A radio frequency (RF) modem for a mobile communications device comprises a monitoring circuit; an RF circuit having a demodulator, the RF circuit being for receiving RF signals; a baseband processing unit, for processing baseband signals; and a controller. The RF modem can enter a sleep mode in which the monitoring circuit is operational and the RF circuit and the baseband processing unit are not operational. The controller is responsive to an indication from the monitoring circuit to control the RF modem to enter a monitoring mode in which the RF circuit is operational and the baseband processing unit is not operational. The RF circuit is configured for data reception in the monitoring mode. The controller then controls the RF modem to exit the monitoring mode and to enter a baseband processing mode in which the baseband processing unit is operational to process data signals provided by the RF circuit.