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We propose a novel method for both downlink (DL) and uplink (UL) blind channel estimation and beamforming in frequency division duplex (FDD) MISO (multiple-input single-output) antenna systems. The method is related to the concept of time reversal mirrors (TRMs). The TRM is applied so that the subscriber unit (SU) uses the UL channel "doubly", and thus there is no transmission overhead. The method's performance is close to that of optimal beamforming. With four antennas at the base station (BS) there is a gain in the range of 2-3 dB relative to a typical space-time block coder without feedback.