## 4 Simulation Results and Discussion
### Simulation Results of the Control Performance for Each Method at 700 Hz  
In the second simulation, the noise reduction of 63,001 near-field observing points in a 5 m \(\times\) 5 m square area can be calculated using Equation (10). The scattered sound field of the 700 Hz primary source and the noise reduction effects of the proposed CLASSO-RLSalgorithm, the LASSO-RLS-\(\gamma_{\text{C}}\) method, the LASSO-RLS-\(\gamma_{\text{NL}}\) method and the Uni-RLS algorithm at 700 Hz are shown in Figure 3.  
Figure 2: Cont.  
Figure 3a shows that scattered sound power is mainly distributed in the forward-scattered sound area (the target area 2) and the backward-scattered sound area (the target area 1). The goal of the noise control is to obtain large noise reduction in these two areas.  
As seen in Figure 3b, there is small noise reduction in two target areas. As shown in Figure 3c-e, compared to the Uni-RLS method, there are larger noise reductions in two target areas using the three secondary loudspeaker-optimized placement algorithms. Figure 3b-e illustrate that the reduction performance and size of the noise reduction areas of all three secondary loudspeaker-optimized placement algorithms are better than that of  
Figure 3: Scattered sound field and the control performance for each method at 700 Hz: (**a**) scattered sound field of the 700 Hz primary source; (**b**) control performance of the Uni-RLS algorithm(700 Hz); (**c**) control performance of the LASSO-RLS-\(\gamma_{C}\) algorithm (**d**) control performance of the proposed CLASSO-RLS algorithm (700 Hz); and (**e**) control performance of the LASSO-RLS-\(\gamma_{NL}\) algorithm (700 Hz).  
Figure 2: Scattered sound field and the results of loudspeaker placement for each method from 400 Hz to 1000 Hz: (**a**) scattered sound field of the 400 Hz primary source; (**b**) scattered sound field of the 700 Hz primary source; (**c**) scattered sound field of the 1000 Hz primary source; (**d**) Uni-RLS (400 Hz); (**e**) Uni-RLS (700 Hz); (**f**) Uni-RLS (1000 Hz); (**g**) CLASSO-RLS (400 Hz); (**h**) CLASSO-RLS (700 Hz); (**i**) CLASSO-RLS (1000 Hz); (**j**) LASSO-RLS-\(\gamma_{C}\) (400 Hz); (**k**) LASSO-RLS-\(\gamma_{C}\) (700 Hz); (**l**) LASSO-RLS-\(\gamma_{C}\) (1000 Hz); (**m**) LASSO-RLS-\(\gamma_{NL}\) (400 Hz); (**n**) LASSO-RLS-\(\gamma_{NL}\) (700 Hz); and (**o**) LASSO-RLS-\(\gamma_{NL}\) (1000 Hz).  
the Uni-RLS algorithm. The noise reduction of the entire error points in two target areas \(NR_{\text{e}}\) (calculated by Equation (11)) of the Uni-RLS algorithm, and the proposed CLASSORLS algorithm, LASSO-RLS-\(\gamma_{C}\) method, and the LASSO-RLS-\(\gamma_{NL}\) method are 13 dB, 27 dB, 20 dB, and 16 dB, respectively. The poor performance of the Uni-RLS algorithm is due to the placement of the secondary loudspeakers at locations that are less critical (Figure 2e), such that the power of the secondary loudspeakers is not fully utilized. However, the secondary loudspeakers of the three optimized algorithms are placed at more important locations (Figure 2h,k,n) that are closer to the forward-scattered and backward-scattered target areas, such that the cancellation of the scattered sound field is better.