A method implemented in a user terminal is disclosed. The method comprises obtaining known precoding matrix P of rank r and modulation and coding scheme assignments used in an original transmission, and a desired retransmission rank r′, forming an approximate channel covariance matrix, estimating a minimum mean square error receiver SINR for each layer to be retransmitted responsive to said forming, and finding a retransmission precoding matrix from a preceding codebook that maximizes a sum-rate for enabling precoding selections for retransmissions in uplink multiple-input multiple-output MIMO hybrid automatic repeat request HARQ. Other methods, apparatuses, and systems also are disclosed.