Binaural hearing system comprising bilateral compression

A binaural hearing system comprising:

• a first hearing device configured for placement at, or in, a first ear of a user, the first hearing device comprising a first microphone arrangement and a first processing unit, wherein the first microphone arrangement comprises a first in-ear microphone configured to pick-up sound pressure associated with a first ear;
• and
• a second hearing device configured for placement at, or in, a second ear of the user, the second hearing device comprising a second microphone arrangement and a second processing unit, wherein the second microphone arrangement comprises a second in-ear microphone arranged to pick-up sound pressure associated with a second ear;
• wherein the first hearing device and the second hearing device are connectable through a wireless communication link;
• wherein the first processing unit is configured to:
• receive a first microphone signal generated by the first in-ear microphone,
• receive contralateral audio data representative of a second microphone signal transmitted from the second hearing device to the first hearing device via the wireless communication link,
• estimate a first interaural level difference based on the first microphone signal and the contralateral audio data,
• determine a first gain for the first microphone signal based on a level of the first microphone signal in accordance with a first level-versus-gain characteristic,
• adjust the first gain, and
• apply the adjusted first gain to the first microphone signal to generate a first output signal.