2.4 Performance Evaluations of 5G OFDM-Based Waveform Candidates
2.4.8 Summary of Simulation Results
In this subsection, we summarize the simulation results obtained from Figs. 2.10-2.23 to highlight the performance gains of the proposed CPS-OFDM for Case 1b, Case 3, and Case 4 with four different transmission types
• T1: multicarrier transmission (K = |K| ≥ 2) with the requirements of low OSBE and no NEP,
• T2: single-carrier transmission (K = |K| = 1) with the requirements of low PAPR and low OSBE,
• T3: single-carrier transmission (K = |K| = 1) using dedicated internal GI with the requirements of low PAPR and low OSBE, and
• T4: single-carrier transmission (K = 2, |K| = 1) with the requirements of ex-tremely low PAPR and low OSBE at the cost of SE.
Table 2.1 displays the numerical results of
• PAPR0 (dB) obtained form Fig. 2.11 and Fig. 2.15 at CCDF = 10−3,
• OSBEP (dBm) obtained form Fig. 2.12 and Fig. 2.16 with the OSB range FOSB
corresponding to the subcarriers indexed by{0, · · · , 207, 264, · · · , 1023},
• BER (%) obtained form Fig. 2.13, Fig. 2.17, and Figs. 2.18-2.21 at Eb/N0 = 25 dB, and
• SE (bit/s/Hz) obtained form Fig. 2.22 and Fig. 2.23,
for the waveforms listed in Subsections 2.4.2 and 2.4.3. Given a transmission type and a metric, the boldfaced numerical value corresponds to the best waveform setting. Benefited from the design flexibility, CPS-OFDM can offer the most satisfactory performance with respect to different scenarios and demands. Based on the results in Table 2.1, CPS-OFDM with NoGI is highly recommended. Besides, CPS-OFDM with NoGI can also fit the 5G trend of unified numerology among different cells discussed in [87, Sec. 3].
Element index (i) of the optimized prototype shaping vector
Element index (i) of the optimized prototype shaping vector
0 5 10 15 20 25 30 35 40 45
Phase(radian)
-π 0 π
(a) for the comparisons with low-OSBE waveforms
Element index (i) of the optimized prototype shaping vector
0 5 10 15 20 25 30 35 40 45
Element index (i) of the optimized prototype shaping vector
0 5 10 15 20 25 30 35 40 45
Phase(radian)
-π 0 π
(b) for the comparisons with low-PAPR waveforms
Figure 2.7: Illustrations of the optimized prototype shaping vectors obtained by Algorithm 1 with respect to different parameter settings of CPS-OFDM in Case 1b.
n
Figure 2.8: Visualization of the optimized CPS-OFDM waveforms for the setting of|K| ≥ 2 with different GI types.
n
Figure 2.9: Visualization of the optimized CPS-OFDM waveforms for the setting of|K| = 1 with different GI types.
Normalized Frequency (MHz) UF-OFDM: Chebyshev, Lf= 72 f-OFDM: SincRC, Lf= 512, NT O= 2.5
CPS-OFDM with NoGI or ZP
Figure 2.10: Simulated PSD results of the waveforms claiming low OSBE in the absence of PA, where WOLA-OFDM, UF-OFDM, and f-OFDM ideally have extremely low OSBE at the cost of increased PAPR and induced IBI.
PAPR0 (dB) UF-OFDM: Chebyshev, Lf= 72 f-OFDM: SincRC, Lf= 512, NT O= 2.5
Figure 2.11: PAPR performance results of the waveforms claiming low OSBE, where CPS-OFDM yields much lower PAPR and so ensures better PA efficiency as compared to the others.
Normalized Frequency (MHz) UF-OFDM: Chebyshev, Lf= 72 f-OFDM: SincRC, Lf= 512, NT O= 2.5
Figure 2.12: Simulated PSD results of the waveforms claiming low OSBE in the presence of PA with the IBO of 3 dB, where CPS-OFDM in practice leads to the lowest amount of OSBE in adjacent bands because of its low PAPR.
Eb/N0 (dB) UF-OFDM: Chebyshev, Lf= 72 f-OFDM: SincRC, Lf= 512, NT O= 2.5
Figure 2.13: Single user detection performance results in terms of uncoded 16-QAM, IBO of 3 dB, and TDL-C-300 channel, where CPS-OFDM with CP possesses the best signal reliability at the receiver.
Normalized Frequency (MHz)
Figure 2.14: Simulated PSD results of the waveforms claiming low PAPR in the absence of PA, where SC-FDMA and SS-SC-FDMA do not address OSBE issues and the controllable passband fluctuation of CPS-OFDM can be seen.
PAPR0 (dB)
Figure 2.15: PAPR performance results of the waveforms claiming low PAPR, where CPS-OFDM can further reduce the PAPR by allowing some NEP (ϵ > 0) for the optimal prototype shaping vector design.
Normalized Frequency (MHz)
Figure 2.16: Simulated PSD results of the waveforms claiming low PAPR in the presence of PA with the IBO of 3 dB, where CPS-OFDM benefited from the design flexibility can handle the issues of OSBE, PAPR, and NEP adaptively.
Eb/N0 (dB)
Figure 2.17: Single user detection performance results in terms of uncoded 16-QAM, IBO of 3 dB, and TDL-C-300 channel, where CPS-OFDM with|K| < K can further improve the BER thanks to the frequency diversity.
Eb/N0 (dB) UF-OFDM: Chebyshev, Lf= 72 f-OFDM: SincRC, Lf= 512, NT O= 2.5
Figure 2.18: Target user BER performance comparison of the waveforms claiming low OSBE in the asynchronous multiuser uplink case with IBO of 3 dB, where CPS-OFDM with CP is much more robust to the relative TOs than the others.
Eb/N0 (dB)
Figure 2.19: Target user BER performance comparison of the waveforms claiming low PAPR in the asynchronous multiuser uplink case with IBO of 3 dB, where CPS-OFDM can outperform the others by selecting proper parameters.
Eb/N0 (dB) UF-OFDM: Chebyshev, Lf= 72 f-OFDM: SincRC, Lf= 512, NT O= 2.5
CPS-OFDM with NoGI or ZP
Figure 2.20: Target user BER performance comparison of the waveforms claiming low OSBE in the mixed numerology multiuser uplink case with IBO of 3 dB, where the supe-riority of CPS-OFDM over the others can be found.
Eb/N0 (dB)
Figure 2.21: Target user BER performance comparison of the waveforms claiming low PAPR in the mixed numerology multiuser uplink case with IBO of 3 dB, where CPS-OFDM offers better detection reliability compared to the others.
Case 1b Case 3 Case 4 UF-OFDM: Chebyshev, Lf= 72 f-OFDM: SincRC, Lf= 512, NT O= 2.5
Figure 2.22: Spectral efficiency comparisons of the waveforms claiming low OSBE in the interference-free single user case, the asynchronous multiuser case, and the mixed numerology multiuser case at Eb/N0 = 25 dB.
Case 1b Case 3 Case 4
Figure 2.23: Spectral efficiency comparisons of the waveforms claiming low PAPR in the interference-free single user case, the asynchronous multiuser case, and the mixed numerology multiuser case at Eb/N0 = 25 dB.
Case1bCase3Case4 PAPR0 (dB)OSBEP (dBm)BER (%)SE (bit/s/Hz)BER (%)SE (bit/s/Hz)BER (%)SE (bit/s/Hz) T1
OFDMA10.300.900.272.441.043.412.593.36 WOLA-OFDM:RC,α=110.57-2.250.822.771.333.402.673.35 UF-OFDM:Chebyshev,Lf=7210.72-2.400.312.690.783.421.643.39 f-OFDM:SincRC,Lf=512,NTO=2.511.930.3520.941.8721.402.7122.112.68 f-OFDM:SincRC,Lf=72,NTO=510.51-2.980.312.850.813.421.953.38 OP-OFDM:Z=210.21-2.620.272.690.543.291.353.26 CPS-OFDM:(K,M,Z,ϵ)=(3,16,3,0),NoGI9.28-4.140.363.190.573.440.963.43 CPS-OFDM:(K,M,Z,ϵ)=(2,24,2,0),CP9.11-2.940.252.880.493.291.333.26 CPS-OFDM:(K,M,Z,ϵ)=(2,24,2,0),ZP9.19-4.200.273.060.613.280.873.27 CPS-OFDM:(K,M,Z,ϵ)=(2,24,2,0),NoGI8.87-4.820.323.350.563.520.843.51 T2
SC-FDMA8.11-0.160.242.700.973.412.143.37 CPS-OFDM:(K,M,Z,ϵ)=(1,48,2,0.2),CP8.02-2.700.202.920.623.281.353.26 CPS-OFDM:(K,M,Z,ϵ)=(1,48,2,0.2),ZP8.04-7.230.223.250.383.290.703.28 CPS-OFDM:(K,M,Z,ϵ)=(1,48,2,0.2),NoGI7.83-7.640.213.500.323.530.663.52 T3ZTDFT-S-OFDM:Z=58.42-5.690.233.190.243.29960.593.2882 CPS-OFDM:(K,M,Z,ϵ)=(1,48,5,0.5),NoGI8.01-7.240.213.320.233.29990.503.2913 T4
SS-SC-FDMA:RRC,α=1,Z=246.87-0.710.131.400.171.720.851.71 CPS-OFDM:(K,M,Z,ϵ)=(2,24,25,0.2),CP7.40-6.060.111.610.021.650.091.65 CPS-OFDM:(K,M,Z,ϵ)=(2,24,25,0.2),ZP6.06-13.540.171.750.051.650.0411.65 CPS-OFDM:(K,M,Z,ϵ)=(2,24,25,0.2),NoGI5.75-13.780.161.880.051.770.0421.77 Table2.1:SummaryofrepresentativesimulationresultsforCase1b,Case3,andCase4withfourdifferenttransmissiontypes.