System Level Modeling and Optimization of the LTE Downlink

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4. Extensions to the L2S ModelThe expression can be simplified by omitting the Tr () term [118], obtainingMSE = ( σ 2 eσ 2 x 0+ σ 2 v) ( ˜H H 0 ˜H 0) −1(4.16)N∑int[+i=1˜H −1 (0 σ2xiH i W i Wi H H H i) ( ) ] H˜H −10 , (4.17)where, assuming all of the entries of H i to have an average power of one, σ xi is theaverage receive power over all antennas for the i-th user (i.e., the transmit powerdivided by the pathloss).For the purpose of model validation, a fixed value for σ 2 e could be used. This settingwould, however, not be realistic. As the quality of the channel estimation varieswith the quality of the pilot symbols from which the estimation is achieved, it istherefore a function of the signal level of the pilots. Adapting from [120], we expressthe channel estimation error σ 2 e as:()σe 2 = c N∑inteσx 2 σn 2 + σx 2 i, (4.18)0i=1where a typical value for c e would be 0.0544 [120, 121] 2 .4.2.1. Model AccuracyThe model is validated in two scenarios: (i) over a SNR range, where no interferersare present and the noise level is varied and (ii) with six interferers placed on ahexagonal grid layout with omnidirectional antennas and evaluating the results onthe points corresponding to the center cell, so as to avoid border map artifacts.In both cases, the model is validated for 2×2 and 4×4 antenna configurations employingCLSM and the standard-defined precoding codebook [39]. The model isvalidated for all the possible number of spatial layers for each antenna configuration,which comprise ν = {1, 2} for the 2×2 case and ν = {1, 2, 3, 4} for the 4×4 case.As the switching between number of layers RI needs to be performed at run-time,it is not in the scope of validating the accuracy of the model to show the combinedperformance when dynamically changing the number of employed layers rather thanto evaluate whether the prediction for any possible rank choice, whichever that onemay be, is accurate.In both cases, the channel matrix is obtained from an implementation of the WinnerPhase II channel model [122], and the precoding matrix chosen so as to maximize2 Assumes a pedestrian simulation and an LMMSE channel estimator.60
4. Extensions to the L2S Modelthe achievable capacity [54]. Since no interference coordination is assumed, eachinterferer is assigned a random precoder from the codebook.As accuracy metric, the post-equalization SINR output by the model and that ofa simulated transmission are compared in the capacity domain, where the capacitymetric is expressed as the sum capacity over all streams and calculated asC sum =ν∑log 2 (1 + γ i ) . (4.19)i=1Figure 4.8 shows the results for the no-interference scenario for the 2×2 and 4×4antenna configuration cases respectively, with c e = 0.0544 [120].Achievable capacity [bit/s/Hz]181614121086421 layer2 layers00 5 10 15SNR [dB]20 25 30Achievable capacity [bit/s/Hz]302520151051 layer2 layers3 layers4 layers00 5 10 15SNR [dB]20 25 30Figure 4.8: 2 × 2 (left) and 4 × 4 (right) results. Solid line: modeled achievable capacity.Dashed line (totally overlapped by the solid line): calculated achievable capacity.This scenario, although at first glance suitable, is unable to depict the capacitydeviation between the predicted and the obtained value from the simulation. Asσe 2 is a linear function of σn, 2 the result is the channel estimation error is effectivelyalways 12 dB below the noise level, its influence in the MSE being thus negligible.Table 4.4.: Simulation parameters: model validation for the interference case.Inter-eNodeB distance500 mBandwidth 15 kHz (single subcarrier)Transmit power (P TX ): 17.7 dBm (43 dBm/5 MHz)Noise density-173 dBm/HzChannel model Winner Phase II [76, 122]Pathloss L = 128.1 + 37.6 log 10 (R) [69]Transmit mode:CLSMAntenna type Omnidirectional, 0 dB gainMinimum coupling loss 70 dB [69]Number of points in the target sector 8 65861
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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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BibliographyThe combined throughput
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System Level Modeling and Optimization of the LTE Downlink

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