## 7 Numerical Results and Discussion
### Results and Discussion
These parameters are set to \(g=1\), \(E_{0}=1\), and \(P=3\) as in [22]. Although ANN lags behind SCF and ICF with a performance gap exceeding 3 dB at the \(10^{-3}\) mark, the proposed scheme manages to maintain a close proximity to within 0.4 dB of SCF and ICF at the same level. Figure (b)b retraces the PSD performance of ANN and the proposed SNN-CF scheme along with the benchmark schemes and unmodified OFDM signals when the solid state HPA is deployed. SLM, SCF, and ICF provide more controlled OoB radiations in the neighborhood of the in-band, where the input back-off of HPA and clipping ratio are set to 3.5 and 6 dB, respectively. Both ANN and SNN-CF exhibit a steady roll-off decline in the neighborhood of the in-band with an almost consistent leakage gap of about 3 dB in favor of SNN-CF. In addition, as we move further away, the gap between ANN and the proposed SNN-CF scheme grows rapidly as ANN roll-off slows down whereas the OoB leakage of the proposed scheme decays significantly and goes below the benchmarks. Although SCF provides better overall PSD performance than the proposed SNN-CF, it requires a noticeably higher processing complexity. Figure 10 shows an alternative view on OoB power leakage of ANN and the proposed SNN-CF for QPSK and 16-QAM. The normalized out-of-band leakage power (NOLP) \(\gamma\) is defined as  
\[\gamma\triangleq 10\log_{10}(P_{l}/P_{in})\,dB\,, \tag{11}\]  
where \(P_{l}\) is the total leaked power and \(P_{in}\) is the power residing within the in-band. Lower NOLP levels are desirable for superior power leakage performance. Therefore, we use the complementary CDF on different threshold values of the NOLP: \(\mathcal{F}(\gamma)\triangleq Pr\{\gamma>\gamma_{0}\}\). The threshold level \(\gamma_{0}\) is varied within the ranges \([-42,-24]\) dB and \([-42,-22]\) dB for QPSK and 16-QAM, respectively, in order to capture the OoB leakage performance from CCDF unity level (corresponding to uncrossable threshold points) to levels as low as \(10^{-3}\) (corresponding to crossable threshold points with 99.9% success rate). As shown in Figure (a)a, the proposed SNN-CF scheme generally outperforms ANN in terms of the reduction achieved on NOLP for QPSK modulation with a performance gap of about 4.25 dB at CCDF level of \(10^{-3}\). In addition, for the 16-QAM case, the proposed SNN-CF scheme exhibits a much more controlled power leakage than ANN does with an approximately 7.25 dB performance gap at the \(10^{-3}\) CCDF mark, as shown in Figure (b)b. This superior performance of SNN-CF compared to ANN is the result of the more accurate peak-tracking of SCF signals, as modeled by the non-linear SNN-CF mapper. Figure 9: Performance evaluation for 16-QAM-OFDM transmissions deploying non-linear HPA with 3.5 dB input back-off and 6 dB clipping ratio: (**a**) BER; and (**b**) PSD. Figure 11 investigates the BER performance of the proposed SNN-CF scheme for higher order QAM modulations. For all three cases of 64-QAM, 256-QAM, and 1024-QAM transmissions, the proposed SNN-CF scheme successfully remains within close performance to original OFDM. For example, the performance gap for 64-QAM-based operation is about 1.25 dB at a BER level of \(10^{-3}\). Similarly, for the 256-QAM and 1024-QAM cases, the performance gaps at the same BER level are about 1.5 and 1.75 dB, respectively. To attain even narrower gaps for higher modulation orders, the underlying neural network module can be expanded by slightly increasing the neurons within the layers, for example, to maintain the complexity within reasonable bounds.