This section demonstrates the effect of code rate assignment on the delay-limited throughput function (RDL) measured as a function of the D-SNR using the opti-
mized code book Copt and the NPA HARQ protocols. To this end, the decoding
instant sets are chosen as D = Ds =Dr =Dd, where D = {1, 2, . . . , 8}. I.e., re-
lay and destination perform a decoding attempt in each ARQ round offered by the mother codebook. Therefore, the HARDQ-MISO protocol gives the outage probability of the HARQ-DDF protocol achieved if the SNR of the source-to- relay channel tends to infinity.
Gaussian Channel Inputs
Figure 6.5 depicts the outage probability of the HARQ protocols considering Gaussian distributed channel inputs for both codebooks. It can be observed that the selection of the codebook does not change the outage probability for the HARQ-SISO and the HARQ-MISO protocol. For the HARDQ-MISO pro- tocol, a negligible performance advantage can be observed for the optimized codebook. The non-optimized codebook outperforms the optimized codebook from an outage probability point of view considering the HARQ-DDF protocol. Furthermore, it can observed that the HARDQ-MISO protocol clearly out- performs the HARQ-MISO protocol for both codebooks for medium to high D-SNR. At low D-SNR, the HARDQ-MISO protocol achieves the performance of the HARQ-MISO protocol. At high D-SNR, also the HARQ-DDF protocol outperforms the HARQ-MISO protocol for both codebooks, but considering the optimized codebook, the performance advantage is negligible. At medium to low D-SNR, the HARQ-MISO protocol outperforms the HARQ-DDF protocol. It is also important to point out that both the HARDQ-MISO and the HARQ- DDF protocol achieve the same diversity as the HARQ-MISO protocol at high D-SNR.
However, for both codebooks, the HARDQ-MISO protocol and the HARQ- DDF protocol show a very good outage probability performance which is at least equivalent or superior to the performance of the HARQ-MISO protocol at
Chapter 6: Numerical Results: Gaussian and Discrete Channel Inputs 80 10-6 10-5 10-4 10-3 10-2 10-1 100 -5 0 5 10 15 20 25 30 Pout D-SNR [dB] HARQ-SISO HARQ-MISO HARDQ-MISO HARQ-DDF
(a)Equal symbol length ARQ rounds.
10-6 10-5 10-4 10-3 10-2 10-1 100 -5 0 5 10 15 20 25 30 Pout D-SNR [dB] HARQ-SISO HARQ-MISO HARDQ-MISO HARQ-DDF
(b)Optimized code rate assignment. Figure 6.5:Comparison of the outage probability of the code booksCnon-optandCoptconsid-
ering Gaussian distributed channel inputs.
0 0.5 1 1.5 2 2.5 3 3.5 4 -5 0 5 10 15 20 25 30 RDL [BPCU] D-SNR [dB] HARQ-SISO HARQ-MISO HARDQ-MISO HARQ-DDF
(a)Equal symbol length ARQ rounds.
0 0.5 1 1.5 2 2.5 3 3.5 4 -5 0 5 10 15 20 25 30 RDL [BPCU] D-SNR [dB] HARQ-SISO HARQ-MISO HARDQ-MISO HARQ-DDF
(b)Optimized code rate assignment. Figure 6.6:Comparison of the delay-limited throughput of the code booksCnon-opt andCopt
high D-SNR.
Figure 6.6 depicts the corresponding delay-limited throughput measured as a function of the D-SNR for the HARQ protocols. For both codebooks, all protocols achieve the maximum throughput at high D-SNR. But it can be ob- served that the optimized codebook outperforms the non-optimized codebook over almost the complete shown D-SNR range. At very low D-SNR, both code- books show equivalent performance. The HARDQ-MISO protocol outperforms the HARQ-DDF protocol, but the performance difference is negligible. Fur- thermore, it can be observed that the HARQ-MISO protocol outperforms the remaining protocols for both codebooks.
Considering the non-optimized codebook, it can be observed that the HARDQ- MISO protocol and the HARQ-DDF protocol outperform the HARQ-SISO pro- tocol for rates up to RDL = 2. For higher rates, the HARQ-SISO protocol is
superior. In comparison, the optimized codebook allows to achieve at least the performance of the HARQ-SISO protocol and is superior for rates RDF > 2.
Furthermore, an interesting observation is that the delay-limited throughput functions show a kink at RDL = 2 BPCU. This observation will be revisited
considering 16-QAM channel inputs in the subsequent analysis.
The comparison of the delay-limited throughput as a function of the D-SNR demonstrates that the optimization of the achievable code rates of the mother codebook offers significant performance gains in terms of delay-limited through- put. From a reliability point of view, equal symbol length ARQ rounds offer a remarkable outage probability measured as a function of the D-SNR for the HARQ-DDF protocol only.
16-QAM Channel Inputs
Figure 6.7 and Figure 6.8 show the outage probability and the delay-limited throughput measured as functions of the D-SNR for the HARQ protocols.
In general, the outage probability functions are very similar in performance to the Gaussian channel inputs. However, the performance advantage of the HARDQ-MISO and the HARQ-DDF protocol over the HARQ-MISO protocol is reduced.
Considering the delay-limited throughput functions in Figure 6.8 and Fig- ure 6.6, major differences can be observed. Primarily, it can be observed that
Chapter 6: Numerical Results: Gaussian and Discrete Channel Inputs 82 10-6 10-5 10-4 10-3 10-2 10-1 100 -5 0 5 10 15 20 25 30 Pout D-SNR [dB] HARQ-SISO HARQ-MISO HARDQ-MISO HARQ-DDF
(a)Equal symbol length ARQ rounds.
10-6 10-5 10-4 10-3 10-2 10-1 100 -5 0 5 10 15 20 25 30 Pout SNR [dB] HARQ-SISO HARQ-MISO HARDQ-MISO HARQ-DDF
(b)Optimized code rate assignment. Figure 6.7:Comparison of the outage probability of the code booksCnon-optandCoptconsid-
ering uniformly distributed 16-QAM channel inputs.
0 0.5 1 1.5 2 2.5 3 3.5 4 -5 0 5 10 15 20 25 30 RDL [BPCU] D-SNR [dB] HARQ-SISO HARQ-MISO HARDQ-MISO HARQ-DDF
(a)Equal symbol length ARQ rounds.
0 0.5 1 1.5 2 2.5 3 3.5 4 -5 0 5 10 15 20 25 30 RDL [BPCU] SNR [dB] HARQ-SISO HARQ-MISO HARDQ-MISO HARQ-DDF
(b)Optimized code rate assignment. Figure 6.8:Comparison of the delay-limited throughput of the code booksCnon-opt andCopt
the functions considering Gaussian channel inputs significantly outperform the functions obtained due to 16-QAM channel inputs. Furthermore, as mentioned earlier, a kink can be observed around RDL = 2 BPCU for Gaussian channel
inputs and the non-optimized codebook. Considering 16-QAM channel inputs, this kink takes a more significant form. This kink stems from the fact the dis- tance between the code rate of the first and the second ARQ round is large. This distance can be overcome only if the D-SNR is high. However, in the op- timized codebook, the distance to the next achievable code rate higher than R = 2 BPCU is smaller and can be overcome at lower D-SNR levels. Therefore, the delay-limited throughput function considering the optimized codebook is smooth.
It can be observed that the optimization of the mother codebook allows signif- icant throughput performance gains considering 16-QAM channel inputs. But the performance gain of the HARDQ-MISO and HARQ-DDF protocol over the HARQ-SISO protocol is less significant than considering Gaussian channel inputs.