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Consider a wireless communication system in flat fading with N transmit and M receive antennas using space-time block coding, where N × 1 code vectors are transmitted over L symbol intervals resulting in an N × L code matrix. A least-squares estimate as well as a minimum mean-square estimate of the channel matrix is obtained from the sequence of Lp pilot code vectors. For the case of linear orthogonal codes with N = L over constant envelope constellations, we obtain an expression for the exact decoding error probability. We also find the coding gain for high average signal-to-noise ratio per diversity branch.