## 3 Numerical Evaluation
### Channel Frequency Response  
To investigate the effect of the receiver position on the channel frequency response characteristics of the hybrid PLC and VLC, three typical receiver position settings, i.e., a central position (2.5, 2.5, 0.85) m, side position (2.5, 0.5, 0.85) m, and corner position (0.5, 0.5, 0.85) m were introduced to the hybrid PLC and VLC systems with distinct optical beam configurations, as is shown in Figure 4. Due to the unique rotational asymmetry of the NSPW non-Lambertian optical beam, one additional position, i.e., a side position 2 (0.5, 2.5, 0.85) m was introduced for the receptive analysis.  
Figure 4: Hybrid PLC and VLC channel frequency response comparisons for typical receiver positions with distinct optical beam configurations: (**a**) baseline Lambertian optical beam configuration, (**b**) LUXEON Rebel non-Lambertian optical beam configuration, and (**c**) NSPW non-Lambertian optical beam configuration.  
For the case of the central receiver position, the direct current (DC) hybrid channel gain is about \(-52.4\) dB, \(-54.3\) dB, and \(-49.4\) dB for the baseline Lambertian optical beam configuration, LUXEON Rebel non-Lambertian optical beam configuration, and NSPW non-Lambertian optical beam configuration, and the according frequency response dynamic range is about \(9.09\) dB (i.e., \(-61.5\) dB\(\rightarrow-52.4\) dB), \(10.0\) dB (i.e., \(-64.3\) dB\(\rightarrow-54.3\) dB), and \(8.5\) dB (i.e., \(-57.9\) dB\(\rightarrow-49.4\) dB), with two frequency response notches that appear at about \(10\) MHz and \(15\) MHz. Once the receiver was removed to the side position, the gain metric of this DC hybrid channel was reduced to about \(-56.3\) dB, \(-55.8\) dB, and \(-57.5\) dB, for discussed three configurations, while the dynamic range of the relevant frequency response was about \(11.8\) dB (i.e., \(-68.1\) dB\(\rightarrow-56.3\) dB), \(11.1\) dB (i.e., \(-66.9\) dB\(\rightarrow-55.8\) dB), and \(14.0\) dB (i.e., \(-71.5\) dB\(\rightarrow-57.5\) dB). Note that unlike the baseline Lambertian optical beam configuration and LUXEON Rebel non-Lambertian optical beam configuration, the frequency response at the side position \(2\), i.e., (\(0.5\), \(2.5\), \(0.85\)) m for the NSPW non-Lambertian beam configuration, provided a superior response amplitude, thanks to the rotated asymmetrical pattern of the NSPW beam. The relevant gain metric of the DC hybrid channel increased to about \(-55.0\) dB and the respective dynamic range of the frequency response was about \(10.4\) dB (i.e., \(-65.4\) dB\(\rightarrow-55.0\) dB).  
Once the optical receiver was further removed into the corner position, the gain performance method of the DC hybrid channel was further reduced to about \(-58.0\) dB, \(-57.6\) dB, and \(-58.6\) dB for the three beam configurations of concern, while the relevant dynamic range of the frequency response was about \(15.2\) dB (i.e., \(-73.2\) dB\(\rightarrow-58.0\) dB), \(14.0\) dB (i.e., \(-71.6\) dB\(\rightarrow-57.6\) dB), and \(22.2\) dB (i.e., \(-80.8\) dB\(\rightarrow-58.6\) dB), which verifies the superiority of the LUXEON Rebel beam in mitigating depth fading.  
To sufficiently eliminate the potential mutual interference between the alternating current (AC) and the information signal on the power line, in the following work, subcarriers between \(0.1\) MHz and \(25\) MHz were utilized to carry the data transmission, which was quite close to the frequency band setting from the work in [11]. For the convenience of the analysis, the subcarrier frequency spacing was \(0.5\) MHz, as is shown in Figure 4.