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The authors first propose a new class of full-rate full-diversity quasi-orthogonal space time block code (QO-STBC), namely QO-STBC with blind precoding (BP-QO-STBC). Based on this code, a novel open-loop multiple-input multiple-output (MIMO) multi-user downlink transmission scheme is derived. Presuming M blocks of BP-QO-STBC (which could be of different code lengths) are transmitted from the access point simultaneously, thus achieving a multiplexing gain of M, we show that the multiplexed signal can be separated by any user with only m RgesM receive antennas, which is much smaller than that required by conventional linear schemes. The proposed scheme is extendable by simple iterative construction to an arbitrary number of transmit antennas. By exploiting the special structure of BP-QO-STBC, we derived two decoding algorithms with different levels of complexities, namely an optimal maximum likelihood decoder that achieves the lowest decoding complexity known for all full-rate full-diversity QO-STBC and a suboptimal linear decoder with even lower complexity. These two decoders combined with the simple construction method of BP-QO-STBC provide flexible tradeoffs between complexity and performance, as well as between diversity and multiplexing gains. A comparison between the proposed scheme and random beamforming in terms of bit error rate and achievable sum throughput is shown via simulation, and the results support our proposed scheme as a better practical candidate for high-speed wireless network.