## 1 Introduction  
In audio reproduction systems for three-dimensional (3D) sound, such as Auro 3D [1] and Dolby Atmos [2], the loudspeakers can generally be divided into two layers: the lower (main) layer and the upper (height) layer. In the context of sound recording made using a microphone array in an acoustic space, the frontal loudspeakers of the main layer, which are located on the horizontal plane, are predominantly used for sound source positioning. Conversely, the height layer, which is typically elevated by between 30\({}^{\circ}\) and 45\({}^{\circ}\), primarily aims to enhance the perceived listener envelopment (LEV) by presenting ambient signals, although it can also be used to reproduce elevated sound sources. When recording for such formats, it is necessary to pay close attention to the amount of direct sound present in the height layer signal. The reason for this is as follows. Should there be excessive direct sound in the height layer then, at the reproduction stage, sound sources may be perceived as vertically-oriented phantom images at intermediate positions between the main and height loudspeaker layers. Additional spatial and timbral effects may also be perceived, depending on the time and level relationships between the direct sounds in the respective layers. Collectively, these properties comprise an interference effect referred to as'vertical interchannel crosstalk'. To date, the few studies that have considered vertical interchannel crosstalk have primarily been concerned with preventing the direct sound present in the height layer from affecting the perceived location of the main channel signal. Although this has received little attention in the literature, suggestions as to the nature of the effect can be garnered from studies undertaken within the context of vertical amplitude panning. Within such studies, the literature generally agrees that increases in interchannel level difference (ICLD) between vertically arranged stereophonic loudspeakers will cause the resultant phantom image to be localised in a position biased towards the loudspeaker of greater amplitude [3; 4; 5; 6; 7]. Despite this, such studies do not necessarily indicate that sufficient ICLD alone will prevent the signal in the height layer from affecting the perceived location of the main channel signal. For example, whilst [PERSON] [5] demonstrated that ICLDs between 6 and 9 dB resulted in the perceived phantom image position matching the physical position of the lower loudspeaker for pink noise and speech sources, [PERSON] et al. [3] and [PERSON] and [PERSON] [7] found that the phantom images remained somewhat elevated for ICLDs up to and including 15 dB when the test stimuli were musical sources, pink noise and speech. It should be noted that differences in the experimental setup and, in particular, the physical position of the loudspeakers might have contributed to these differences in results. With respect to more direct experiments into the effects of vertical interchannel crosstalk, [PERSON] [8] conducted an analysis into the 'localisation threshold', which was defined as the minimum amount of attenuation of direct sound necessary in the height layer for the main channel signal to be localised at the position of the main layer. It is important to note that the localisation threshold is not a complete masking of the direct sound in the height layer. Instead, although the perceived location of the main channel signal would be unaffected, the aforementioned spatial and timbral effects of vertical interchannel crosstalk would remain somewhat audible. In [8], cello and bongo sources were presented from vertically-arranged stereophonic loudspeakers located directly in front of the listening position. With respect to the listening position, the lower (main) loudspeaker was not elevated, whilst the upper (height) loudspeaker was elevated by 30\({}^{\circ}\). Delays ranging from 0 to 50 ms were applied to the height loudspeaker with respect to the main. A subsequent study conducted by [PERSON] et al.