# Polynomial Cancellation Coded DFT-s-OFDM for Low-PAPR Uplink Signaling
## 4 Simulation and Discussion
### Bit Error Rate  
Figure 7 shows uncoded BER performance comparisons of PCC-DFT-s-OFDM over the AWGN channel at \(d=0,\;1,2,\;3\) for single-user \(\pi/2\)-BPSK, QPSK, and 16-QAM signals. When \(\pi/2\)-BPSK at \(d=0\), the BER curve is almost identical to the lower bound, implying that \(\pi/2\)-BPSK has a high tolerance for PA nonlinearity. For QPSK, there is a slight degradation in BER at \(d=0\). However, its performance  
Figure 5: Single-user power spectral density (PSD) performances of polynomial cancellation coded (PCC) discrete Fourier transform-spread orthogonal frequency division multiplexing (DFT-s-OFDM) for different modulations at (**a**) \(d=0\), (**b**) \(d=1\), (**c**) \(d=2\), and (**d**) \(d=3\). Figure 6: Two-user power spectral density (PSD) performances of polynomial cancellation coded (PCC) discrete Fourier transform-spread orthogonal frequency division multiplexing (DFT-s-OFDM) for 16-quadrature amplitude modulation (16-QAM) signals at (**a**) \(d=0\), (**b**) \(d=1\), (**c**) \(d=2\), and (**d**) \(d=3\). The frequency is normalized to User 1’s bandwidth. can be improved to match the lower bound at \(d=1\). For 16-QAM, the BER improvement is remarkable at \(d=1\), 2 but moderate at \(d=3\) owing to the inferior PAPR performance. Figure 8, Tables 3 and 4 show the BER results over AWGN and Rayleigh fading channel. The performance of 16-QAM signals improves significantly at \(d=1\) while appearing close to the undistorted signals at \(d=2,\ 3\). The results for \(\pi 2\)-BPSK and QPSK are almost the same as those for the undistorted signals at each value of \(d\). Despite this, it is interesting that the proposed method essentially enhances the immunity of DFT-s-OFDM to frequency-selective fading thanks to a property akin to the SS technique. As shown in Figure 3, the band of the PCC-DFT-s-OFDM signals becomes narrower through the higher order of PCC symbols, mitigating the interference from the frequency-selective fading channel. Figure 8: Single-user bit error rate (BER) performances of polynomial cancellation coded (PCC) discrete Fourier transform-spread orthogonal frequency division multiplexing (DFT-s-OFDM) over additive white Gaussian noise (AWGN) and Rayleigh fading channel for different values of \(d\). Figure 7: Single-user bit error rate (BER) performances of polynomial cancellation coded (PCC) discrete Fourier transform-spread orthogonal frequency division multiplexing (DFT-s-OFDM) over the additive white Gaussian noise (AWGN) channel for different values of \(d\). Figure 9 presents the BER performances of two spectrum-adjacent users whose PSD refer to Figure 6. Clearly, serious BER degradation was found when inter-user interference is further considered. By applying PCC to DFT-s-OFDM, the BER of both users is greatly improved because their side-lobes have been suppressed to avoid interfering with the main-beam of each other. However, since more allocated bandwidth causes a greater side-lobe component than that of other users, the BER of User 1 mainly improves at \(d=1\) (see Figure 9a,c) while that of User 2 mainly improves at \(d=2\) (see Figure 9b,d).