Tendencia promedio de variables

Figure 5.10 shows the BER versus the SNR for the RAx channel model when an emulated speed of 200 km/h is obtained considering I = 1 (no interpolation) and I = 2, for the cases of OFDM and FBMC (Hermite prototype filter). Analytic curves for both AWGN and Rayleigh channels for OFDM and FBMC are also included. It can be seen that such analytic curves almost overlap, ensuring that a fair comparison is performed. With respect to the simulation results, the curves corresponding to OFDM for the emulated speed v = 200 km/h obtained by considering the interpolations factors I = 1 and I = 2 almost overlap, hence showing that our technique performs adequately, being the same effect appreciated for the curves corresponding to FBMC. Moreover, there is an excellent agreement between the OFDM and FBMC results for most SNR values. This shows that the performance of both modulation schemes is very similar for v = 200 km/h and the RAx channel model. Only slight differences are appreciated for the maximum SNR value of 30 dB, since the random effects due to the noise are minimized and hence do not hide the other sources of disagreement in the results. Therefore, SNR = 30 dB will be considered for the results of BER versus emulated speed which are shown below, as it is the worst case for the proposed high speed emulation technique.

0 5 10 15 20 25 30 10−4 10−3 10−2 10−1 100 SNR [dB] BER OFDM, I=1, v=200 km/h FBMC (PHYDYAS), I=1, v=200 km/h OFDM, I=2, v=100 km/h FBMC (PHYDYAS), I=2, v=100 km/h OFDM analytical (Rayleigh) OFDM analytical (AWGN)

FBMC (PHYDYAS) analytical (Rayleigh) FBMC (PHYDYAS) analytical (AWGN)

Figure 5.11: BER versus SNR for the RAx channel model, OFDM and FBMC (PHYDYAS) modulations, I = 1, 2, and for an emulated speed of 200 km/h. Curves corresponding to different interpolation factors almost overlap, showing the accuracy of the proposed technique. No differences in the performance achieved by OFDM and FBMC with the PHYDYAS prototype filter are appreciated.

Figure 5.11 is similar to the previous figure, but it includes the results for OFDM and FBMC with the PHYDYAS prototype filter. The plot shows again the good behavior of the proposed technique, since the curves corresponding to the same modulation and emulated speed almost overlap regardless of the considered interpolation factor. However, in this case no noticeable performance differences between OFDM and FBMC with the PHYDYAS prototype filter can be appreciated, regardless of the considered SNR value.

The performance in terms of EVM versus SNR is shown in Fig. 5.12 for the RAx channel model and the three modulation schemes, for an emulated velocity of 200 km/h. These results are in accordance with those obtained for the BER. Again, an excellent level of agreement between the curves obtained for different interpolation factors can be observed, thus validating the proposed technique for inducing high-speed effects while evaluating the system under test at much lower velocities. Moreover, it can be seen that FBMC with the Hermite prototype filter performs better in terms of EVM for the high SNR regime.

Figure 5.13 shows the BER versus the emulated speed for the RAx channel model and considering OFDM and FBMC with the PHYDYAS prototype filter. Interpolation factors I = 1, 2, 3are considered. On the one hand, the three OFDM curves corresponding to the three interpolation factors show an excellent level of agreement. The same effect is observed for the FBMC (PHYDYAS) curves. On the other hand, a significant performance difference between OFDM and FBMC (PHYDYAS) is appreciated for speeds above 300 km/h. This is because the PHYDYAS prototype filter is much better localized in frequency than the OFDM one, and

0 5 10 15 20 25 30 −20 −15 −10 −5 0 5 SNR [dB] EVM [dB] OFDM, I=1, v=200 km/h FBMC (Hermite), I=1, v=200 km/h FBMC (PHYDYAS), I=1, v=200 km/h OFDM, I=2, v=100 km/h FBMC (Hermite), I=2, v=100 km/h FBMC (PHYDYAS), I=2, v=100 km/h

Figure 5.12: EVM versus SNR for the RAx channel model, OFDM and FBMC (Hermite and PHYDYAS) modulations, I = 1, 2 and for an emulated speed of 200 km/h. Curves corresponding to different interpolation factors almost overlap, showing the accuracy of the proposed technique. FBMC with Hermite prototype filter performs slightly better than the other modulation schemes for the high SNR regime.

hence it accounts better for the channel time dispersion. In other words, the FBMC PHYDYAS prototype filter helps in combating the effect of the ICI better than OFDM. However, for practical HST velocities (below 350 km/h) the performance difference is not very significant. Figure 5.14 shows also the BER versus the emulated speed for the RAx channel model but for the two FBMC prototype filters considered (Hermite and PHYDYAS). Again, an excellent agreement is shown between the results for emulated speeds obtained by means of different interpolation factors regardless of the considered modulation scheme. Figure 5.14 also shows that the performance obtained for the Hermite prototype filter is better than that exhibited by the PHYDYAS one, specially for those speeds which are more practical in the HST environment. The reason for this behavior is that the Hermite prototype filter is slightly worse localized in frequency than the PHYDYAS one, but it is better localized in time, thus simultaneously minimizing both ICI and ISI.

Figures 5.15 and 5.16 show the BER versus the emulated speed for the TUx channel model and considering OFDM and FBMC (PHYDYAS prototype filter) modulation schemes in the first case, and both FBMC schemes (PHYDYAS and Hermite prototype filters) in the latter. Given that the TUx channel model is more frequency selective than the RAx one, the BER results are worse than those obtained for the RAx channel model. On the other hand, the level of agreement between the curves corresponding to the three interpolation factors is also slightly worse than in the RAx case. Besides the performance curves, BER relative error curves are

0 200 400 600 800 1000 1200 1400 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 Emulated Speed [km/h] BER OFDM, I=1, v=200 km/h FBMC (PHYDYAS), I=1, v=200 km/h OFDM, I=2, v=100 km/h FBMC (PHYDYAS), I=2, v=100 km/h OFDM, I=3, v=66.6 km/h FBMC (PHYDYAS), I=3, v=66.6 km/h

Figure 5.13: BER versus emulated speed for the RAx channel model, OFDM and FBMC (PHYDYAS) modulations and I = 1, 2, 3. Curves corresponding to different interpolation factors almost overlap, showing the accuracy of the proposed technique. FBMC with PHYDYAS prototype filter performs better than OFDM for speeds above 300 km/h, whereas negligible performance differences are appreciated for lower speeds. 0 200 400 600 800 1000 1200 1400 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 Emulated Speed [km/h] BER FBMC (Hermite), I=1, v=200 km/h FBMC (PHYDYAS), I=1, v=200 km/h FBMC (Hermite), I=2, v=100 km/h FBMC (PHYDYAS), I=2, v=100 km/h FBMC (Hermite), I=3, v=66.6 km/h FBMC (PHYDYAS), I=3, v=66.6 km/h

Figure 5.14: BER versus emulated speed for the RAx channel model, FBMC (Hermite and Phydyas) modulation and I = 1, 2, 3. Curves corresponding to different interpolation factors almost overlap, showing the accuracy of the proposed technique. The Hermite prototype filter provides a better performance than the PHYDYAS one for practical HST speeds.

also included in Fig. 5.17 for the worst case (TUx channel model). Three types of relative error curves are included, which are (a) relative difference between the results obtained when

0 200 400 600 800 1000 1200 1400 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 Emulated Speed [km/h] BER OFDM, I=1, v=200 km/h FBMC (PHYDYAS), I=1, v=200 km/h OFDM, I=2, v=100 km/h FBMC (PHYDYAS), I=2, v=100 km/h OFDM, I=3, v=66.6 km/h FBMC (PHYDYAS), I=3, v=66.6 km/h

Figure 5.15: BER versus emulated speed for the TUx channel model, OFDM and FBMC (PHYDYAS) modulations and I = 1, 2, 3. The performance is lower than that for the RAx channel model, since the frequency selectivity of the channel is higher. This also causes that the level of agreement between the curves corresponding to the three interpolation factors is also slightly worse than in the RAx case.

the interpolation factor I = 2 is employed and actual speeds are used; (b) relative difference between the results obtained when the interpolation factor I = 3 and the actual speeds are considered; and (c) relative difference between the results obtained for the interpolation factors I = 3and I = 2. These curves are computed as explained in Section 5.3.2. It can be seen that the obtained error values are below 0.2 % in any case.

The performance in terms of EVM versus emulated speed is shown in Fig. 5.18 for the RAx channel model, and in Fig. 5.19 for the TUx channel model. These results are in accordance with those obtained for the BER. Again, an excellent level of agreement between the curves obtained for different interpolation factors can be appreciated, thus validating the proposed technique for inducing high-speed effects while evaluating the system under test at much lower velocities.