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Combining multiple-input multiple-output orthogonal frequency division multiplexing (MIMO-OFDM) with a massive number of transmit antennas (massive MIMO-OFDM) is an attractive way of increasing the spectrum efficiency or reducing the transmission energy per bit. The effectiveness of Massive MIMO-OFDM is strongly affected by the channel state information (CSI) estimation method used. The overheads of training frame transmission and CSI feedback decrease multiple access channel (MAC) efficiency and increase the CSI estimation cost at a user station (STA). This paper proposes a CSI estimation scheme that reduces the training frame length by using a novel pilot design and a novel unitary matrix feedback method. The proposed pilot design and unitary matrix feedback enable the access point (AP) to estimate the CSI of the signal space of all transmit antennas using a small number of training frames. Simulations in an IEEE 802.11n channel verify the attractive transmission performance of the proposed methods.