# Tolerance-Aided Interference Degradation for Optical OFDM in Power-Constrained Systems
## 4 Numerical Results and Comparison
Our findings reveal that, with 64-QAM, the proposed algorithm yields a comparable best BER performance to DCO-OFDM and ACO-OFDM using 32-QAM. Given that the effective transmitted data symbol rate remains consistent for fair comparison, the proposed algorithm attains a 20% higher data rate than the other compared techniques while achieving a similar BER. \begin{table}
\begin{tabular}{l l} \hline \hline Responsivity, \(\rho\) & 0.5 A/W \\ Peak optical power limit, \(P_{\max}\) & 5 mW \\ Number of subcarriers, \(N\) & 64 \\ Noise spectral density, \(N_{0}\) & \(5\times 10^{-10}\) mW/Hz \\ Transmitted data symbol rate, \(R_{s}\) & 18 Msps \\ Channel loss & 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters Used for Numerical Results. Figure 5: BER comparison of DCO-, ACO-, and CEO-OFDM and the proposed algorithm with different modulation indexes. Ideal channel is assumed. As discussed in this paper, CEO-OFDM and the proposed technique require the widest bandwidth among the compared techniques. In the numerical results illustrated in Figure 5; we specifically compare the outcomes obtained with 64-QAM for the proposed algorithm against those with 32-QAM for DCO-OFDM and ACO-OFDM. Given the capability to achieve a comparable best BER performance through modulation index adjustments, we can deduce that the bandwidth efficiency of DCO-OFDM, denoted as \(\eta_{\text{DCO}}\), is twice that of ACO-OFDM, denoted as \(\eta_{\text{ACO}}\). Furthermore, we observe that \(\eta_{\text{DCO}}\) is approximately 2.5 times that of the proposed algorithm, denoted as \(\eta_{\text{proposed}}\), based on the equation \(\eta_{\text{DCO}}\approx 3\cdot\frac{\log_{2}32}{\log_{2}64}\eta_{\text{proposed}}\). In the context of a bandlimited channel, we extend our analysis to compare the BER performances of the proposed algorithm with DCO-OFDM, ACO-OFDM, and CEO-OFDM. The corresponding numerical results are presented in Figure 6. Given that ACO-OFDM and CEO-OFDM exhibit lower bandwidth efficiency compared to that of DCO-OFDM, their BER performances deteriorate when targeting the same transmitted data rate. Leveraging the benefits of the proposed TAID algorithm, the effective added noise is substantially reduced, leading to an enhanced SINR with TAID. Consequently, the BER performance surpasses that of DCO-OFDM, ACO-OFDM, and CEO-OFDM when utilizing the given parameters. The decision tolerance stands as a crucial design parameter that demands careful adjustment to attain optimal BER. Figure 7 presents the BER performances for various modulation indexes with increasing values of \(\Delta\). In this depiction, we introduce the ratio \(\frac{P_{\text{max}}-\Delta}{P_{\text{max}}}\) to denote the separation between the peak power and the decision threshold. When \(\frac{P_{\text{max}}-\Delta}{P_{\text{max}}}\leq 1\), the decision threshold is lower than \(P_{\text{max}}\). Across all scenarios, we observe a trend wherein as the ratio escalates, the BER performance improves. This behavior is attributed to the fact that the decision tolerance, as it increases, effectively mitigates a portion of the additive noise. However, when the ratio is further increased, bringing \(\Delta\) closer to \(P_{\text{max}}\), it leads to the introduction of more added noise, resulting in a deterioration of the BER. In this paper, we delve into the relationship between the scale of the transmitted signal and the optimal decision tolerance. The numerical results, depicted in Figure 8, elucidate the evolving pattern of the ratio \(\frac{P_{\text{max}}-\Delta}{P_{\text{max}}}\) as the transmitted signal scale increases. Figure 6: BER comparison of DCO-, ACO-, and CEO-OFDM and the proposed algorithm with different modulation indexes. The 3 dB bandwidth of the channel is 15 MHz. 32-QAM is applied. From this figure, it becomes apparent that the optimal ratio \(\frac{P_{\max}-\Delta}{P_{\max}}\) for achieving the best BER exceeds one when the signal scale is small.