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Fundamental limits of channel state information

Fundamental limits of channel state information. Sijie Xiong and Sujie Zhu. Outline. Introduction to previous work Fisher Information Theory Time Delay Error Bound Simplified Model Evaluation and Conclusion. 2. previous work. RSSI and LDPL( Log-distance path loss ) model

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Fundamental limits of channel state information

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  1. Fundamentallimitsofchannelstateinformation SijieXiongandSujieZhu

  2. Outline • Introductiontopreviouswork • FisherInformationTheory • TimeDelayErrorBound • SimplifiedModel • EvaluationandConclusion 2

  3. previouswork • RSSIandLDPL(Log-distance path loss)model RSSI->distance&triangulation location multipatheffect-> rough!!!!! • Fingerprintlocalization locationisrelatedtothecharacteristicofrssi takethemultipathintoaccount • CSI(ChannelStateInformation) amplitudeandphasetogetsubmeter-levelaccuracy 3

  4. DinaKatabiwork Phase of the signal𝜋 4

  5. Motivation • Inreality,themeasurementofRSSIandphasearebothaffectedbythenoiseaswellasthemultipatheffect. • Thiscausesthemeasuredresulthasdeviationfromthetheoreticalvalue. • Thedeviationaffectsthelocalizationprecision. • Canweevaluatethemeasurementerror? • Canwegiveanerrorboundofthemeasurementresult?

  6. FisherInformationMatrix When there are N parameters, so that then the Fisher information takes the form of an N × N matrix,the Fisher Information Matrix (FIM), with typical element: Wheref(X; θ)istheprobability densityfunction for Xundertheparametersθ 6

  7. FIMfor Multivariate normal distribution The FIM for a N-variate multivariate normal distribution, X ~ N (μ(θ),Σ(θ)), has a special form. Let the K-dimensional vector of parameters be θ = [θ1 , . . . , θk ]T , and the vector of random normal variables be X =[ X1 , . . . , XN]T, with mean values μ(θ) = [μ1 (θ),...,μN (θ)]T, and let Σ(θ) be the covariance matrix. 7

  8. The construction of parameter vector The received signal: The parameter vector: 8

  9. PDF of received signal Discretization process: …… Covariance matrix: where E is the identity matrix

  10. The fisher information matrix The elements of the information matrix：

  11. Equivalent Fisher Information Matrix Given The FIM where EFIM

  12. A simplified model The parameter vector: The FIM： The time delay error bound：

  13. Analyze SNR ↑ error bound ↓ Supposing The time delay error bound：

  14. Future work The relationship between T/N and bound AP deployment Experiments to confirm results

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