# Deep Learning-Enhanced Autoencoder for Multi-Carrier Wireless Systems
## 4 Simulation Results
Performance decreases as the training SNR is either increased or decreased from this value. Specifically, the GRU-MC-AE model exhibits around a 1.25 dB improvement when it is trained at 7 dB compared to 5 dB and 10 dB training SNRs at 15 dB SNR. Thus, all the experiments for this model are conducted using a 7 dB training SNR. The BLER for different values of \(M\) is shown in Figure 8. We compare the performance for the configurations \((N,M)=\) (4, 16), (4, 32), and (4, 64). From the results, it can be observed that while our proposed model demonstrates good performance across all setups, the performance decreases as the size of \(M\) increases. Specifically, for \(M=32\) and 64, the GRU-MC-AE model shows a degradation of approximately 1.125 dB and 1.7 dB, respectively, compared to \(M=16\). Figure 6: The BLER performance of the proposed GRU-based MC-AE system for varying batch sizes and epochs. In Figure 9, the performance of the proposed model configured as (4, 16), is evaluated against ML-based OFDM and OFDM-IM, MMSE-based S-OFDM, and the DNN-based MC-AE [32] system under ideal channel conditions at a spectral efficiency (SE) of 1 bps/Hz. Figure 8: BLER performance of the proposed model for different values of \(M\) under perfect channel condition. Figure 7: BLER performance of the proposed model for different training SNRs under perfect channel condition with (4,16) setup. The results indicate that the proposed GRU-MC-AE model consistently outperforms the alternative models. While its performance closely aligns with that of the DNN-based MC-AE system at lower SNR levels, the proposed model demonstrates a notable gain of approximately 1.15 dB in performance at higher SNR levels. A comparative BER performance of the proposed model with the configuration \((4,16)\) is illustrated in Figure 10. This figure considers the results under perfect channel conditions at a SE of 1 \(\mathrm{bps}/\mathrm{Hz}\). The performance of our proposed system is compared against several benchmarks, including a turbo-style DNN-based MC-AE system [33], an LSTM-based OFDM-IM system [22], a Y-BLSTM-based OFDM-IM system [23], and a greedy detector (GD)-based OFDM-IM system [49]. It is important to note that all OFDM systems are configured with a \((4,1,4)\) setup, while the turbo-style MC-AE uses a \((4,16)\) configuration. From the results, it is evident that the proposed model outperforms all other system models. Although the GRU-MC-AE model demonstrates slightly inferior performance at lower SNRs, particularly around 5 dB SNR, it exhibits approximately a 1 dB performance gain compared to the turbo MC-AE model at higher SNR levels. The BLER performance of the GRU-MC-AE model under uncertain channel conditions is presented in Figure 11, using a configuration of \((4,16)\) and a training SNR of 7 dB. The figure compares the performance of the GRU-MC-AE system with a DNN-based MC-AE system, as well as ML-based OFDM, OFDM-IM, and S-OFDM systems, at a SE of 1 \(\mathrm{bps}/\mathrm{Hz}\). It is important to highlight that the proposed approach is evaluated using MMSE-based imperfect CSI, despite being trained under perfect CSI conditions. As shown, the GRU-MC-AE model surpasses all other systems. While it effectively outperforms S-OFDM and the DNN-based MC-AE, it exhibits a more significant advantage over OFDM and OFDM-IM systems. Notably, at 15 dB SNR, the proposed model offers approximately a 0.7 dB improvement over the DNN-based MC-AE system and 0.9 dB improvement over the ML-based S-OFDM system. Figure 9: The BLER performance comparison between the proposed model and other models under perfect channel conditions at a SE of 1 \(\mathrm{bps}/\mathrm{Hz}\). Figure 12 shows two plots that analyze the performance of a system in terms of SE and EE as a function of SNR under perfect channel conditions for different data settings. This performance is calculated with a training SNR of 7 dB, assuming a fixed circuit power of 0.25 W [50]. In Figure 12a on the left, SE is plotted against SNR for three different data settings.