Hearing aid with signal enhancement

A binaural hearing aid system, comprising:

• at least one microphone for provision of at least one microphone audio signal in response to sound received at the at least one microphone;
• a signal separation unit configured to provide an estimate of one of a target signal and a noise signal based on the at least one microphone audio signal;
• a phase shift circuit configured to phase shift the estimate;
• a phase shift adder connected to provide a phase shifted signal, wherein the phase shifted signal is based at least in part on the phase shifted estimate of one of the target signal and the noise signal;
• a first receiver for conversion of a first receiver input signal into a first acoustic signal for transmission towards a first eardrum of a user of the binaural hearing aid system;
• and
• a second receiver for conversion of a second receiver input signal into a second acoustic signal for transmission towards a second eardrum of the user;
• wherein one of the first receiver input signal and the second receiver input signal represents the phase shifted signal, and the other one of the first receiver input signal and the second receiver input signal represents the sound received at the at least one microphone.