4.2 Performance
4.2.4 Spatial Diversity
vector with CP, the user velocity would have to be in the order ofv = 1000 km/h.
Table 4.3: NumbersNt in Figures 4.8 and 4.9 and their relation to the coherence time.
Nt 1 4 12 24 48
∆T /Tc 0.01 0.05 0.16 0.33 0.66
The results can be explained as follows. The increased slope of the curves indicates the increased diversity order through exploitation of spatial diversity. For a low number of subcarrier blocks, i.e., for low frequency diversity, the exploitation of spatial diversity results in a considerable reduction of the effect of the channel fading and, thus, results in a considerable performance improvement. For a high number of subcarrier blocks, the effect of the channel fading is already reduced by the exploitation of frequency diversity. Thus, the effect of spatial diversity is less pronounced but still considerable.
From the performance improvement due to the exploitation of spatial diversity it can be concluded that the combination of B-IFDMA with an Alamouti STBC can be considered as a promising solution for improving the performance of B-IFDMA.
In the following, the amount of spatial diversity that is exploited is further increased by the introduction of multiple receive antennas at the base station. It is assumed that nR = 2 receive antennas are used. The antenna distance at the receiver is assumed to be 5λ. At a carrier frequency of 3.7 GHz, an antenna distance of 5λ corresponds to
≈ 40 cm that can be considered as a typical antenna distance for a base station. In addition to the application of an Alamouti STBC at the transmitter, Maximum Ratio Combining (MRC) is applied at the receiver. Figures 4.13-4.15 show the resulting performance normalized to the array gain, i.e. in terms of the BER versusEb/(nR·N0), i.e., Eb/N0 normalized to the number of receive antennas. Again, as a reference, the single antenna performance is depicted.
In Figures 4.13-4.15 it can be seen that due to the additional use of multiple receive antennas the performance is further increased, even if the array gain is not consid-ered. Again, the performance gain compared to the single antenna transmission is the higher the lower the frequency diversity provided by B-IFDMA. The reason is that the introduction ofnR = 2 receive antennas provides a significantly improved diversity order, especially due to the fact that the antenna distance at the receiver is consider-ably larger than the wavelength and, thus, the receive antennas can be assumed to be almost uncorrelated.
In Figure 4.16, the required Eb/N0 is depicted for a BER of 10−3. Again, the array gain for MRC is not considered because it would cause only a shift of the curves for B-IFDMA with Alamouti and MRC of 3 dB. Figure 4.16 shows the performance gains due to frequency diversity for different antenna configurations. The amount of frequency diversity is reflected in the difference of the required Eb/N0 normalized to nR between low values ofLand high values of L for a given value ofQ and for a given antenna configuration. It can be seen that, for a transmission applying STBC at the transmitter, compared to single antenna transmission, the performance gains due to frequency diversity are lower. This effect is further increased if, in addition to STBC at
Figure 4.10: BER versus Eb/N0 for coded transmission of B-IFDMA with Alamouti STBC at Q= 128 subcarriers per user, i.e., at 4.44 Mbps.
Figure 4.11: BER versus Eb/N0 for coded transmission of B-IFDMA with Alamouti STBC at Q= 64 subcarriers per user, i.e., at 2.22 Mbps.
Figure 4.12: BER versus Eb/N0 for coded transmission of B-IFDMA with Alamouti STBC at Q= 32 subcarriers per user, i.e., at 1.11 Mbps.
Figure 4.13: BER versus Eb/(nR·N0) for coded transmission of B-IFDMA with Alam-outi STBC and MRC at Q= 128 subcarriers per user, i.e., at 4.44 Mbps.
Figure 4.14: BER versus Eb/(nR·N0) for coded transmission of B-IFDMA with Alam-outi STBC and MRC at Q= 64 subcarriers per user, i.e., at 2.22 Mbps.
the transmitter, also MRC at the receiver is applied. E.g., regarding the transmission at an instantaneous net bit rate of 1.11 Mbps, for B-IFDMA with Alamouti STBC, the difference between the required Eb/N0 at a BER of 10−3 forL= 1 and for L= 32 is≈ 5 dB. For B-IFDMA with Alamouti and MRC it reduces to≈3 dB, whereas for single antenna transmission it is≈ 9 dB. The reason is that, compared to the single antenna case, if spatial diversity is exploited, the effect of the channel fading is already reduced.
Thus, if spatial diversity is exploited the performance gains through frequency diversity are lower compared to the single antenna case. However, it can be concluded that even if spatial diversity is exploited at transmitter and receiver, the performance gains due to an exploitation of frequency diversity are still significant.
In the following, the new approach for application of STBCs to B-IFDMA from Section 3.3 is compared to an approach where the coloration of the noise due to the STBC decoder, cf. Section 3.3.5.2, is not considered at the receiver. Again, an Alamouti STBC and an antenna distance ofλ/2 are assumed at the transmitter. At the receiver, nR = 1 receive antenna is assumed. The corresponding results are depicted in Figure 4.17.
It can be seen that the new approach considerably outperforms the approach that does not consider the coloration of the noise. Thus, the new approach is shown to provide a better performance compared to approaches that are state-of-the-art, cf. Section 3.3.2.
Figure 4.15: BER versus Eb/(nR·N0) for coded transmission of B-IFDMA with Alam-outi STBC and MRC at Q= 32 subcarriers per user, i.e., at 1.11 Mbps.
Figure 4.16: RequiredEb/(nR·N0) at a BER of 10−3for different data rates dependent on the number L of subcarrier blocks for different antenna configurations.
The performance gain of the new approach is almost independent of the number Q of subcarriers per user.
Figure 4.17: BER versus Eb/N0 for coded transmission of B-IFDMA with Alamouti STBC at Q = L = 128 and Q =L = 64 subcarriers per user, i.e., at 4.44 Mbps and 2.22 Mbps, respectively.