System Level Modeling and Optimization of the LTE Downlink

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