# Adaptive Binaural Cue-Based Amplitude Panning in Irregular Loudspeaker Configurations
## 1 Introduction  
Spatial sound field reproduction seeks to establish an immersive acoustic environment within a predefined region, enabling the listener to experience a virtual yet realistic replication of the original sound field. Techniques that physically recreate an acoustic field are referred to as sound field synthesis [1]. Examples include Wave Field Synthesis (WFS) [2, 3, 4, 5, 6], Higher Order Ambisonics (HOA) [7, 8, 9], and the pressure matching method [10, 11]. In contrast, amplitude panning methods attempt to create a plausible spatial perception by delivering the relevant psychoacoustic cues to the listener's ears. These perceptually motivated reproduction techniques distribute the source signal across multiple loudspeakers, assigning a gain to each to create a sound image or virtual sound source from the desired direction. Such methods are advantageous for practical applications, offering low computational complexity, absence of destructive interference in the'sweet spot', high timbral quality, and gradual degradation of sound quality outside the'sweet spot' [12]. Vector-based amplitude panning (VBAP) [13, 14, 15, 16] is the most widely used perceptually motivated method for two- and three-dimensional multi-loudspeaker reproduction, forming the basisof spatial and object-based audio standards, such as MPEG-H [17]. The multiple direction amplitude panning (MDAP) method [18] extends VBAP by introducing additional virtual sources around the intended source position, allowing for the synthesis of both uniform and variable source spreads. The distance-based amplitude panning (DBAP) method [19] is used for irregular setups, taking the actual positions of the loudspeakers in space as the point of departure. All-Round Ambisonic Panning (AIIRAP) [20] creates phantom sources with stable loudness and adjustable source width. Additionally, a convex optimization-based method has been proposed to allow the precise control of source spread [12; 21; 22]. The Compensated Amplitude Panning (CAP) method [23; 24; 25] is proposed by considering the orientation of the listener's head. Frequency-dependent gain panning methods [26; 27] have been proposed to maintain consistent loudness and localization. Most amplitude panning methods assume that the listener is positioned at the'sweet spot', with loudspeakers arranged equidistantly and symmetrically around them. However, achieving such an idealized listening environment can be challenging, particularly in domestic and cabin settings. In consumer systems, where loudspeaker positions may deviate from their canonical locations, the perceived direction of the virtual sound source may shift away from its intended location. To address this problem, techniques such as time-aligning and loudness-matching loudspeakers based on distance [28] have been proposed. A modified panning approach for non-equidistant loudspeakers, considering the composite contributions of direct sound from multiple loudspeakers, has also been suggested [29]. However, these compensation methods for amplitude panning assume each loudspeaker behaves as an omnidirectional point source in a free field, thereby neglecting frequency-dependent factors, including room modes, loudspeaker directivity, and inter-loudspeaker variations. Moreover, these methods frequently presume that, after compensation, the reproduction system approximates an ideal listening environment, enabling the application of panning methods predicated on idealized conditions. This assumption disregards the persistent effects of irregular setups and various listening environments, ultimately leading to inaccuracies in the perceived direction of virtual sound sources. To enhance the listening experience in acoustic environments with irregular loudspeaker configurations, this paper introduces an adaptive binaural cue-based amplitude panning algorithm designed to accurately reproduce the azimuth angle of virtual sound sources.