  Binaural reproduction for headphone-centric listening has become a focal
point in ongoing research, particularly within the realm of advancing
technologies such as augmented and virtual reality (AR and VR). The demand for
high-quality spatial audio in these applications is essential to uphold a
seamless sense of immersion. However, challenges arise from wearable recording
devices equipped with only a limited number of microphones and irregular
microphone placements due to design constraints. These factors contribute to
limited reproduction quality compared to reference signals captured by
high-order microphone arrays. This paper introduces a novel optimization loss
tailored for a beamforming-based, signal-independent binaural reproduction
scheme. This method, named iMagLS-BSM incorporates an interaural level
difference (ILD) error term into the previously proposed binaural signal
matching (BSM) magnitude least squares (MagLS) rendering loss for lateral plane
angles. The method leverages nonlinear programming to minimize the introduced
loss. Preliminary results show a substantial reduction in ILD error, while
maintaining a binaural magnitude error comparable to that achieved with a MagLS
BSM solution. These findings hold promise for enhancing the overall spatial
quality of resultant binaural signals.
