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We propose a new joint receiver for the blind detection of synchronous co-channel multiuser signals modulated with orthogonal space-time block codes (OSTBC). We exploit the algebraic structure of the orthogonal space-time block codes and the constellation feature of Quadrature Amplitude Modulation (QAM) signals to develop a blind zero-forcing (ZF) detector based on quadratic programming (QP) with desirable convergence properties. Focusing on high rate space-time block codes in synchronous co-channel multiuser systems, we propose a successive processing joint receiver based on the proposed blind detector with low computational complexity and fast convergence. For signal detection in single user MIMO systems, the proposed QP algorithm has performance similar to that of maximum-likelihood receiver with wireless channel information. Unlike many existing techniques, our new receiver is applicable to full-rate orthogonal space-time block codes such as the practically popular Alamouti code. Furthermore, our QP receiver for multiuser detection relaxes stringent conditions on the number of receive antennas of the multi-input-multi-output (MIMO) transceiver systems.