# Optimization of Virtual Loudspeakers for Spatial Room Acoustics Reproduction with Headphones
## 2 Virtual loudspeaker Position Optimization
### Listening Test Setup and Sound Signals  
The listening test setup is illustrated in Figure 2. The setup consisted of a desk, a computer and noise canceling headphones (Bose QuietComfort 25) and was located in the corner of a quiet open plan office. The listener's head was tracked with a commercial tracking system (Optitrack V100 and TrackingTools software, version 2.5.3; 2012 by NaturalPoint Inc., Corvallis, OR, USA) that utilizes six infrared cameras surrounding the listening space. To reduce visual distractions, the front field of view of the subject was obscured with a curtain. The listening test program was built on the Unity engine and it utilized head tracking in six degrees of freedom. HRTFs were generated from a scanned human head with a fast boundary element method [18] in far field. All the participants used the same HRTF set containing 836 directions. No interpolation was used between the HRTFs and the filter was swapped without cross-fading. The experiment consisted of two test sets. Both sets introduced different listening conditions in order to compare loudspeaker optimization performance. The acoustic spaces were a studio control room in Helsinki, Finland and Musikverein concert hall, Vienna, Austria, later referred to as a \"small room\" and a \"concert hall\", respectively. The small room RIRs had been measured with stereo pair of loudspeakers, whereas the acoustic response of the concert hall had been captured by using loudspeaker orchestra [7]. Based on these prior measurements, the SDM analysis had been done for both rooms in advance. Both sets contained four different virtual loudspeaker setups; two position optimized setups and two uniformly distributed setups with fixed virtual loudspeaker positions for direct sounds. In Figures 3 and 4, all these conditions have been illustrated for both spaces. The optimized loudspeaker setups were visually inspected for potential loudspeaker clusters, and uniform setups were based on Platonic solids. Figure 2: A sketch of the listening test setup. The listener (in the middle) is surrounded by six infrared cameras (red) that track the movements of the noise-canceling headphones. The field of view has been obscured with a curtain. The sound signals used were typical for both rooms. Since the small room was measured with traditional stereo setup, a stereo signal was used. In our case, a 34-s excerpt from the beginning of [PERSON]'s song \"Because You Loved Me\" was selected. For the concert hall, the music signal selected for the loudspeaker orchestra was [PERSON]'s Lemminkainen suite, 1 st part, 851-885 s. The orchestra signals were captured in professional recording with 21 close microphones for different instrument groups as quasi-anechoic material, which were then mapped to 24 measurement source channels in the loudspeaker orchestra. Figure 4: Loudspeaker setups used in the concert hall samples: **(a)** uniform setup with 16 loudspeakers; **(b)** uniform setup with 24 loudspeakers; **(c)** optimized setup with 16 loudspeakers; and **(d)** optimized setup with 24 loudspeakers. Figure 3: Loudspeaker setups (white circles) overlaid with the spatial map of overall sound energy in the small room case: **(a)** uniform setup with 14 loudspeakers; **(b)** uniform setup with 22 loudspeakers; **(c)** optimized setup with 14 loudspeakers; and **(d)** optimized setup with 22 loudspeakers. The reproduction levels of all presented stimuli were equalized. This was accomplished by computing the equivalent level \(L_{eq}\) of combined virtual loudspeaker channels as  
\[L_{eq}=20\log\left(\sqrt{\frac{\sum_{i=1}^{M}\sum_{n=1}^{N}x_{i,n}^{2}}{N}}\right) \tag{9}\]  
where \(M\) is the number of channels, \(N\) is the length of one signal and \(\mathbf{x}_{i}=\{x_{i,1}\ldots x_{i,N}\}\) is the input signal of channel \(i\). This level was then used to calculate level alignment coefficient \(C_{eq}\):  
\[C_{eq}=10^{((L_{eq,0}-L_{eq})/20)} \tag{10}\]  
where \(L_{eq,0}=-25\) dB was the target level.