A binaural hearing system comprising a first hearing device to be worn at or at least partly in a first ear of a user and a second hearing device to be worn at or at least partly in a second ear of the user, each of the hearing devices comprising: a receiver unit for wirelessly receiving Radio Frequency, RF, signals, comprising a measurement unit for measuring a quality of the received RF signals so as to provide for an ipsilateral RF signal quality parameter, a control unit, and a signal processing unit for processing input audio signals so as to generate processed audio signals to provide hearing assistance; wherein the control unit comprises: an offset adapter unit for adjusting the ipsilateral RF signal quality parameter to produce an adjusted ipsilateral RF signal quality parameter, which is supplied to the ipsilateral signal processing unit, and a filter unit for providing a filtered ipsilateral RF signal quality parameter by filtering the ipsilateral RF signal quality parameter; wherein the control unit is configured to: receive a filtered contralateral RF signal quality parameter from the other hearing device, and adjust the offset adapter unit according to a difference between the filtered ipsilateral RF signal quality parameter and the filtered contralateral RF signal quality parameter; and wherein the control unit is configured to receive an adjusted contralateral RF signal quality parameter from the other hearing device (10, 12), and wherein the signal processing unit comprises a spatial awareness module to which the adjusted contralateral RF signal quallity parameter and the adjusted ipsilateral RF signal quality parameter provided by the offset adapter unit are supplied as input and wherein the spatial awareness module is configured to estimate from a difference between the adjusted ipsilateral RF signal quality parameter and the adjusted contralateral RF signal quality parameter an angular localization of a transmission unit (26, 28) which transmits the RF signal received by the two hearing devices. each of the hearing devices comprising: a receiver unit for wirelessly receiving Radio Frequency, RF, signals, comprising a measurement unit for measuring a quality of the received RF signals so as to provide for an ipsilateral RF signal quality parameter, a control unit, and a signal processing unit for processing input audio signals so as to generate processed audio signals to provide hearing assistance; a receiver unit for wirelessly receiving Radio Frequency, RF, signals, comprising a measurement unit for measuring a quality of the received RF signals so as to provide for an ipsilateral RF signal quality parameter, a control unit, and a signal processing unit for processing input audio signals so as to generate processed audio signals to provide hearing assistance; wherein the control unit comprises: an offset adapter unit for adjusting the ipsilateral RF signal quality parameter to produce an adjusted ipsilateral RF signal quality parameter, which is supplied to the ipsilateral signal processing unit, and a filter unit for providing a filtered ipsilateral RF signal quality parameter by filtering the ipsilateral RF signal quality parameter; an offset adapter unit for adjusting the ipsilateral RF signal quality parameter to produce an adjusted ipsilateral RF signal quality parameter, which is supplied to the ipsilateral signal processing unit, and a filter unit for providing a filtered ipsilateral RF signal quality parameter by filtering the ipsilateral RF signal quality parameter; wherein the control unit is configured to: receive a filtered contralateral RF signal quality parameter from the other hearing device, and adjust the offset adapter unit according to a difference between the filtered ipsilateral RF signal quality parameter and the filtered contralateral RF signal quality parameter; and receive a filtered contralateral RF signal quality parameter from the other hearing device, and adjust the offset adapter unit according to a difference between the filtered ipsilateral RF signal quality parameter and the filtered contralateral RF signal quality parameter; and wherein the control unit is configured to receive an adjusted contralateral RF signal quality parameter from the other hearing device (10, 12), and wherein the signal processing unit comprises a spatial awareness module to which the adjusted contralateral RF signal quallity parameter and the adjusted ipsilateral RF signal quality parameter provided by the offset adapter unit are supplied as input and wherein the spatial awareness module is configured to estimate from a difference between the adjusted ipsilateral RF signal quality parameter and the adjusted contralateral RF signal quality parameter an angular localization of a transmission unit (26, 28) which transmits the RF signal received by the two hearing devices.