# The Extended SLM Combined Autoencoder of the PAPR Reduction Scheme in DCO-OFDM Systems
## 3 Results and Discussion
### BER Analysis  
Then, we investigated the BER performance of the DCO-OFDM system when the optical channel is assumed to be a LOS channel modeled by an AWGN channel. As seen in Figure 5, the comparison  
Figure 4: Complementary cumulative distribution function (CCDF) of peak to average power ratio (PAPR) comparison of ESLM-AE, Autoencoder, clipped DCO-OFDM, DCO-OFDM and SLM. The clipping ratios, \(\gamma\), used for ESLM-AE and Autoencoder is 1.5.  
results show that the proposed scheme can result in a lower BER compared to the conventional methods in the whole SNR range. At BER =\(10^{-3}\), the SNR requirements of the ESLM-AE are 4 dB, 4.7 dB and 7 dB less than that of the SLM \(U=128,B_{DC}=7\)dB, clipped DCO-OFDM \(\gamma=1.5\) and clipped DCO-OFDM \(\gamma=1.2\) respectively. Additionally, the BER performance of ESLM-AE and AE is almost same. Since the error due to the clipping results in an increased BER in the DCO-OFDM at high SNR values, a larger DC Bias and a lower BER are achieved by using the proposed scheme in the high SNR range. In VLC systems, the channel is generally modeled as a multi-path propagation environment. Consequently, in our scenario, Rician distribution is taken into account to simulate the multipath effects with the LOS path to be dominant [42; 43; 44]. The Rician \(K\)-factor gives the ratio of the squared signal power of the LOS link over that of the signal from the non-LOS link [45]. Here \(K=1\) and 5 is taken into consideration and the BER performance of the proposed method with Rician effects and AWGN is given in Figure 6. Notably compared to SLM \(U=128\), signal deterioration of the proposed ESLM-AE scheme is much smaller. Simultaneously, the system inside an environment with Rician fading \(K=5\) needs an additional 2.8 dB SNR in order to obtain the same performance (BER =\(10^{-4}\)) as when it operates inside an AWGN channel due to the multipath fading. With the increase of \(K\), the probability of encountering a deep fade reduces. On the contrary, if \(K\) decreases, the dominant path degenerates in amplitude. When \(K\) is reduced to 0, the Rician distribution reverts to Rayleigh. Simultaneously, a comparison with the experiment results is carried out to verify the BER performance of the proposed system under a diffused optical wireless (DOW) channel. The DOW channel is modeled by the sum of a set of positive taps as Equation (17) [46]. \[q(t)=\sum_{n=0}^{V-1}p_{n}\delta(t-\tau_{n}), \tag{17}\]  
where \(q(t)\) is the channel impulse response at the time slot \(t\), \(p_{n}\) and \(\tau_{n}\) are the amplitude and time delay of the \(n\)th path, \(V\) is the number of channel taps. Figure 5: Bit error rate (BER) comparison of the clipped DCO-OFDM, SLM, Autoencoder and the proposed scheme under the line-of-sight (LOS) channel. The diffuse fading follows the exponentially decaying and ceiling bounce models as described in [47] for DOW channels. In the simulation, 32-sample long CP is inserted. We set \(V=11\) and suppose that the time delay is uniformly distributed from 2 to 20 ns. Figure 7 demonstrates the improvement in the BER performance by adopting the proposed scheme under the DOW channel. Note that the results in Figure 6 are achieved by setting a CP larger than the multipath delay where no inter-symbol interference (ISI) exists. Numerically, the BER of the proposed ESLM-AE scheme can reach and even be less than the order of magnitude of \(10^{-3}\), which is much better than the clipped DCO-OFDM and SLM methods, although the BER performances of all schemes degrade due to the multipath fading. Figure 6: BER comparison of the ESLM-AE and SLM under the Rician fading channel with additive white Gaussian noise (AWGN). Figure 7: BER comparison of the clipped DCO-OFDM, SLM, Autoencoder and the proposed scheme under the DOW channel. To demonstrate the influence of ISI, we set a shorter CP of 4-samples while the maximum delay of the multipath channel is 11. Figure 8 gives the comparison of BER performance of the above methods in DOW channel with and without ISI.