Method of operating an authentication system of a vehicle for authenticating a portable ID transponder to the vehicle for enabling vehicle functions for a user who carries the portable ID transponder, wherein the authentication system comprises the portable ID transponder and a vehicle-side authentication arrangement, the authentication arrangement comprising a number of UWB antennas (6, 7) with at least a first UWB antenna and a second UWB antenna arranged spaced apart from each other on the vehicle, wherein the method comprises at least the following steps: A) selecting a UWB antenna (6, 7) from the number of UWB antennas (6, 7) of the authentication arrangement as the selected UWB antenna, wherein the selection of the UWB antenna in step A) comprises the creation of a list, which specifies a prioritization of the UWB antennas, so that an order of the available UWB antennas is already determined before a UWB communication is carried out, in which order the UWB antennas are addressed, wherein the selection of the UWB antenna is carried out at least - depending on a received signal strength of an LF signal transmitted between the ID transponder and an LF interface (8, 9) of the authentication arrangement, and/or - depending on a received signal strength of an RF signal transmitted between the ID transponder and an RF interface of the authentication arrangement, and/or - depending on a proximity signal from a proximity sensor (10, 11) arranged on the vehicle; wherein at least steps B)-E) are repeated sequentially for each UWB antenna of the prioritizing list, taking into account the prioritization of the UWB antennas given by the list, until a predetermined termination condition is reached, B) driving the selected UWB antenna to perform UWB communication between the ID transponder and the authentication arrangement; C) performing UWB communication between the ID transponder and the authentication arrangement; D) detecting a propagation delay of a UWB signal of the UWB communication between the ID transponder and the selected UWB antenna; E) checking whether the propagation time of the UWB signal is less than a specified maximum propagation time. A) selecting a UWB antenna (6, 7) from the number of UWB antennas (6, 7) of the authentication arrangement as the selected UWB antenna, wherein the selection of the UWB antenna in step A) comprises the creation of a list, which specifies a prioritization of the UWB antennas, so that an order of the available UWB antennas is already determined before a UWB communication is carried out, in which order the UWB antennas are addressed, wherein the selection of the UWB antenna is carried out at least - depending on a received signal strength of an LF signal transmitted between the ID transponder and an LF interface (8, 9) of the authentication arrangement, and/or - depending on a received signal strength of an RF signal transmitted between the ID transponder and an RF interface of the authentication arrangement, and/or - depending on a proximity signal from a proximity sensor (10, 11) arranged on the vehicle; wherein at least steps B)-E) are repeated sequentially for each UWB antenna of the prioritizing list, taking into account the prioritization of the UWB antennas given by the list, until a predetermined termination condition is reached, - depending on a received signal strength of an LF signal transmitted between the ID transponder and an LF interface (8, 9) of the authentication arrangement, and/or - depending on a received signal strength of an RF signal transmitted between the ID transponder and an RF interface of the authentication arrangement, and/or - depending on a proximity signal from a proximity sensor (10, 11) arranged on the vehicle; wherein at least steps B)-E) are repeated sequentially for each UWB antenna of the prioritizing list, taking into account the prioritization of the UWB antennas given by the list, until a predetermined termination condition is reached, B) driving the selected UWB antenna to perform UWB communication between the ID transponder and the authentication arrangement; C) performing UWB communication between the ID transponder and the authentication arrangement; D) detecting a propagation delay of a UWB signal of the UWB communication between the ID transponder and the selected UWB antenna; E) checking whether the propagation time of the UWB signal is less than a specified maximum propagation time.