## 2 Principle and Experiment  
Here, the principle of the PowDM will be presented. Without loss of generality, we illustrate the principle of PowDM by assuming that the data are divided into two individual signals, \(x_{i}\), where \(i=1\) and \(2\). The corresponding transmission powers are \(P_{i}\), where \(i=1\)and 2. In the system, there is a single LD at the Tx and a single photodiode (PD) at the Rx. The sum of total power \(P_{i}\) is equal to \(P\). The transmitted signal is shown in Equation (1). \[x=\sqrt{P_{1}}x_{1}+\sqrt{P_{2}}x_{2} \tag{1}\]  
The received signal can be illustrated in Equation (2),  
\[y_{i}=h_{i}x+n_{i} \tag{2}\]  
where \(h_{i}\) is the channel response between the Tx and Rx, and the \(n_{i}\) represents the noises. According to Equation (1), different individual signals in the PowDM signal should maintain a certain power ratio for the successful decoding of individual signals, Data 1 and Data 2 at the Rx. At the Rx, the SIC process is performed and the decoding priority is based on the order of the increasing channel gain. With the example of 2 individual signals with \(P_{2}>P_{1}\), \(x_{2}\) signal will be recovered first without the need of SIC since it has a higher power than \(x_{1}\). Then, the decoded \(x_{2}\) will be used to retrieve \(x_{1}\) in the SIC process [32] by subtracting itself from the received signal. Based on the Shannon-Hartley equation, the channel capacity \(C\) is related to the theoretical limit of the information data rate, which is equal to the channel bandwidth \(B\) times the logarithm of one pulse the signal-to-noise ratio (SNR). Hence, the total capacity of the PowDM signal can be written in Equation (3). \[ \begin{array}{ll}C&=C_{2}+C_{1}\\ &=B\log_{2}\Bigl{(}1+\frac{|h_{2}|_{2}P_{2}}{|h_{1}|_{2}P_{1}+P_{N}}\Bigr{)}+ B\log_{2}\Bigl{(}1+\frac{|h_{1}|_{2}P_{1}}{P_{N}}\Bigr{)}\end{array}  \tag{3}\]  
As shown in Equation (3), the total channel capacity \(C\) is equal to the capacities of the two individual signals \(C_{2}\) and \(C_{1}\). The channel responses of individual Data 2 and Data 1 are \(h_{2}\) and \(h_{1}\) respectively. Since there is only one Tx and one Rx, the Data 2 and Data 1 share the same bandwidth \(B\) and noise power \(P_{N}\). It is worth noting that for Data 2, the capacity \(C_{2}\) is affected by the transmission noise \(P_{N}\) plus the interference from the Data 1 (\(P_{1}\)) during the PowDM. For Data 1, the capacity \(C_{1}\) is affected by \(P_{N}\) only. However, a certain ratio of \(P_{2}\) to \(P_{1}\) should be maintained in PowDM, and the power level of \(P_{1}\) is limited. This will also affect the capacity \(C_{1}\). In this proof-of-concept demonstration, only 2 power-division channels are used. More channels can be supported if the SNR of the transmitted signal is high enough [34]. Figure 1 shows the principle of encoding and decoding of the proposed PowDM VLC system. At the Tx side, two individual data signals (Data 1 and Data 2) are first mapped to quadrature phase shift keying (QPSK) formats. Then the signals are allocated to subcarriers according to channel conditions. After this, the two signals at different power levels are combined with superposition code (SC) [32], which realizes multiplexing in the power domain. Hence the constellation diagrams are shaped according to the power allocation. This can be implemented by multiplying the signals by specified power levels \(P_{1}\) or \(P_{2}\). Inverse fast Fourier transformation (IFFT) is used to convert the signal from the frequency domain into time domain. Hermitian symmetry is utilized to produce real-valued OFDM signal for driving the LD. After this, parallel-to-serial (P/S) conversion and the addition of a cyclic prefix (CP) are performed. After the PowDM OFDM signal is generated, it is applied to a LD via a digital-to-analog converter (DAC). The signal will then be received by a PD via an optical channel. The received PowDM OFDM signal will be converted into a digital signal via an analog-to-digital converter (ADC). Synchronization schemes are applied.