A communication system with a plurality of devices with a communication unit (CU1) arranged to communicate on a first wireless communication channel (CH1), e.g. GSM, in an active mode. Otherwise, the communication unit (CU1) is in an in-active power saving mode. A receiver unit (R1, R2) receives a wake-up signal on a second wireless communication channel (CH2, CH3), e.g. RFID. The receiver unit (R1, R2) then switches the communication unit (CU1) into active mode. The second wireless communication channel (CH2, CH3) is dedicated for wake-up signals and is in a different frequency band than the first wireless communication channel (CH1). Further, the first wireless communication channel (CH1) has a larger distance range than the second wireless communication channel (CH2, CH3). A coordinator device (CD) receives a call on the first wireless communication channel (GSM) and transmits a wake-up signal on the second wireless communication channel (RFID) in order to activate communication units (D1, D2, D3, D4) in a group of the plurality of devices (D1, D2, D3, D4). Hereby power can be saved to the typically more power demanding communication unit (CU1) arranged for long distance communication, while only limited or even zero power is used to monitor for wake-up signals on a short range channel (CH2, CH3). The system is suitable for groups of a plurality of rather closely spaced devices (D1, D2, D3, D4), where one active coordinator device (CD) is used to receive incoming calls on behalf of a group of devices (D1, D2, D3, D4) having their communication units in power saving mode until the coordinator device (CD) activates them.