System Level Modeling and Optimization of the LTE Downlink

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A. SNR-independence of the CLSM Precoder Choicebeen quantified by simulation for the 4 × 4, 4 × 2, and 2 × 2 antenna configurations.For a set of 100 000 uncorrelated independent channel realizations, the sum spectralefficiency over all layers for each precoder is calculated and the deviation betweenthe high-SNR approximation and the optimum choice calculated.Figure A.2 shows the results of the 4 × 4 antenna configuration. The left plotdepicts, for each SNR point, the failure ratio of the high-SNR approximation, whichas expected, decreases with SNR. Although for the higher ranks the probability ofchoosing a wrong precoder may seem high, it is not significant whether the precoderchoice was correct, rather than how inaccurate is the throughput result of the high-SNR approximation relative to the optimum choice.model failure ratio0.450.40.350.30.250.20.150.10.050−5 0 5 10 15 20 25SNR [dB]avg. rel. capacity deviation [%]1.81.61.41.210.80.60.40.204x4, rank 14x4, rank 24x4, rank 34x4, rank 4−5 0 5 10 15 20 25SNR [dB]Figure A.2: 4×4 antenna configuration: High-SNR CLSM precoder choice accuracy resultsfor each possible rank choice. Left: model failure rate. Right: deviation interms of capacity (% the optimum choice).model failure ratio0.250.20.150.10.050−5 0 5 10 15 20 25SNR [dB]avg. rel. capacity deviation [%]2.521.510.504x2, rank 14x2, rank 2−5 0 5 10 15 20 25SNR [dB]Figure A.3: 4×2 antenna configuration: High-SNR CLSM precoder choice accuracy resultsfor each possible rank choice. Left: model failure rate. Right: deviation interms of capacity (% the optimum choice).The right plot in Figure A.2 depicts the average relative capacity deviation thatresults from this error. Results for the 4 × 2 antenna configuration are provided inFigure A.3, and show results similar to those found for the 4 × 4 case. For the 2 × 2case, due to the smaller codebook size, the model was found to have a failure rate88
A. SNR-independence of the CLSM Precoder Choiceof zero. The 95% confidence intervals are shown as vertical bars on the curves.The high-SNR approximation is shown to be always accurate for the rank-one transmission,with the ratio of a wrong optimum precoder choice growing with the numberof layers. For the four-layer case, a suboptimal precoder was chosen in average between40% to 20% of the cases in the -5 dB-25 dB SNR range are observed, whichalbeit seemingly big, maps to an error between 1.6% to 0.6% in terms of sum spectralefficiency. For the 4×2 case, the worst-case deviation ranges from 2.3% to 0.4%.Further decreasing the impact of the deviation is the fact that at low SNR, a highrankprecoder will very probably not be used. Figure A.4 depicts the average sumspectral efficiency for the optimum precoder choice over SNR for the 4×2 and 4×4antenna configurations for the low-SNR range of -5 dB to 5 dB SNR.avg. sum capacity [bit/cu]4.543.532.521.514x2, rank 14x2, rank 20.5−5 0 5SNR [dB]avg. sum capacity [bit/cu]76543214x4, rank 14x4, rank 24x4, rank 34x4, rank 40−5 0 5SNR [dB]Figure A.4: Sum-capacity over SNR with an optimum precoder choice for each possible rankchoice. Left: 4×2 antenna configuration. Right: 4×4 antenna configurationAs the UE feedback algorithm is to choose the PMI and RI combination maximizingthe sum capacity, a low RI value is to be chosen at low SNR with high probability,which is exactly where the model is most precise.rank choice ratio10.90.80.70.60.50.40.30.20.104x2, rank 14x2, rank 2−5 0 5 10 15 20 25SNR [dB]rank choice ratio0.90.80.70.60.50.40.30.20.104x4, rank 14x4, rank 24x4, rank 34x4, rank 4−5 0 5 10 15 20 25SNR [dB]Figure A.5: Rank of the optimum precoder choice over SNR.This effect is shown in Figure A.5, where for each channel realization, the rankdistribution of the optimum PMI-RI combination is shown. For the 4 × 4 case, a89
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DissertationSystem Level Modeling a
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I hereby certify that the work repo
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KurzfassungDie vorliegende Arbeit p
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ContentsContents1 Motivation and Sc
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Contentsix
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1. Motivation and Scope of Work1. M
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1. Motivation and Scope of Worklaye
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1. Motivation and Scope of Workperf
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BibliographyThe combined throughput
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2. 3GPP Long Term Evolution2. 3GPP
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2. 3GPP Long Term Evolutionup to 30
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2. 3GPP Long Term EvolutionNAS proc
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2. 3GPP Long Term Evolutionchannel
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2. 3GPP Long Term EvolutionSince th
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2. 3GPP Long Term EvolutionThe chan
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2. 3GPP Long Term EvolutionTable 2.
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3. Physical Layer Modeling and LTE
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System Level Modeling and Optimization of the LTE Downlink

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