A method minimizes a rate for feeding back channel state information from a receiver to a transmitter in a multi-input, multi-output communications systems. A temporal autocorrelation function of the channel between the transmitter and the receiver is determined. A spatial covariance information is estimated of the channel. Then, the minimum rate for feeding back channel state information from the receiver to the transmitter is based on actual channel state information and the estimated spatial covariance information and the temporal autocorrelation function.