## 1 Introduction
Figure 1: Waveforms of RIRs in the living room (\(T_{60}=380\) ms). (**a**) Using a conventional loudspeaker (DRR: \(-2.2\) dB). (**b**) Using a PAL (DRR: 16.2 dB). Conventional Construction of a VSS Based on Radiation Direction Control Using Parametric-Array Loudspeakers  
Figure 2 illustrates the conventional method. Multiple PALs are arranged in a linear formation, creating a linearly arranged PAL array. By forming the focal point of the sound emitted from each PAL, a VSS is constructed at the focal point. In addition, pan and tilt units are mounted onto the PALs to electrically control the direction of an object. This allows for easy adjustment of the placement angle of each PAL and precise control over the position of the VSS. Furthermore, the proposed method enables control of the direction of radiation of the VSS. As shown in Figure 2, when constructing a VSS with a radiation direction of \(\beta\) [deg. ], we weight the output signal of each PAL to simulate the radiation characteristics of a real sound source (RSS) placed in the radiation direction \(\beta\). By doing so, we can construct a VSS with the desired characteristics and radiation angle. By implementing this processing in both software and hardware, we can construct a VSS at any point in the air with the desired radiation direction. However, a major drawback of this approach in surround sound applications is that it requires a very large number of PALs, which must be arranged to enclose a linear array of PALs. Proposed Virtual Sound Source Construction Based on Direct-to-Reverberant Ratio Control Using Multiple Pairs of Parametric-Array Loudspeakers and Conventional Loudspeakers  
In this paper, we propose a method for controlling the distance and direction of a virtual sound source (VSS) using multiple pairs of parametric-array loudspeakers and conventional loudspeakers. Figure 3 provides an overview of the proposed method with four pairs of PALs and loudspeakers. In this arrangement, the proposed method can be used to construct a VSS in all directions on the horizontal plane. In the gain control process for each output in Figure 3, the gain coefficients are calculated for each output, and the input audible sound signal is weighted with these gain coefficients. In addition, the signals for the PALs consist of amplitude-modulated ultrasonic waves, where the input audible sound signal is amplitude-modulated with a carrier wave of an ultrasonic sine wave. Depending on the direction of the VSS, the driven loudspeakers are changed as follows:  
Figure 2: Overview of the conventional method. * **The VSS in the front area (\(-45^{\circ}\) to \(45^{\circ}\))**: The front L-ch PAL, the front L-ch loudspeaker, the front R-ch PAL, and the front R-ch loudspeaker in Figure 3 are driven;
* **The VSS in the right area (\(45^{\circ}\) to \(135^{\circ}\))**: The front R-ch PAL, the front R-ch loudspeaker, the rear R-ch PAL, and the rear R-ch loudspeaker in Figure 3 are driven;
* **The VSS in the rear area (\(135^{\circ}\) to \(-135^{\circ}\))**: The rear R-ch PAL, the rear R-ch loudspeaker, the rear L-ch PAL, and the rear L-ch loudspeaker in Figure 3 are driven;
* **The VSS in the left area (\(-135^{\circ}\) to \(-45^{\circ}\))**: The front L-ch PAL, the front L-ch loudspeaker, the rear L-ch PAL, and the rear L-ch loudspeaker in Figure 3 are driven. Here, the output signals can be calculated using the same algorithm even if the driven loudspeakers are changed. Thus, we provide an overview of the output signal design using the proposed method in the front area (\(-45^{\circ}\) to \(45^{\circ}\)), as shown in Figure 4.  
As can be seen, the output signals are designed so that the VSS is located in the front area, with two pairs of PALs and loudspeakers used for the front area. The weighting functions for the direction of the VSS are calculated using a linear ratio of the angle as follows:  
\[h_{\text{L}_{\theta}} = \frac{45-\theta}{90}, \tag{1}\] \[h_{\text{R}_{\theta}} = \frac{45+\theta}{90} \tag{2}\]  
where \(\theta\) [deg.]