A radio communication system comprises a primary station (100) for transmitting information signals on a downlink channel (122) and for receiving signals from one or more secondary stations (110) on an uplink random access packet channel (RACH) (124), the downlink and uplink channels being independent of each other. Power control is applied to the transmitted downlink signals by at least one of the secondary stations transmitting indicia indicating the prevailing radio channel characteristics of the uplink channel, the indicia being used by the primary station to apply power control to the downlink signals.If the uplink signals are CDMA signals the indicia may comprise a timing offset which has a value related to the quantity to be signalled.