# Tolerance-Aided Interference Degradation for Optical OFDM in Power-Constrained Systems
## 4 Numerical Results and Comparison  
In this section, we present the numerical results pertaining to the system performance when employing the proposed TAID algorithm. Unless explicitly stated otherwise, we utilize the parameters as outlined in Table 1, which is typical for indoor spaces and used as a benchmark [7; 15]. To facilitate an equitable comparison of system performance, we assume a channel loss factor of one, as it does not significantly impact the analysis and ensures consistency across the test scenarios. Given the inherent characteristics of light sources, we employ a first-order low-pass filter to emulate the transmitter. As per preliminary investigations, the 3 dB bandwidth of such filters typically spans a range of several tens of megahertz for commonly used lighting LEDs, as documented in [23]. Conversely, LDs and IR LEDs often exhibit larger bandwidths, reaching approximately a few hundred megahertz, as confirmed by studies such as [24; 25; 26]. In this study, we evaluate scenarios encompassing both large and small bandwidths. Furthermore, it is imperative to acknowledge that the constraints imposed by the light source's driving current lead to limitations of the peak transmitted optical power. This constraint results in the clipping of signals with magnitudes exceeding the power constraint, thereby introducing nonlinear distortion into the system. In this study, we employ the direct current-biased optical OFDM (DCO-OFDM), asymmetrically clipped optical OFDM (ACO-OFDM), and clipping-enhanced optical OFDM (CEO-OFDM) techniques as the benchmark for evaluating system performance. To ensure an equitable and meaningful comparison, identical parameters are adopted across all tested techniques. For DCO-OFDM, a bias is introduced with a magnitude of \(\frac{P_{\text{max}}}{2}\), striking a balance between mitigating peak power and zero clipping. It is important to note that the transmitted data symbol rate provided in Table 1 reflects the effective data symbol rate, accounting for spectral utilization efficiency considerations. Comparing the performances of DCO-, ACO-, and CEO-OFDM and the proposed algorithm at the same transmitted data rate, we can calculate the required bandwidths for the compared techniques as  
\[B_{\text{DCO}}=\frac{1}{2}B_{\text{ACO}}=\frac{1}{3}B_{\text{CEO}}=\frac{1}{3} B_{\text{proposed}}. \tag{20}\]  
From this relationship, the ACO- and CEO-OFDM require twice and three times larger bandwidth than DCO-OFDM, respectively. Figure 5 presents a comparative analysis of BER performances among the proposed TAID algorithm, DCO-OFDM, ACO-OFDM, and CEO-OFDM techniques operating through an ideal channel, as the modulation index increases. For the proposed TAID algorithm, the figure showcases the minimum BER attained for various modulation indexes, with this minimum achieved through an exhaustive search for the optimal decision tolerance parameter \(\Delta\). In general, as the modulation index increases, the BER performance improves across all the discussed techniques. However, a notable trend emerges whereby a further increase in signal scale results in more pronounced clipping distortion. When the clipping distortion becomes dominant over the additive noise, the BER performance deteriorates. Because of ACO-OFDM's utilization of only odd-numbered subcarriers for signal modulation, its bandwidth efficiency is reduced by half compared to DCO-OFDM. Consequently, ACO-OFDM necessitates twice the bandwidth of DCO-OFDM for equivalent data throughput. Similarly, CEO-OFDM requires three times the bandwidth of DCO-OFDM for an equitable comparison. The numerical results depicted in this figure demonstrate that the proposed algorithm consistently achieves the lowest BER among the discussed techniques while employing the same modulation constellation size. Moreover, the proposed algorithm exhibits a broader dynamic modulation index range than those of DCO-OFDM, ACO-OFDM, and CEO-OFDM, maintaining a BER below \(10^{-3}\).