# Mixed-Carrier Communication for Technology Division Multiplexing
## 4 Technology Division Multiplexing Trade-Off  
MCC is designed to serve multiple technologies simultaneously in what could be considered as technology division multiplexing. One of the main challenges of embedding multiple modulation techniques within MCC is the performance trade-off per technology. This section discusses the allocated power per modulation technique and its impact on BER performance and the overall spectral efficiency, assuming a line-of-sight (LOS) flat fading VLC channel for the analysis simplicity. In Figure 5, the impact of embedding an OFDM waveform within an MCC envelope on the BER performance of BPM is illustrated. Additionally, BPM BER with and without OFDM is benchmarked against OOK and PPM as shown in Figure 5a. For fairness in BER performance comparison, both optical power \(P\) and data rate \(R_{b}\) are unified for all PPM, BPM, and OOK modulations. Thus, the optical intensity of an OOK pulse becomes \(2P\) for a duration of \(1/R_{b}\); however, for \(L_{1}\)-PPM, it is \(L_{1}P\) for a duration of \(T_{\text{PPM}}\). As for \(L_{1}\)-BPM, the required optical intensity to maintain optical power of \(P\) is \(2L_{1}P\), where the beacon duration \(T_{b}\) is the same as \(T_{\text{PPM}}\). According to [25], assuming a high SNR, BER is dominated by the two nearest signals, BER of an AWGN channel of a double-sided power spectral density (PSD) of \(N_{o}/2\), zero mean and variance of \(\sigma^{2}\) can be approximated as  
\[\text{BER}\approx Q(\frac{d_{\text{min}}}{\sqrt{2\ N_{o}}}) \tag{12}\]  
where \(d_{\text{min}}\) is the minimum Euclidean distance between any pair of valid modulation signals as shown in Equation (13),  
\[d_{\text{min}}=\min_{i\
eq j}\int(x_{i}(t)-x_{j}(t))^{2}dt \tag{13}\] \begin{table}
\begin{tabular}{c c} \hline \hline Transmitter & \(\mathcal{O}(\max(L_{2},L_{1},\log(N)))\) \\ \hline High-speed receiver & \(\mathcal{O}(\log(N))\) \\ \hline Low-speed receiver & \(\mathcal{O}(max(L_{1},L_{2}))\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Complexity analysis summary. Accordingly, OOK and \(L_{1}\)-PPM BER behaviors are approximately performing as follows:  
\[\text{BER}_{\text{OOK}}\approx Q(\sqrt{\frac{E_{b}}{N_{o}}}) \tag{14}\]  
\[BER_{\text{PPM}}\approx Q(\sqrt{\frac{E_{b-\text{PPM}}\log_{2}(L_{1})}{N_{o}}}) \tag{15}\]  
A PWM modulated beacon has twice the optical intensity to maintain the same average optical power \(P\), thus BPM has twice the \(E_{b-\text{PPM}}/N_{o}\) ratio. Therefore, BPM BER performance follows Equation (16):  
\[\text{BER}_{\text{BPM}-\text{NO OFDM}}\approx Q(\sqrt{\frac{2\,E_{b-\text{ PPM}}\,log_{2}(L_{1})}{N_{o}}}) \tag{16}\]  
As shown in Figure 5a, OOK and 2-PPM BER curves match, while \(L_{1}\)-BPM requires 3 dB less electrical power to achieve the same BER compared to \(L_{1}\)-PPM. For \(L_{1}\)-PPM and \(L_{1}\)-BPM modulation schemes, the error is confined to the symbol in which it occurs, and thus a single-slot error impacts \(log_{2}(L_{1})\) bits. Assuming full synchronization between the transmitter and a hard decision decoding using a threshold detector in an AWGN channel, the orthogonality between symbols increases as the PPM modulation order \(L_{1}\) increases. As a result, higher PPM modulation orders have better error performance at the same \(E_{b}/N_{o}\). Figure 5: Impact of embedding OFDM within the MCC envelope on BPM BER. (**a**) BPM No-OFDM; (**b**) 2-BPM; (**c**) 16-BPM; (**d**) 64-BPM. Embedding an ACO-OFDM within an MCC envelope acts as a source of noise to the other modulation types including BPM. According to [21], ACO-OFDM is accurately modeled as a Gaussian random process with zero mean and variance of \(\sigma^{2}_{\text{OFDM}}\). Accordingly, there is a performance trade-off between embedded OFDM waveform and other MCC embedded modulation techniques, including BPM.