Authentication system for a vehicle, comprising a portable ID transmitter and a vehicle-side authentication arrangement, wherein the authentication arrangement comprises a number of UWB antennas with at least a first UWB antenna and a second UWB antenna arranged at a distance from each other on the vehicle, wherein the ID transmitter has a housing: - a supply battery, - a microcontroller, - UWB transmitter and receiver circuits controlled by the microcontroller for communication with a control unit on the vehicle, - an LF receiver circuit coupled to the microcontroller for receiving LF wake-up signals transmitted in the LF frequency range, whereby the microcontroller is set up to, when the LF receiver circuit has received an LF wake-up signal, transmit a UWB signal for reception by a UWB interface of the vehicle, which is coupled to the vehicle's control unit, to receive a UWB response signal, to capture the time difference between sending the UWB signal and receiving the UWB response signal, to check whether the time difference or a value derived from the time difference does not exceed a specified maximum value, and depending on the result of the checking, transmit a radio signal to the vehicle's control unit that has an enable value wherein the ID transmitter is designed to check a number of LF signals for an identity identifier, to detect signal strength values for the LF signals and to respond to the reception of the LF signals with an RF response signal which includes the identity code of the LF signal with the strongest signal strength value and/or a list of identity codes with the assigned signal strength values, whereby the authentication arrangement is designed to carry out: selecting a UWB antenna from the number of UWB antennas of the authentication arrangement as the selected UWB antenna, the UWB antenna being selected at least as a function of the received signal strength or the received signal strengths of the at least one LF signal which is transmitted between an LF interface of the authentication arrangement and the ID transmitter; and controlling the selected UWB antenna to perform UWB communication between the ID transmitter and the authentication device. wherein the ID transmitter has a housing: - a supply battery, - a microcontroller, - UWB transmitter and receiver circuits controlled by the microcontroller for communication with a control unit on the vehicle, - an LF receiver circuit coupled to the microcontroller for receiving LF wake-up signals transmitted in the LF frequency range, - a supply battery, - a microcontroller, - UWB transmitter and receiver circuits controlled by the microcontroller for communication with a control unit on the vehicle, - an LF receiver circuit coupled to the microcontroller for receiving LF wake-up signals transmitted in the LF frequency range, whereby the microcontroller is set up to, when the LF receiver circuit has received an LF wake-up signal, transmit a UWB signal for reception by a UWB interface of the vehicle, which is coupled to the vehicle's control unit, to receive a UWB response signal, to capture the time difference between sending the UWB signal and receiving the UWB response signal, to check whether the time difference or a value derived from the time difference does not exceed a specified maximum value, and depending on the result of the checking, transmit a radio signal to the vehicle's control unit that has an enable value wherein the ID transmitter is designed to check a number of LF signals for an identity identifier, to detect signal strength values for the LF signals and to respond to the reception of the LF signals with an RF response signal which includes the identity code of the LF signal with the strongest signal strength value and/or a list of identity codes with the assigned signal strength values, whereby the authentication arrangement is designed to carry out: selecting a UWB antenna from the number of UWB antennas of the authentication arrangement as the selected UWB antenna, the UWB antenna being selected at least as a function of the received signal strength or the received signal strengths of the at least one LF signal which is transmitted between an LF interface of the authentication arrangement and the ID transmitter; and controlling the selected UWB antenna to perform UWB communication between the ID transmitter and the authentication device. selecting a UWB antenna from the number of UWB antennas of the authentication arrangement as the selected UWB antenna, the UWB antenna being selected at least as a function of the received signal strength or the received signal strengths of the at least one LF signal which is transmitted between an LF interface of the authentication arrangement and the ID transmitter; and controlling the selected UWB antenna to perform UWB communication between the ID transmitter and the authentication device.