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4.1. LIJADO MANUAL
In [159], the authors characterized both the effects of pilot spacing and those of the number of pilots separately. Moreover, both of these effects can be treated jointly as those of the pilot power. Therefore, below we characterize the effects of different pilot powers. As shown in Section 4.3.2.1, both the number
4.3.3. Numerical Results and Discussions 146
Bit Error Probability for AF Relaying in Correlated Rayleigh Fading Channel
Eb/N
Figure 4.11: Effect of Doppler frequencies on BEP in the ReS coded H-ARQ system of Fig. 4.1 for AF relaying: fSRlTs = fRlDTs = {0.001, 0.005, 0.01, 0.02, 0.03}, fSDTs = 2fSRlTs, the remaining parameters provided as in Table 4.5. The corresponding goodput results evaluated from Eq. (4.20) are shown in Fig. 4.12.
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Goodput of RS Coding for AF Relaying in Correlated Rayleigh Fading Channel
Eb/N0 (dB)
Figure 4.12: Effect of different normalized Doppler frequencies on the achievable goodput in the ReS coded H-ARQ system of Fig. 4.1 using AF relaying, where we have fSRlTs = fRlDTs = {0.001, 0.005, 0.01, 0.02, 0.03}, fSDTs = 2fSRlTs, the remaining parameters are provided in Table 4.5. The corresponding BEP results evaluated from Eq. (4.37) are shown in Fig. 4.11.
4.3.3. Numerical Results and Discussions 147
BEP of ReS coding for DF relaying in correlated Rayleigh fading channel
Eb/N
Figure 4.13: Effect of Doppler frequencies on BEP in the ReS coded H-ARQ system of Fig. 4.1 using DF relaying: fSRlTs= fRlDTs= {0.001, 0.005, 0.01, 0.02, 0.03}, the remaining parameters provided as in Table 4.5. The corresponding goodput results evaluated from Eq. (4.20) are shown in Fig. 4.14.
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Goodput of ReS coding for DF relaying in correlated Rayleigh fading channel fSDTs=fSR
Figure 4.14: Effect of different normalized Doppler frequencies on the achievable goodput in the ReS coded H-ARQ system of Fig. 4.1 using DF relaying, where we have fSRlTs = fRlDTs = {0.001, 0.005, 0.01, 0.02, 0.03}, the remaining parameters are provided in Table 4.5. The corresponding BEP results evaluated from Eq. (4.46) are shown in Fig. 4.13.
4.3.3. Numerical Results and Discussions 148 of pilots and their spacing are related to the pilot oversampling factor of Eq. (4.31). The same power is assigned to all the data and pilot symbols. Hence, we will study the effect of the pilot oversampling factor Lp instead of the pilots’ power.
It is plausible that increasing the pilot oversampling factor Lp, or - equivalently - the number of pilots, is expected to reduce the CE MSE. However, this automatically reduces the useful data symbols’ energy at a fixed total power budget. Consequently, the BEP would be increased. Hence, the optimal pilot oversampling factor Lopt has to be determined.
In a mobile relaying aided network, the available number of cooperating nodes, their position and channel characteristics are time-variant. Thus, optimizing the pilot oversampling factor for the SS is feasible. As shown in Eq. (4.40), the BEP is a monotonically decreasing function of the instantaneous received SNR ¯γ. Therefore, we have to find the highest value of ¯γ in Eq. (4.42) in order to minimize the BEP. As demonstrated in Appendix IV.B, the optimal pilot oversampling factor Lpopt should be set to
The BEP for the proposed AF system of Fig. 4.1 is shown in Fig. 4.15 . It can been seen that there is a gain of 2 dB in the BEP, when the optimization process was employed. The number of pilot symbols required for three different normalized Doppler frequencies is portrayed in Fig. 4.16. As shown in the figure, the number of symbols required decreases in accordance with the increases of the Eb/N0 values and the normalized Doppler frequencies.
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10−3 10−2 10−1 100
Bit Error Probability for AF Relaying in Correlated Rayleigh Fading Channel
Eb/N
Figure 4.15: Effect of the pilot oversampling factor Lp on BEP in the ReS coded H-ARQ system of Fig. 4.1 using AF relaying, where we have Lp = {1, 3, Lpoptf or BEP, 20, 50}, the remaining parameters are provided in Table 4.5. The corresponding goodput results evaluated from Eq. (4.20) are shown in Fig. 4.17 while the corresponding optimized number of pilots is shown in Fig. 4.18.
The goodput performance of the ReS coded AF relaying aided H-ARQ system of Fig. 4.1 is further characterized in Fig. 4.17, but in contrast to Fig. 4.12, it is now parameterized by Lp. According to
4.3.3. Numerical Results and Discussions 149
Figure 4.16: Effect of Doppler frequencies on the optimized and minimum number of pilots in the ReS coded H-ARQ system of Fig. 4.1 using AF relaying, where we have fSRlTs = fRlDTs = {0.001,
Goodput of RS Coding for AF Relaying in Correlated Rayleigh Fading Channel
Eb/N0 (dB)
Figure 4.17: Effect of the pilot oversampling factor Lp on the achievable goodput in the ReS coded H-ARQ system of Fig. 4.1 using AF relaying, where we have Lp = {1, 3, 50, 150, Lpopt f or BEP, Lpopt f or G}, the remaining parameters are provided in Table 4.5. The corresponding BEP evaluated from Eq. (4.37) results are shown in Fig. 4.15 while the corresponding optimized number of pilots is shown in Fig. 4.18.
4.3.3. Numerical Results and Discussions 150
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0 50 100 150 200 250 300
Eb/N0 (dB)
Number of Pilots
Optimized Number of Pilots
Optimized for BEP Optimized for Goodput (Npmin): Lp = 1
Figure 4.18: Optimized number of pilots in the ReS coded H-ARQ system of Fig. 4.1 using AF relaying, where we have Lp = {Lpopt f or BEP, Lpopt f or G, 1}, the remaining parameters are provided in Table 4.5. The corresponding BEP results evaluated from Eq. (4.37) are shown in Fig. 4.15 while the goodput results evaluated from Eq. (4.20) are shown in Fig. 4.17.
the figure, the optimized value of Lp shifts the goodput curve to the left, which is illustrated by the asterisk-dashed line, but its maximum value is lower than those of Lp = 1 and Lp = 5. This can be explained by the fact that upon minimizing the BEP by optimizing Lp, the effective rate Re is also reduced. Thus, the goodput of the optimized scenario is also reduced. This problem may be overcome by optimizing the Lp value in Eq. (4.20) instead of that in Eq. (4.40). The results of this optimization process are also shown in Fig. 4.17. Clearly, the optimized goodput curve represented by the bold continuous line in the figure indeed reaches the maximum achievable goodput value of unity. The number of pilot symbols per ReS codeword versus Eb/N0 curves seen in Fig. 4.18 provides a clearer view. During the BEP optimization, the SS kept the number of pilot symbols constant, even when the BEP was low. By contrast, the number of pilots was reduced during the goodput optimization, resulting in an increased goodput.
Similar results were obtained for the DF relaying schemes. As shown in Fig. 4.20, the system may save 2 dB power at a given BEP, when the optimized pilot oversampling factor is employed.
However, the goodput, which is represented by the thin continuous line in Fig. 4.20, does not reach its maximum value, when the optimization process is applied. This can be explained by the fact that upon employing the above optimization procedure, the effective rate Re is also reduced. Therefore, the goodput cannot increase, even when the channel conditions are improved. In order to improve the achievable goodput, a modified optimized pilot oversampling factor should be implemented, which is based on Eq. (4.20). The modified results are also shown in Figs. 4.20, and 4.21. It can be seen from these figures that the value of Lp remains constant in the high-SNR region, namely above 10 dB during the BEP optimization. Meanwhile, during the goodput optimization process the value of Lp
continues to be reduced, until reaching its minimum value, resulting in an increased goodput.
4.3.3. Numerical Results and Discussions 151
BEP of ReS coding for DF relaying in correlated Rayleigh fading channel
Eb/N
Figure 4.19: Effect of the pilot oversampling factor Lp on BEP in the ReS coded H-ARQ system of Fig. 4.1 using DF relaying, where we have Lp = {1, 5, 50, 100, Lpopt f or BEP, Lpopt f or G}, the remaining parameters are provided in Table 4.5. The corresponding goodput results evaluated from Eq. (4.20) are shown in Fig. 4.20, while the optimized number of pilots is shown in Fig. 4.21.
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Goodput of ReS coding for DF relaying in correlated Rayleigh fading channel Lp = 1
Figure 4.20: Effect of the pilot oversampling factor Lp on the achievable goodput in the ReS coded H-ARQ system of Fig. 4.1 using DF relaying, where we have Lp = {1, 5, 50, 100, Lpopt f or BEP, Lpopt f or G}, the remaining parameters are provided in Table 4.5. The corresponding EBP results evaluated from Eq. (4.46) are shown in Fig. 4.19, while the optimized number of pilots is shown in Fig. 4.21.
4.3.3. Numerical Results and Discussions 152
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0 50 100 150
The number of Pilots for DF relaying in correlated Rayleigh fading channel
Eb/N0 (dB)
Number of Pilots
Lp = 1 Optimized L
p for BEP Optimized L
p for G
Figure 4.21: Optimized number of pilots in the ReS coded H-ARQ system of Fig. 4.1 using DF relaying where we have Lp = {1, Lpoptf or BEP, Lpoptf or G}, the remaining parameters are provided in Table 4.5. The corresponding goodput results evaluated from Eq. (4.20) are shown in Fig. 4.19, while the corresponding goodput results are shown in Fig. 4.20.