## 1 Introduction
Although this method allows for the construction of a VSS at any point in the air, the previously proposed approach requires a very large number of PALs. Thus, we are currently proposing a VSS construction method based on DRR control of the room impulse responses (RIRs) using multiple pairs of PALs and loudspeakers, which are of a comparable scale to a surround system [43; 44]. This method leverages the difference in the DRRs between the PAL and the loudspeaker. In this approach, gain weighting is applied to the input signals of the PAL and the loudspeaker to achieve the desired DRR corresponding to the VSS distance, while additional gain weighting is used to control the direction of the VSS using vector-based amplitude panning (VBAP). Furthermore, we have introduced distance attenuation into this method [45]. In previous studies, the DRRs obtained using this method tended to be lower than those of real sound sources. In this paper, we propose a VSS construction method based on a new DRR control technique using multiple pairs of PALs and loudspeakers. In the proposed method, we employ a weighting function based on the energy ratio for the PALs and a linear ratio for the loudspeakers in VBAP for distance and a weighting function based on the linear ratio in VBAP for the direction. For near distances around the listener's head, DRR correction is introduced,as the DRRs deviate from those of real sound sources when the proposed method is used without DRR correction. The proposed method can easily construct a moving VSS and multiple VSSs based on simple gain control in all directions on the horizontal plane. In the proposed method, the direct-to-reverberant ratio is controlled by adjusting the direct sound produced by parametric loudspeakers relative to the reflected sound and the reverberation generated by conventional loudspeakers installed in the actual environment. Therefore, the reflections from the room's walls in the proposed method create a result that closely resembles the conditions in which a real sound source is placed in this location. In other words, the listener perceives the natural reflections and reverberation (the room transfer function) of the room, and the proposed method causes little discomfort. The reflections and reverberation of the actual environment arrive at the listener's ears from all directions, and as the listener's head moves, the room transfer function changes. If the room transfer function were to be simulated and applied to the PAL, it would be necessary to recalculate the room transfer function in real time without any delay in response to the listener's head movements. However, achieving this is extremely difficult. This mismatch in the room transfer function causes significant discomfort to the listener. On the other hand, in the proposed method, even if the listener's head moves, only the spatial transfer function of the actual environment changes, resulting in almost no mismatch in the room transfer function. Therefore, the listener can perceive the virtual sound source within the sweet spot of the proposed method without experiencing any discomfort, even when moving. Finally, we confirmed the effectiveness of the proposed method through evaluation experiments. Analysis of Room Impulse Responses Using Parametric-Array Loudspeakers and Conventional Loudspeakers  
Figure 1a,b show the RIRs of a conventional loudspeaker and a PAL under the condition that the distance between the listener and the loudspeaker is 2.0 m.  
As shown in Figure 1, the RIRs of a PAL and a conventional loudspeaker have different direct-to-reverberant ratios (DRRs) under the same experimental conditions. A PAL can achieve super-directivity by utilizing rectilinear ultrasonic waves. The RIR of a PAL has a high DRR, characterized by a large-amplitude direct wave and low-amplitude reverberations. Thus, a PAL causes the VSS to be perceived as closer to the listener. On the other hand, a conventional loudspeaker causes the VSS to be perceived as farther from the listener because the sound it emits has a low DRR.