# A Measure Based on Beamforming Power for Evaluation of Sound Field Reproduction Performance
## 4 Experimental Example  
### Pre-Experiment with One Source On  
As a pre-experiment, the proposed measure was compared with the spatial error in a real reproduction room where only one loudspeaker was turned on. The reproduction room was an acoustically-damped room (4.5 m \(\times\) 4.4 m \(\times\) 2.5 m) [27; 28; 30] built at the Technical University of Denmark, where the reverberation time \(T_{30}\) was 0.16 s in the 125 Hz octave band, and below 0.1 s for higher frequencies. The loudspeaker was located at (0, 1.8 m). Figure 7 illustrates this setup, and the loudspeaker is indicated as #1.  
The measurement was conducted with a planar array of 60 (6 \(\times\) 10) microphones (B&K type 4957) at 15 positions (5 \(\times\) 3). The measurement region was a square in the horizontal plane (2.25 m \(\times\) 2.25 m) indicated in Figure 7, and the spacing of the measurement points was 7.5 cm. The total number of the measurement points was, thus, 900 (30 \(\times\) 30) (Figure 7). The microphones were calibrated, and the phase difference among the microphones was \(\pm\)5\({}^{\circ}\) up to 3 kHz. The microphone signals were recorded with a multi-channel analyzer (B&K frontend frame 3560D, modules 7537A and 3038B). To synchronize the measurement at each position, the signal fed into the loudspeaker was also measured. The background noise was lower than 10 dB SPL above 80 Hz, and the temperature and the humidity were 21 \({}^{\circ}\)C and 42%. The sampling frequency was 16,384 Hz.  
The control region was assumed to be a circular region (\(kr<N\)) with the maximum order \(N=7\). The measurement points located in the control region were used for the beamforming and, thus, the number of the measurement points varied with the frequency. For frequencies lower than 340 Hz, the entire control region was not measured because some of the control region was outside the measurement region. The late reflections that arrived after the mixing time were excluded by the time window as used in the simulation.  
Figure 8 shows the error measures with frequency. The spatial error varies from around \(-\)10 to 0 dB values at all frequencies, which is a considerable amount. Since only one loudspeaker was used, the sound field was close to that generated by a monopole at the loudspeaker position, except for room reflections, and human localization is expected to be stable because the room is acoustically  
Figure 7: The listening room, loudspeaker array, and virtual sources.  
damped. Informal listening tests also confirmed a stable localization performance. In contrast, the beam-power error has values lower than -20 dB above 200 Hz. The spatial error has periodic fluctuations approximately every 280 Hz. The period of this frequency corresponds to the time delay between the direct sound and the reflection from the floor. Hence, the floor reflection is the main cause of the periodic increased spatial error, whereas the beam-power error is hardly affected by such reflections. The beam-power error is mainly affected by the difference in the angle \(\phi_{c}\) of the maximum beam-power between the desired and the reproduced field.