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Most existing MIMO (multiput-input multiput-output) schemes optimize only either the diversity gain or the multiplexing gain. To obtain a good tradeoff between these two, the quasi-orthogonal group space-time (QoGST) architecture is proposed, wherein the transmit stream is subgrouped but encoded via an inter-group space-time block encoder, with group interference suppression at the receiver. This paper also considers another combined space-time coding and layered space-time architecture, which we refer to as group layered space-time (GLST), where space-time block coding is employed within each group. Under the assumption of Rayleigh fading and a prior perfect channel state information at the receiver, a performance analysis will demonstrate that both QoGST and GLST can achieve a good diversity-multiplexing tradeoff. QoGST is even superior to GLST. Simulation results will validate our analysis and further show that compared to the existent layered space-time block code (LSTBC) scheme, both QoGST and GLST can achieve a significant performance gain.