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Closed-loop space-time block codes (STBCs) for multiple transmit antennas, using phase feedback, have recently been proposed. These codes, with perfect phase feedback, achieve full diversity. However, a large number of feedback bits are required, which is not practical. In this paper, we analyze a quantized two-phase feedback scheme for eight transmit antennas and one receive antenna system with full rate. Simulation results show that this quantized phase feedback scheme provides nearly ideal transmit diversity gain for eight transmit antennas.