A method of transmitting from a transmitter to a receiver over a wireless multiple-input-multiple-output channel comprising a series of frequency intervals, the method comprising: based on one or more performance criteria evaluated in relation to a previously received transmission from the transmitter, selecting at the receiver a first precoding matrix out of a predetermined set of precoding matrices for transmitting from the transmitter to the receiver on a first of said frequency intervals; and for each successive frequency interval in the series: determining, from said predetermined set of precoding matrices, a subsetof precoding matrices; based on one or more performance criteria evaluated in relation to the previously received transmission, selecting at the receiver a respective precoding matrix from said predetermined set for transmission from the transmitter to the receiver on said successive frequency interval; and feeding back an index of that respective precoding matrix from the receiver to the transmitter using a differential encoding scheme whereby the respective index is indicated relative to said subset of precoding matrices; characterized by, wherein said subset for each successive frequency interval is a subset of most-probable precoding matrices having a conditional probability of being selected for transmission from the transmitter to the receiver, the conditional probability being computed by accumulating data on previous observed transitions in the selected precoding matrix and being used to determine the subset. based on one or more performance criteria evaluated in relation to a previously received transmission from the transmitter, selecting at the receiver a first precoding matrix out of a predetermined set of precoding matrices for transmitting from the transmitter to the receiver on a first of said frequency intervals; and for each successive frequency interval in the series: determining, from said predetermined set of precoding matrices, a subsetof precoding matrices; based on one or more performance criteria evaluated in relation to the previously received transmission, selecting at the receiver a respective precoding matrix from said predetermined set for transmission from the transmitter to the receiver on said successive frequency interval; and feeding back an index of that respective precoding matrix from the receiver to the transmitter using a differential encoding scheme whereby the respective index is indicated relative to said subset of precoding matrices; characterized by, wherein said subset for each successive frequency interval is a subset of most-probable precoding matrices having a conditional probability of being selected for transmission from the transmitter to the receiver, the conditional probability being computed by accumulating data on previous observed transitions in the selected precoding matrix and being used to determine the subset. determining, from said predetermined set of precoding matrices, a subsetof precoding matrices; based on one or more performance criteria evaluated in relation to the previously received transmission, selecting at the receiver a respective precoding matrix from said predetermined set for transmission from the transmitter to the receiver on said successive frequency interval; and feeding back an index of that respective precoding matrix from the receiver to the transmitter using a differential encoding scheme whereby the respective index is indicated relative to said subset of precoding matrices; characterized by, wherein said subset for each successive frequency interval is a subset of most-probable precoding matrices having a conditional probability of being selected for transmission from the transmitter to the receiver, the conditional probability being computed by accumulating data on previous observed transitions in the selected precoding matrix and being used to determine the subset.