## 3 Numerical Evaluation
### Achievable Rate Performance  
In this section, we investigated the achievable rate performance of the hybrid PLC and VLC channels by applying different optical beam configurations. Figure 5 shows the achievable rate versus the transmitted power when applying distinct optical beam configurations at different receiver positions. For the case of the baseline Lambertian optical beam configuration, when the transmitted power is increased to \(50\) W from the original \(5\) W, the achievable rates are increased from \(152.5\) Mbps to \(194\) Mbps for the central position, while the counterpart of the corner position is enhanced to \(118\) Mbps from the original \(77.3\) Mbps. As for the side position, the achievable rate was accordingly increased to \(147.8\) Mbps from the original \(106.4\) Mbps. This means that, for the Lambertian optical beam configuration, although the transmitted power is increased to \(50\) W, the fluctuation range of the achievable rate (i.e., the rate difference between the maximum and minimum among all concerned positions for one certain transmitted power) varied slightly, increasing to \(76\) Mbps from the original \(75.2\) Mbps. On the other hand, as is shown in Figure 5b, once the LUXEON Rebel non-Lambertian optical beam configuration was applied, even for the central receiver position, the original achievable rate was just \(131.9\) Mbps; when the available transmitted power was increased to \(50\) W, this transmission rate gradually increased to \(173.4\) Mbps. As for the corner position, this counterpart was respectively enhanced to \(127.3\) Mbps from the original \(86.2\) Mbps. A similar trend could be observed for the side position, where the achievable rate was enhanced to \(155.3\) Mbps from the original \(113.8\) Mbps. From the view of the fluctuation range of the achievable rate, this performance metric was changed to \(46.1\) Mbps from the original \(45.7\) Mbps. Based on the above analysis, it could be identified that, for the hybrid PLC and VLC channel, the LUXEON Rebel non-Lambertian optical beam configuration could steadily achieve a reduction of about \(29.5\) Mbps in the fluctuation of the achievable rate, which means that a much more uniform transmission coverage could be derived by using the LUXEON Rebel non-Lambertian optical beam configuration. Finally, once the NSPW non-Lambertian optical beam configuration was applied to the constructed hybrid PLC and VLC channel, for the central receiver position, the original achievable rate could be up to 180.1 Mbps; when the transmitted power was further increased to 50 W, this transmission rate gradually increased to 222.4 Mbps, which indicates that a rate gain of about 28 Mbps can be achieved compared with the baseline Lambertian optical beam configuration. A similar trend could be observed for the side position, where the achievable rate was enhanced to 127.8 Mbps from the original 86.6 Mbps. Thanks to the inherent rotational asymmetry of the NSPW non-Lambertian optical beam configuration, the other nearby side position (i.e., side position 2) could achieve an original rate of 124.2 Mbps. This performance metric could be increased to 165.7 Mbps, which means that a rate gain of about 17.8 Mbps could be provided by the LUXEON Rebel non-Lambertian optical beam configuration. At the same time, it should be noted that for the more challenging corner position, the original achievable rate is just 64.7 Mbps. Although it  
Figure 5: Comparison of achievable rate versus transmitted power of hybrid PLC and VLC channel: (**a**) baseline Lambertian optical beam configuration, (**b**) LUXEON Rebel non-Lambertian optical beam configuration, and (**c**) NSPW non-Lambertian optical beam configuration. could be further scaled to 102.1 Mbps, the rate loss is more than about 21.5 Mbps compared with the respective metrics of the baseline Lambertian optical beam configuration.