## 3 Numerical Simulation  
In this section, we compared the BER performance of two types of DSP receivers. To ensure the validity and precision of our experimental results, a simulation comparison is conducted first. The first receiver uses a conventional cascaded structure of a matched filter and an LMS equalizer, with the matched filter set to 241 taps and the LMS equalizer set to 43 taps. The second receiver employs an NNWSC with an input dimension of 241. Both receivers have the same input dimensions, ensuring a fair and direct comparison of their performance. We evaluated both receivers based on BER. To ensure unbiased results, the NNWSC training and testing sets were generated using different random number generators, avoiding potential overfitting issues. For fairness, the conventional receiver processed only the test data, enabling a direct BER performance comparison with the NNWSC-based receiver under identical conditions. Keeping the transmission channel fixed, we train the parameters of the NNWSC-based receiver. After the training is completed, the NM-CAP signals are transmitted through an additive white Gaussian noise (AWGN) channel using two transmitters. The signal-to-noise ratio (SNR) of the channel is set to 10 dB. The computational complexity of both receivers was also analyzed. For the conventional receiver, the complexity of the matched filter is given by 2 NKs1 MF, where lMF is the number of taps in the matched filter. In contrast, the NNWSC's complexity is calculated as K(lNN1l+l1l2+2 Nl2), where K represents the number of sampling periods, and lNN1, l1, and l2 and 2N correspond to the sizes of the input layer, two hidden layers, and output layer of the neural network, respectively [28]. Despite both receivers having the same input dimension of 241, the complexity per sampling period for the conventional receiver is calculated to be 2 \(\times\) 3 \(\times\) 20 \(\times\) 241 = 28,920, while for the NNWSC, it is reduced to 241 \(\times\) 10 \(\times\) 10 \(\times\) 6 + 6 \(\times\) 6 = 2506. The NNWSC significantly reduces computational complexity by 91.33%, which directly performs the waveform-to-symbol conversion, demonstrating its potential advantages in terms of both performance and efficiency. In this configuration, we conducted simulations to analyze the effect of the sub-band spacing factor on the BER of each sub-band for roll-off factors of 0.4. The simulation results in Figure 3 show the BER variations for each sub-band across different sub-band spacing factors. The simulation results indicate that, under all three roll-off factors, the BER trend for each sub-band is consistent. For each sub-band, the BER decreases initially and then stabilizes as the sub-band spacing factor increases. When the sub-band spacing factor is less than \(1\), all sub-bands are non-orthogonal. As the coefficient approaches \(1\), the overlap between adjacent sub-bands reduces, reaching a point where BER achieves its minimum value and no longer decreases. Additionally, since S2 is subject to IBI from both S1 and S3, the overall BER for S2 is higher than that for S1 and S3, regardless of whether the receiver is NNWSC-based or conventional. At smaller sub-band spacing factors, the BER of the NNWSC-based receiver is significantly lower than that of the conventional receiver, demonstrating superior interference resilience when handling strong IBI. Notably, at narrower spacings, the NNWSC-based receiver effectively manages IBI, significantly reducing BER, whereas the conventional receiver performs poorly under these conditions. As the sub-band spacing increases, the performance gap between the two receivers gradually narrows until it levels off. At larger spacings, where the conventional receiver is not constrained by low-level IBI, the NNWSC does not exhibit a performance advantage.