## 2 Experiment I: Directivity-Controlled Auditory Distance in Auralized Rooms
### Experimental Setup  
The effect is evaluated in a first listening experiment, in which the variable-directivity source in a room is auralized using the image source method. The room is shoebox-shaped with a frequency-independent absorption coefficient \(\bar{a}\). Specular reflections up to 3 rd order are considered [13] and diffuse reflections are simulated as spherical harmonics using the software tool MCRoomSim [14]. For simplicity, diffuse reverberation of an omni-directional excitation is considered. Playback employed a ring of 24 equally-distributed Genelec 8020 loudspeakers with a radius of \(r=1.5\,\mathrm{m}\) placed in an anechoic laboratory. Each listener was sitting in the center of the arrangement with ear height adjusted to the loudspeaker ring, cf. Figure 2.  
On the circular setup each specular reflection is auralized by the loudspeaker with the closest azimuth angle. This avoids timbral effects of amplitude panning [15]. Elevated specular reflections are attenuated in the auralization by the cosine of their elevation. Diffuse reflections are played back in Ambisonics format. The impulse response \(h_{l}(t)\) of the \(l\)-th loudspeaker is obtained after superimposing specular and diffuse reflections using MATLAB. Obviously, a two-dimensional representation of a three-dimensional sound field is not optimal, but findings in [16] indicate that reflections from floor and ceiling do not have a significant influence on the auditory distance. Each impulse response was convolved with the signals \(S_{1...3}\), yielding a 24-channel audio file for each condition. Audio playback was controlled by the open source software Pure Data on a standard PC with RME MADI audio interface and DirectOut D/A converters. To monitor the influence of room acoustics, three different layouts were tested, including two rooms and two source-listener distances, cf. \(R_{1...3}\) in Table 2.  
Figure 1: Beampattern designs \(A\), \(B\), \(C\) controlling the D/R ratio. Figure 2: Experimental setup in the anechoic laboratory. Geometry and reverberation time of the auralized rooms are based on two rooms at our institute, namely the IEM CUBE, a \(10.3\,\mathrm{m}\times 12\,\mathrm{m}\times 4.8\,\mathrm{m}\) large room with \(T_{60}=700\,\mathrm{ms}\), and the IEM Lecture Room, \(7.6\,\mathrm{m}\times 6.8\,\mathrm{m}\times 3\,\mathrm{m}\) with \(T_{60}=570\,\mathrm{ms}\). Both rooms were chosen as they are typical venues for concerts or experiments with the IKO as a variable-directivity source [17; 18]. The simulated sound source was placed near the corners of the room at a distance of \(2\,\mathrm{m}\) and \(3\,\mathrm{m}\) (IEM CUBE) and \(1\,\mathrm{m}\) and \(2\,\mathrm{m}\) (IEM Lecture Room). The listening position was chosen at a virtual distance of \(d=1.7\,\mathrm{m}\) to the sound source. Additionally, for the IEM CUBE an increased source-listener distance of \(d=2.9\,\mathrm{m}\) was tested. The listener was facing the sound source simulated at height of \(1.8\,\mathrm{m}\) above the floor with an angular offset of \(\Delta\phi=15^{\circ}\) with regard to the sidewalls. Figure 3 shows the setup of the auralized room using the 24-channel loudspeaker ring and Table 2 lists rooms and source-listener distances tested in the experiment. The signals fed into auralization were chosen to investigate the influence of speech versus noise, noise spectrum, and noise envelope to the effect: female speech (\(S_{1}\)), a sequence of irregular artificial bursts (\(S_{2}\)), and Gaussian white noise shaped to speech spectrum (\(S_{3}\)) as listed in Table 2. For \(S_{3}\), envelope fluctuations were slightly accentuated by multiplying the noise with its Hilbert envelope and by restriction to its original bandwidth, cf. [19]. By this procedure, \(S_{1}\) and \(S_{3}\) have similar spectra and kurtosis, which measures the envelope fluctuation, whereas \(S_{2}\) is more transient with more energy at frequency above \(1\,\mathrm{kHz}\). All signals were normalized to their RMS value for level equalization. The above signals are anechoic.