## 1 Introduction  
### Background  
Audio reproduction systems for surround sound are currently in a state of evolution. Audio engineers and researchers are increasingly looking to improve on the spatial impression and realism that are offered by conventional 5.1 systems through the incorporation of loudspeakers in the vertical domain. The implementation of these so-called 'height channels' has seen audio reproduction systems move into the third dimension, with systems, such as Dolby Atmos [1] and Auro-3D [2] becoming more widely utilized in film and music productions. Such developments inevitably have implications for the sound recording process, as additional height layers of microphones are required alongside the pre-existing main channel layer to capture the necessary spatial information. In the context of three-dimensional (3D) sound recording using microphones, it is necessary to consider interchannel crosstalk oriented between vertically arranged microphones in terms of vertical phantom image localisation. Consider a 3D microphone array that consists of two vertical layers of microphones. For most classical music settings, the lower (main) layer would be typically used to mainly capture direct sounds for horizontal source imaging, whilst the upper (height) layer would be used to capture more reflections and reverberation to enhance perceived listener envelopment (LEV). Ideally, in this case the height layer signals should not interfere with the vertical localisationof source images presented from the main loudspeaker layer. If there were excessive amounts of direct sounds present in the height microphone signals, however the vertically-oriented phantom images may be perceived at intermediate positions between the main and height loudspeakers layers in reproduction. The direct sound present in the height layer is referred to as vertical interchannel crosstalk (VIC) [3]. Conceptually, the phantom image localisation in the presence of VIC can be compared with the precedence effect between the lead and lag signals [4; 5]. In horizontal stereophonic reproduction, it is well known that the precedence effect operates when an interchannel time difference (ICTD) is introduced between the loudspeaker signals; a time delay that is greater than around 1 ms would cause the resulting phantom image to be fully localised at the position of the earlier loudspeaker. If the same effects were also effective in the vertical stereophonic reproduction, VIC from a vertically spaced pair of omni-directional microphones would not cause such vertical localisation interference. However, a previous study by the present authors [6] showed that the precedence effect would not be triggered in vertical stereophony, with the influence of ICTD on vertical localisation being mainly dependent on comb-filtering of the ear-input signals. This necessitates the suppression of VIC in the height microphone signals. From the above background, previous studies [3; 7; 8; 9] subjectively measured the minimum amount of level reduction that is necessary in the upper loudspeaker for the resultant phantom image to be localised at the position of the sound presented from the lower loudspeaker only, which is commonly referred to the'vertical localisation threshold' (VLT). The loudspeakers were arranged at 0\({}^{\circ}\) (listener's ear height) and 30\({}^{\circ}\) elevations in the median plane (i.e., vertical stereophonic setup). Various types of sound sources (cello and bongo [3], conga, quartet, speech, guitar, and oboe [9], broadband and octave-band noises [8], as well as a range of ICTDs, were tested in those studies. The results from the studies largely agreed, in that the VLT for natural sources were commonly around \(-\)7 dB for the ICTDs of 1 to 10 ms, and \(-\)9.5 dB for the ICTD of 0 ms [9].