# Mixed-Carrier Communication for Technology Division Multiplexing
## 5 Evaluation and Discussion  
As shown in Figure 7, \(f_{\text{PWM}}\) is inversely proportional with MCC spectral efficiency gain \(\eta_{g}\). This indicates as \(\gamma_{f}\) increases, _i.e._, \(f_{\text{PWM}}\) decreases, \(\eta_{g}\) is fairly noticeable as BPM and BnPSK modulation orders increase. To maximize the spectral efficiency, an optimization problem is formulated constrained by a BER per modulation of \(3.8\times 10^{-3}\) as follows:  
\[M,L_{1},L_{2},T_{\text{PWM}} \eta_{\text{MCC}-(\text{ACO-OFDM})}=\frac{log_{2}(M)}{5}+\frac{ log_{2}(L_{1}L_{2})\ T_{\text{OFDM}}}{L_{1}L_{2}T_{\text{PWM}}}\] s.t. \[T_{r}=150 ms,\] \[200 Hz\leq f_{\text{PWM}}\leq\frac{\Delta f}{2}, \tag{24}\] \[\text{BW}_{\text{LED}}\leq 10 MHz,\] \[T_{b}\geq 2\ T_{\text{PWM}},\] \[\text{BER}\leq 3.8\times 10^{-3}\]  
The optimization problem is constrained by several constraints related to MCC design and performance. This optimization problem is defined as a nonlinear problem that is solved using the optimization toolbox by MATLAB, based on initialized values. MCC is designed to support localization on top of communications based on the signal strength of received beacons. Thus, the envelope duration \(T_{r}\) is constrained by 150 ms to provide a reasonable advertising interval for reliable positioning accuracy for a walking person within an indoor space. This setting allows a maximum of 300 ms advertising time if one beacon is located at the beginning of an envelope while the consecutive beacon is located at the end of the following envelope. According to [28; 29], 100-350 ms is an acceptable range for a stable indoor positioning system of a mobile object at a normal walking speed. According to [7], \(f_{\text{PWM}}\) is constrained by a lower limit of 200 Hz to provide flicker-free illumination and an upper limit of \(\Delta_{f}\), i.e., \(1/T_{\text{OFDM}}\), to mitigate PWM harmonics interference with OFDM sub-carriers. In addition, most commercial LEDs have limited bandwidth not exceeding 10 MHz. Additionally, to comply with minimum Nyquist sampling requirements, \(T_{b}\) has to be larger than twice \(T_{\text{PWM}}\). Subsequently, Figure 9 shows the maximum spectral efficiency obtained by MCC compared to ACO-OFDM at different PWM frequencies, targeting the FEC BER threshold for all modulation techniques. At a lower PWM frequency range of 200 Hz-1 kHz, MCC does not show an obvious enhancement in terms of achievable maximum spectral efficiency compared to ACO-OFDM. As \(f_{\text{PWM}}\) increases, MCC shows a better performance which is more obvious at the upper PWM frequency limit of 78.125 kHz, where MCC with L = 4 offers the highest maximum  
Figure 8: Power requirements by MCC for embedding BPM with respect to \(\text{SINNR}_{\text{OFDM}}\). spectral efficiency compared to higher BPM and BnPSK modulation orders. In Figure 10, the relation between the required OFDM SINR and MCC SNR to target the FEC BER threshold for BPM modulation, at different BnPSK modulation orders, is illustrated. As shown in the figure, it is clear that the required \(\text{SNR}_{\text{MCC-LS}}\) increases with the increase of \(\text{SINR}_{\text{OFDM}}\). As the \(L_{2}\) BnPSK modulation order is higher, more \(\text{SNR}_{\text{MCC-LS}}\) is needed at the same \(\text{SINR}_{\text{OFDM}}\). However, the \(\text{SNR}_{\text{MCC-LS}}\) requirement, with a range of interest below 40 dB, is decreased as \(L_{1}\) BPM modulation order is higher. This is highlighted in Figure 11, which shows MCC SNR requirements against OFDM SINR for 8-BnPSK at varying BPM modulation orders to target the BER threshold for 8-BnPSK.