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© 2005, it - instituto de telecomunicações. Todos os direitos reservados. Pedro Santos (pedro.salgueiro@fe.up.pt) Traian Abrudan (tabrudan@fe.up.pt) Ana Aguiar (anaa@fe.up.pt) João Barros (jbarros@fe.up.pt) Impact of Position Errors on Device-to-Device Wireless Channel Estimation 17 th RTCM Seminar DCC/FCUP, Porto, July 19 th 2013

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2 Impact of Position Errors in Device-to-Device Wireless Channel Estimation 1. Motivation 2. Channel Model for 2.4 GHz in Forested Environments 3. Error of Distances Computed from GPS Coordinates 4. Channel Estimation Under Distance Uncertainty 5. Conclusions Outline | 17 th RTCM Seminar – DCC/FCUP, Porto, July 19 th 2013

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3 Motivation Smartphones are becoming more and more ubiquitous Support for WiFi ad-hoc, mesh networks is emerging A number of applications can use this networking paradigm E.g.: localization services, data exchange, instant messaging, VoIP. Accurate channel models for Device-to-Device (D2D) become necessary Predict quality of the signal depending on distance between devices Provides relevant information for the design of protocols and applications E.g.: maximum communication range | 17 th RTCM Seminar – DCC/FCUP, Porto, July 19 th 2013 Impact of Position Errors in Device-to-Device Wireless Channel Estimation

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4 Motivation Channel models require measurement campaigns to be carried out We selected a forest as an example scenario, and undertook a measurement campaign to estimate a channel model It consists in taking many signal strength measurements at known distances between transmitter and receiver. But… How to efficiently obtain a very large number of RSSI and distance measurement pairs in a obstacle-ridden environment such as forest? GPS is the most practical solution, but it has an inherent error. How will it affect the estimated channel model? Can we model that error? And can we correct the estimated channel model for it? | 17 th RTCM Seminar – DCC/FCUP, Porto, July 19 th 2013 Impact of Position Errors in Device-to-Device Wireless Channel Estimation

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5 Chanel Model for 2.4 GHz In Forested Environments Pathloss Model Experiment Methodology Measurement Results | 17 th RTCM Seminar – DCC/FCUP, Porto, July 19 th 2013 Impact of Position Errors in Device-to-Device Wireless Channel Estimation

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6 The Pathloss model is one of the most widely used propagation models. Formula in the logarithmic domain: It models the received signal strength ρ at a distance d from the transmitter. The parameters of the model are α, the attenuation factor, and ρ 0, the received power strength at a reference distance (usually 1m). X σ ρ is an R.V. that models fading. It follows a Normal distribution N(0, σ ρ ) in the logarithmic domain (it is log-normal). Pathloss Channel Model 2 | 17 th RTCM Seminar – DCC/FCUP, Porto, July 19 th 2013 Impact of Position Errors in Device-to-Device Wireless Channel Estimation

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7 Problem Statement However, it is not practical to measure the distance between transmitter and receiver for every single RSSI sample. We need a lot of samples, but there are trees and obstacles everywhere! The best option to obtain a large number of measurements is to use GPS. But GPS has an inherent error. How will it affect the parameter estimation? Using GPS distances will result in different values for parameters α and ρ 0 Y is an R.V. that accounts for both the log-normal fading and the GPS errors. We need to study how do GPS distances affect the estimated model with respect to the actual model. | 17 th RTCM Seminar – DCC/FCUP, Porto, July 19 th 2013 Impact of Position Errors in Device-to-Device Wireless Channel Estimation

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8 We conceived an experiment to evaluate the impact of using GPS distances. 1.We set the TX at a fixed location, sending beacons once a second. 2.At reference distances from the TX, we used the RXs to record RSSI and GPS samples. Chosen distances were 0, 1, 2, 4, 8, 16, 32 and 64 meters (equally-spaced in log-scale). 3.We repeated the procedure for four radials, separated by 45º. Experiment Methodology | 17 th RTCM Seminar – DCC/FCUP, Porto, July 19 th 2013 Impact of Position Errors in Device-to-Device Wireless Channel Estimation

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9 Setting: Most measurements were taken in a clean ground area, with only tree trunks. Occasionally, some isolated trees or dense vegetation interfered. Hardware: Three comercial off-the-shelf smartphones, and a laser range meter. An app was used to record GPS and RSSI data at each distance. Experiment Setting and Hardware 32 meters | 17 th RTCM Seminar – DCC/FCUP, Porto, July 19 th 2013 Impact of Position Errors in Device-to-Device Wireless Channel Estimation

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10 Experiment Results Parameter valuesαρ0ρ0 σ ρ (m) Actual distances model2.22-42.635.64 GPS distances model3.00-24.829.56 ρ(d) = ρ 0 – 10 α log10 (d) | 17 th RTCM Seminar – DCC/FCUP, Porto, July 19 th 2013 Impact of Position Errors in Device-to-Device Wireless Channel Estimation

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11 Error of Distances Computed from GPS Coordinates GPS Inaccuracy Sources Location Error Model Distances Error Model Model Validation | 17 th RTCM Seminar – DCC/FCUP, Porto, July 19 th 2013 Impact of Position Errors in Device-to-Device Wireless Channel Estimation

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12 GPS Error Model GPS inaccuracy sources have different reach and behaviors over time Spatial arrangement of the satellites Tropospheric/Ionospheric attenuation Satellite signal phase delay estimation Multipath/receiver noise Ephemeris/satellite clock error - Affects each sample, at each device differently; - The aggregate of their contributions can be considered Gaussian – N(0, σ GPS ) - Affects all devices within a given area (larger than measurement area); - Frequency of changes is smaller than duration of measurement campaign. Bias vector b Error RV 2 | 17 th RTCM Seminar – DCC/FCUP, Porto, July 19 th 2013 Impact of Position Errors in Device-to-Device Wireless Channel Estimation

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13 These errors components, the bias vector b and the error RV, affect every GPS location measurement. Consequently, distances computed from GPS locations also have errors. Which distribution do distances computed from GPS coordinates follow? GPS Error Model 2 x y x y | 17 th RTCM Seminar – DCC/FCUP, Porto, July 19 th 2013 Impact of Position Errors in Device-to-Device Wireless Channel Estimation ~ N(0, σ GPS ) in each axis

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14 GPS Error Model The GPS distance is the Euclidean norm between two GPS coordinates: The random variable d GPS can be expressed more compactly, as: Random variables of this kind follow the Rice distribution, where the actual distance d is a parameter of the distribution. Their probability density function is as follows, where σ R = 2σ GPS : 22 | 17 th RTCM Seminar – DCC/FCUP, Porto, July 19 th 2013 Impact of Position Errors in Device-to-Device Wireless Channel Estimation

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15 GPS Error Model | 17 th RTCM Seminar – DCC/FCUP, Porto, July 19 th 2013 Impact of Position Errors in Device-to-Device Wireless Channel Estimation

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16 GPS Error Model Validation σ GPS,LS = 10.09 m | 17 th RTCM Seminar – DCC/FCUP, Porto, July 19 th 2013 Impact of Position Errors in Device-to-Device Wireless Channel Estimation

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17 Estimating the Channel Under Distance Uncertainty Distance Uncertainty Monte Carlo Experiment Preliminary Results | 17 th RTCM Seminar – DCC/FCUP, Porto, July 19 th 2013 Impact of Position Errors in Device-to-Device Wireless Channel Estimation

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18 Distance Uncertainty Actual distances model: GPS distances model: The two equations hold on the Least-Squares sense. | 17 th RTCM Seminar – DCC/FCUP, Porto, July 19 th 2013 Impact of Position Errors in Device-to-Device Wireless Channel Estimation

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19 If we have only the GPS distance for each RSSI sample, can we recover, or at least approximate, the actual channel parameters? We used Monte Carlo simulations for this purpose A model of the error is used to generate error-affected data. This data is then reverted to the case in which is not affected by the error. Many samples from the error distribution (Rice, in our case) need to be taken for meaningful results. Our error model is: Channel Estimation under Distance Uncertainty | 17 th RTCM Seminar – DCC/FCUP, Porto, July 19 th 2013 Impact of Position Errors in Device-to-Device Wireless Channel Estimation

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20 1.Select set of 2.. 3.. 4.Pair with 5.Apply Least Squares fitting Monte Carlo Experiment (Approximation to actual model) (GPS distances model) | 17 th RTCM Seminar – DCC/FCUP, Porto, July 19 th 2013 Impact of Position Errors in Device-to-Device Wireless Channel Estimation 1248 163264

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21 Parameter valuesαρ0ρ0 Actual distances model2.22-42.63 GPS distances model3.00-24.82 Monte Carlo approximation2.04-39.51 Results of Monte Carlo Experiment | 17 th RTCM Seminar – DCC/FCUP, Porto, July 19 th 2013 Impact of Position Errors in Device-to-Device Wireless Channel Estimation

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22 Conclusion We have estimated the channel model parameters for wireless propagation in the range of 2.4 GHz in forested environments using smartphones. We have modeled the error of distances computed from GPS coordinates and verified it against experimental data. We proposed a method to recover or approximate the actual channel parameters when only GPS data is available. | 17 th RTCM Seminar – DCC/FCUP, Porto, July 19 th 2013 Impact of Position Errors in Device-to-Device Wireless Channel Estimation

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23 Questions? | 17 th RTCM Seminar – DCC/FCUP, Porto, July 19 th 2013 Impact of Position Errors in Device-to-Device Wireless Channel Estimation

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