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Reckon for the considerable beamforming gain, eigen-based beamforming (EBB) has been proved to be a promising case to ensure cell edge link robustness. For simplicity, both spatial multiplexing gain and beamforming gain can be obtained with conventional rank adaptive EBB scheme, however, former researches suggest that it doesn't work well at cell edge region. A novel ACK/NAK aided rank adaptive algorithm (AARAA) is proposed for EBB system in this paper with the aim to enhance the spectral efficiency and obtain a Block Error Ratio (BLER) convergence. AARAA employs the HARQ feedback information from previous transmissions as an adjustable factor for rank adaptation, thus the BLER of the first transmissions is controlled in order to lower the retransmission probability and increase resource efficiency. Simulation results show that AARAA can achieve balanced cell average spectrum efficiency and cell edge user spectrum efficiency. Furthermore, AARAA can obtain less BLER than conventional rank adaptive scheme.