## 4 Results
### Coded Bit LLR Extraction Comparison  
For coded bit LLR extraction, each CNN consumes the output from the FFT and produces as output the corresponding number of bit LLRs. To measure the BER for each model independently of any error correction coding benefits, the sigmoid of each LLR was calculated for the probability of each bit being a 1. Therefore, any sigmoid output larger than 0.5 would be interpreted as a 1, with a 0 corresponding to any value less than 0.5, which is subsequently compared against the coded bits utilized at the transmitter just prior to the transmitter's modulation stage. Each test was conducted over an SNR range of 5-35 dB. The combined results for the Rician channel are shown in Figure 4.  
These results show an improved performance for all tested models against the traditional receiver. For QPSK, all models show a performance improvement of at least 1 dB over the traditional receiver, with the 200 k-parameter model requiring higher SNR to eliminate errors compared to the other tested models. However, three models for 16-QAM and 64-QAM, respectively, once again exhibit similar model performance, while retaining a bit error plateau, albeit at a much improved BER level compared to their traditional receiver counterparts. This is likely due to the models performing well, but not perfectly, when encountering the distortions resulting from the scattered path signal energies resulting in the Rician fading model. A surprising insight resulting from these tests is the relative lack of improvement achieved by the 1.2 M parameter model compared to the 800 k parameter model, which may be caused by the 800 k parameter model learning up to the theoretical limit for the noise on the channel. From these results, we can see that a relatively modest CNN model can achieve significant performance improvements compared to other, far larger models.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multicolumn{4}{c}{**LLR Extraction**} \\ \hline Paper & Depth & Weights & Modulation Scheme \\ \hline
[8] & 5–13 ResNet Blocks & 292 k–725 k & 64-QAM \\ \hline
[3] & 11 ResNet Blocks & 1.2 M & 4–256 QAM \\ \hline
[2] & 8 DenseNet and Convolutional Blocks & Unlisted & BPSK-QPSK \\ \hline
[7] & LSTM-4 Hidden Units and 4 Dense Layers & Unlisted & QPSK \\ \hline Proposed Method & 3–5 Convolutional Blocks & 200 k–1.2 M & 4–64 QAM \\ \hline \multicolumn{4}{c}{Channel Decoding} \\ \hline Paper & Depth & Weights & Codes Tested \\ \hline
[9] & 2 MLP with 40 Hidden Units & 20 k & (63, 45) BCH, (6, 3) LDPC, 5G LDPC \\ \hline
[10] & 2–3 MLP Layers with 40–64 Hidden Units & 2440–9489 & (7, 4), (63, 45) BCH, (6, 3) LDPC, 5G LDPC \\ \hline Proposed Method & 6 Convolutional Layers & 20 k–80 k & (1998, 1512) LDPC \\ \hline \hline \end{tabular}
\end{table}
Table 4: Computational complexity.  
Each model was subsequently trained and evaluated for each modulation scheme against the previously outlined 3 GPP LOS channel models, with our evaluation conducted and completed in the same manner as for the Rician channel model. These results, shown in Figure 5, outline a much larger performance gain than what we observed in the Rician channel models, with the CNN models converging to 0 bit errors at 16 dB SNR, whereas the traditional receiver plateaus around a BER of 4 \(\times\) 10\({}^{-4}\) 16-QAM and 64-QAM begin to show the advantages of the larger models compared to the 200 k parameter model, with 800 k and 1.2 M parameter model's BER plateauing at a much better BER value. All of these results, however, are very promising, as even the worst-performing model still far outperforms the traditional receiver across all of our tests.