A hearing device (100, 300L, 300R) of a binaural hearing system adapted for being located in or at an ear of a user and comprising - an input transducer, which is configured to detect and convert an acoustic input signal to an electric input signal; - an output transducer, which is configured to receive and convert an electric output signal to an acoustic or vibrational output signal; - a feedback-path estimation unit, which is configured to estimate a feedback path from the output transducer to the input transducer by performing an adaptive feedback-path estimation algorithm; wherein - the feedback-path estimation unit is further configured to provide to the output transducer an electric estimation-control signal for generating an acoustic feedback-path estimation signal having an amplitude spectrum, CHARACTERIZED IN THAT the amplitude spectrum has at least one first frequency band with non-zero amplitude and at least one second frequency band with zero amplitude or with a non-zero amplitude smaller than the amplitude in the first frequency band and smaller than a level of background noise (BN') in the respective second frequency band; - the feedback-path estimation unit is further configured to control the input transducer to detect background noise (BN') in the at least one second frequency band while the feedback-path estimation signal is provided; and to estimate a background-noise amplitude in the at least one first frequency band for obtaining an estimate of the background-noise amplitude spectrum, the hearing device (300L, 300R) further comprising - a link unit (310L, 310R), which is configured to exchange, in a binaural operation mode of the hearing device, signals with an external link unit (310R, 310L) of a second hearing device (300R, 300L) that together with the hearing device forms the binaural hearing system, wherein - the link unit (310L, 310R) is configured to receive from the external link unit and provide to the feedback-path estimation unit (308L, 308R) noise-estimation signals (BNR', BNL') representing background-noise amplitudes in at least one of the second frequency bands (IIL, IIR), and wherein - the feedback-path estimation unit (308L, 308R) is configured to estimate the background-noise amplitudes (BNEL, BNER) in the corresponding at least one of the first frequency bands (IL, IR) using the received noise-estimation signals (BNR', BNL'), thereby obtaining the estimate of said background-noise amplitude spectrum to which the input transducer is exposed. - an input transducer, which is configured to detect and convert an acoustic input signal to an electric input signal; - an output transducer, which is configured to receive and convert an electric output signal to an acoustic or vibrational output signal; - a feedback-path estimation unit, which is configured to estimate a feedback path from the output transducer to the input transducer by performing an adaptive feedback-path estimation algorithm; wherein - the feedback-path estimation unit is further configured to provide to the output transducer an electric estimation-control signal for generating an acoustic feedback-path estimation signal having an amplitude spectrum, CHARACTERIZED IN THAT the amplitude spectrum has at least one first frequency band with non-zero amplitude and at least one second frequency band with zero amplitude or with a non-zero amplitude smaller than the amplitude in the first frequency band and smaller than a level of background noise (BN') in the respective second frequency band; - the feedback-path estimation unit is further configured to control the input transducer to detect background noise (BN') in the at least one second frequency band while the feedback-path estimation signal is provided; and to estimate a background-noise amplitude in the at least one first frequency band for obtaining an estimate of the background-noise amplitude spectrum, the hearing device (300L, 300R) further comprising - the feedback-path estimation unit is further configured to control the input transducer to detect background noise (BN') in the at least one second frequency band while the feedback-path estimation signal is provided; and - a link unit (310L, 310R), which is configured to exchange, in a binaural operation mode of the hearing device, signals with an external link unit (310R, 310L) of a second hearing device (300R, 300L) that together with the hearing device forms the binaural hearing system, wherein - the link unit (310L, 310R) is configured to receive from the external link unit and provide to the feedback-path estimation unit (308L, 308R) noise-estimation signals (BNR', BNL') representing background-noise amplitudes in at least one of the second frequency bands (IIL, IIR), and wherein - the feedback-path estimation unit (308L, 308R) is configured to estimate the background-noise amplitudes (BNEL, BNER) in the corresponding at least one of the first frequency bands (IL, IR) using the received noise-estimation signals (BNR', BNL'), thereby obtaining the estimate of said background-noise amplitude spectrum to which the input transducer is exposed.