Access control system (1) for buildings (2) with a stationary unit (20) and a mobile unit (10), wherein the mobile unit (10) has a mobile
transceiver (11) which is designed to wirelessly and encryptedly transmit signals (S) for
authentication and
authorization of the mobile unit (10) with respect to the stationary unit (20) and for control of the stationary unit (20) by the mobile unit (10) to a stationary
transceiver (21) of the stationary unit (20), which has at least a first
antenna array (23A) and a second
antenna array (23B), wherein the antennas (23) of the respective
antenna array (23A, 23B) lie in a common antenna
reference plane (E1, E2) and the antenna reference planes (E1, E2) of the antenna arrays (23A, 23B) are tilted relative to one another, wherein the stationary unit (20) comprises a control device (22) which is designed to determine a distance (r) and an angle (Φ) as a position of the mobile unit (10) relative to the stationary unit (20) from signals (S) transmitted from the mobile
transceiver (11) to the stationary transceiver (21), so that the position of the mobile unit (10) can be specified as polar coordinates of a polar coordinate
system lying in a horizontal plane, in whose coordinate origin the stationary transceiver (21) is arranged, and to control a function when a control command for triggering the function is transmitted to the stationary unit (20) by a mobile unit (10) authenticated and authorized by the stationary unit (20) and / or the position of the mobile unit (10) is within a predetermined access area (30), and wherein the control device (22) is designed to determine a respective reception angle (Φ1, Φ2) specific for the respective antenna array (23A, 23B) from signals (S) transmitted from the mobile transceiver (11) to the stationary transceiver (21) and received by the antenna arrays (23A, 23B), to determine a quadrant of the polar coordinate
system in which the position lies from the reception angles (Φ1, Φ2), and to determine the angle (Φ) of the position from the reception angle (Φ1, Φ2), which lies in an
angular range predetermined for the respective antenna array (23A, 23B) with a predetermined low measurement error, and the quadrant.