System Level Modeling and Optimization of the LTE Downlink

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A. SNR-independence of the CLSM Precoder Choicewhere Λ 2 contains the eigenvalues of H⎡λ 2 1 0 . . . 0Λ 2 0 λ=2 2 . . . 0⎢ .⎣ . . .. .0 0 . . . λ 2 Kand P depends on the precoder. Thus,⎤⎥⎦ ,(A.4)γ ZF,k =1[ρ (PΛP H ) −1] , (A.5)kkFor the full-rank case, where H and W are square, P is unitary, and the per-layerpost-equalization SINR can be expressed asγ ZF,k =1ρ [PΛ −2 P H ] kk=1, (A.6)K∑ |p k,i | 2ρthus simplifying the matrix inverse, where p k,i [P] k,i. The spectral efficiency givena precoder W can then be written asC = log 2K ∏k=1⎛⎜1 +⎝ρi=1λ 2 i1. (A.7)K∑ |p k,i | 2 ⎟⎠i=1λ 2 i⎞The optimum precoder choice employs an approximation for the high-SNR regime(1 + γ k ≈ γ k ) 1 . The rationale for applying the high-SNR regime approximation onthe full SNR range and assuming independence of the noise value stems from thelimited precoder choice. For the two-transmit antenna case, the codebook size islimited to four precoders, while for the four transmit antenna case, there are sixteenpossible choices. Given such a small precoder codebook size, we argue that a goodprecoder choice would very probably remain good regardless of the noise level, whichwe show in the simulation results in the next section.[ (PΛ 1 For the non-full-rank cases, it will not be possible to write2 P H) ] −1kkform, thus the matrix product must be computed.in such a compact86
A. SNR-independence of the CLSM Precoder ChoiceA.1. Simulation ResultsFigure A.1 depicts, for a 4 × 4 antenna configuration, the overall spectral efficiencyfor all the combinations of precoder index (16 choices) and rank (4 choices). Theemployed channel matrix H is shown below, and has been purposely chosen to depicta case where relative precoder performance changes over SNR.⎡⎤−0.808 + 0.128i 0.921 − 1.557i 0.072 + 0.372i −0.606 − 0.226iH 4x4 =−0.442 + 0.896i −0.420 − 0.548i 0.846 + 1.077i −0.120 + 0.578i⎢⎣−0.827 − 0.178i 0.309 − 0.985i 0.085 + 1.272i −0.136 + 0.347i⎥⎦0.278 − 0.145i −0.357 − 0.273i −0.733 − 0.083i −0.612 + 0.541i(A.8)Sum capacity over layers [bit/cu]121086420204x4, rank 1 precoder 18 4x4, rank 2 precoder1614121086420Sum capacity over layers [bit/cu]Sum capacity over layers [bit/cu]2520151050184x4, rank 3 precoder 16 4x4, rank 4 precoder14121086420−5 0 5 10 15 20 25SNR [dB]Sum capacity over layers [bit/cu]−5 0 5 10 15 20 25SNR [dB]Figure A.1: Sum spectral efficiency for the channel matrix H shown in Equation (A.8) for the16 precoders defined for the four-transmit-antenna configuration defined by theLTE standard [39]. Zommed (top-right): crossing in the mutual-informationwiseprecoder performance.In the high-SNR regime, the precedence in terms of performance between any twogiven precoders is independent of the SNR. However, at low SNR, crossings mayappear, such as for the rank 2 case at 5 dB SNR.The effect of applying the high-SNR approximation on the whole SNR range has87
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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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Page 51 and 52: 3. Physical Layer Modeling and LTE
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System Level Modeling and Optimization of the LTE Downlink

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