A precoder for an effective channel linking a wireless receiver to a wireless transmitter includes a precoder report and a precoder update report, the effective channel including a propagation channel, transmit filters and receive filters. A structured frequency-selectivity of the effective channel is determined, the structured frequency-selectivity being induced by one or more long term and/or persistent parameters of the effective channel. The precoder update report is generated based on the structured frequency-selectivity. The precoder update report includes frequency-dependent phase compensation which accounts for the structured frequency-selectivity. The precoder report is generated for the effective channel based on channel state information determined for the effective channel. The precoder report and the precoder update report are transmitted to the wireless transmitter. The transmitter determines a transmission operation based on the precoder report and the precoder update report, and transmits data to the wireless receiver in accordance with the transmission operation.