh fading and Rician fading, respectively. Fading coefficients of the Rician channel are considered to be correlated. Different scenarios are then considered for the Rician channel. We derive exact expressions for the moment-generating function (mgf) and the first and second moments of the instantaneous signal-to-noise ratio (SNR) at the destination to statistically characterize system behavior. We also derive the exact expressions for the probability density function (pdf) and the cumulative distributive function (cdf) to discuss system behavior with the Rician factor. We then analyze system performance by deriving new analytical expressions for the bit error rate (BER), outage probability, amount of fading (AoF), diversity order, and array gain. These performance metrics reveal that strong line-of-sight (LoS) components between a relay-destination link always limit the performance promised by the MIMO scattering environment when both nodes have multiple antennas.