## 6 Simulation Results and Discussions
### PAPR Simulation Results
#### 6.3.2 PAPR Simulation Results on Receiver Side  
We now investigate the effect of channel noise on the PAPR performance of the waveforms considered in this paper. PAPR performance of each of the four waveforms considered are compared for 4-QAM and 16-QAM modulation at 0 dB, 5 dB, 10 dB, 15 dB, 20 dB, and 25 dB SNR values. The effects of different mother wavelets on the PAPR performance of the proposed waveform are shown in Figure 11 for 4-QAM modulation at 15 dB SNR value on the receiver side. The best PAPR performance is obtained when the proposed waveform is implemented using the lazy wavelet and the worst PAPR performance is obtained using the db7 mother wavelets. The performance of the proposed waveform implemented using the other mother wavelets considered is between the performance obtained using these two mother wavelets. Because the best performance of the proposed waveform is obtained using the lazy mother wavelets, in the rest of this sub-section we will use this mother wavelets. The comparison of PAPR performance curves at receive side for conventional OFDM, GFDM, WHT-GFDM, and proposed waveforms is shown in Figure 12 for 4-QAM modulation and SNR of 15 dB. From Figure 12, we can observe that the proposed waveform outperforms the conventional OFDM and GFDM waveforms, and gives approximately 1.0 dB PAPR gain for \(1\times 10^{-3}\) CCDF level. On the other hand, it is understood that the proposed waveform and the WHT-GFDM waveform exhibit approximat  
Figure 11: The influences of the different mother wavelets on PAPR performance of proposed waveform in 15 dB of SNR value for 4-QAM signal. The comparison of PAPR performance curves of the proposed waveform and WHT-GFDM waveform is shown in Figure 13 for 4-QAM modulation and SNR values at receiver side between 0 and 25 dB. When PAPR performances in Figure 13 are examined, it is seen that PAPR dB gain is provided from 0 dB to 15 dB of SNR values with both waveforms. However, it is understood that PAPR dB gains are approximately the same after 15 dB of SNR value. In other words, it is observed that no PAPR dB gain is provided after 15 dB of SNR value. The influences of diverse mother wavelets on the PAPR performance of the proposed waveform are shown in Figure 14 for 16-QAM modulation at 20 dB SNR value on the receiver side. Investigating Figure 14, it is observed that the best outcome is obtained using the lazy mother wavelets and the worst outcome is obtained using the db7 mother wavelets. The PAPR performance of the proposed waveform at the receiver side obtained using the other mother wavelets considered is between the performance obtained using these two mother wavelets. As the best performance of the proposed waveform is obtained using the lazy  
Figure 12: The PAPR performance comparisons of conventional OFDM, GFDM, WHT-GFDM, and WHT-LWT-GFDM waveforms in case of 4-QAM modulation for a SNR of 15 dB at receiver side. Figure 13: The PAPR performance comparison of the proposed waveform (**a**) and WHT-GFDM waveform (**b**) in between 0–25 dB of SNR values for 4-QAM modulation. mother wavelets, it will be used in the following to compare the proposed waveform with other waveforms. The comparison of PAPR performance curves of conventional OFDM, GFDM and WHT-GFDM waveforms with the proposed waveform is given in Figure 15 for 16-QAM modulation at 20 dB SNR value in the receiver. Analyzing Figure 15, it is observed that the proposed waveform outperforms the conventional OFDM and GFDM waveforms and gives nearly 0.6 dB PAPR enhancement for \(1\times 10^{-3}\) CCDF level. On the other hand, it is understood that the proposed waveform and the WHT-GFDM waveform perform very close to each other. The comparison of PAPR performance curves of the proposed waveform and WHT-GFDM waveform is given in Figure 16 for 16-QAM modulation considering the interval of SNR values at the receiver side between 0 and 25 dB. Figure 14: The influences of the different mother wavelets on PAPR performance of proposed waveform in 20 dB of SNR value for 16-QAM modulation.