Implementation of Algorithms for Fast Linear Transformations

Implementation of Algorithms for Fast Linear Transformations
DVT Research Group – Fraunhofer IIS and TU Ilmenau SE/3 e SE/8 - IME Caio M. O. De Almeida, Rafhael J. Lima, Sebastian Semper, Christoph Wagner, Thomas Sasse Ilmenau, Fachgebiet Hochfrequenz- und Mikrowellentechnik

Overall Idea & Motivation
Usable library/API; Provides Fast Matrix Operations; Provide accurate results for engineering and scientific fields; Uses world-widely known IT tools;

State of the Art Numpy and Scipy libraries;
MatLab toolbox of signal processing; SciLab mathematical tools; Octave (for short comparisons);

Chronogram 1/3 Currently Done (23.09.2016):
Understanding FastMat’s objective; Usage of ambient tools; Understanding and Continous Study of Python and LaTeX; Study of Vandermonde Algorithms for best CPU processing; Partial Implementation of Vandermonde (dimension restricted); Implementation of “Power” class;

Some Classes Power: Let “M” be a squared matrix, and “k” a positive integer. “Power” is a class which computes: 𝑦= 𝑀 𝑘 .𝑥 Vandermonde: The Vandermonde matrix is defined by its second column and take the following format: 𝑉= 1 𝑥 0 𝑥 𝑥 1 𝑥 𝑥 2 𝑥 ⋯ 𝑥 0 𝑛 𝑥 1 𝑛 𝑥 2 𝑛 ⋮ ⋱ ⋮ 1 𝑥 𝑛 𝑥 𝑛 2 ⋯ 𝑥 𝑛 𝑛

Chronogram 2/3 Next Steps: 07.10.2016:
Improvement of “Vandermonde” class’ (encompass other dimensions); Implementation of “Cauchy” class; : Optimization of Vandermonde class; Optimization of Cauchy class; 𝑎 𝑖𝑗 = 1 𝑥 𝑖 − 𝑦 𝑗

Chronogram 3/3 Final steps – 09.12.2016:
Production of a paper according to accurate and convenient results; Have the maximum number of classes implemented;

References DRISCOLL, J. R., HEALY, D. M., ROCKMORE, D. N. FAST DISCRETE POLYNOMIAL TRANSFORMS WITH APPLICATIONS TO DATA ANALYSIS FOR DISTANCE TRANSITIVE GRAPHS. Available at: < > Last access on 22nd September 2016. MOORE, S. B., HEALY, D. M., ROCKMORE, D. N. SYMMETRY STABILIZATION FOR FAST DISCRETE MONOMIAL TRANSFORMS AND POLYNOMIAL EVALUATION. Available at: < > Last access on 22nd September 2016.

Thanks for your attention!

Measurement and simulations in Lorentz force eddy current testing
DVT Research Group – Fraunhofer IIS and TU Ilmenau SE/8 - IME José A. S. M. A. Costa, Konstantin Weise, Reinhard Schmidt, Gorges Stephan Ilmenau, Fachgebiet Hochfrequenz- und Mikrowellentechnik

Outline DVT Motivation Overall idea Next Steps Chronogram References
EMT

Motivation Confirm the structural integrity of components.
Identify and prevent failure of socially relevant parts of our life.

Outline Motivation Overall idea Next Steps Chronogram References

Overall Idea LET differs from traditional eddy current testing methods, the ECT, in the way how the eddy currents are induced and how signals are evaluated LET permits the inspection of moving specimens Fig 1 – First LET machine Fig 2 – The new LET machine

Overall Idea Fig 3 – The lab

Next Steps G code and M code
G90 (default mode when starting the system) ZE=0 ZM=0 X=0 (axis) G130 Y=100 (restrict the acceleration of the axis) N10: (sub routine) G01 Y=10 F30000 (move Y to 10 mm with a velocity of 30000mm/min) #TIME 0.2 (wait for 0.2 seconds) G01 Y=1100 F (move Y to 1100 mm with a velocity of mm/min) $GOTO N10 (go to sub routine) M30 (program end) Fig 3 – New LET machine

Chronogram Until October: Trainning and studying
October, November and December: Setup the machine, programming for the measurements, executing the measurements and also studying

References WEISE, K. Advanced Modeling in Lorentz Force Eddy Current Testing. Ilmenau, Dissertation.Technischen Universität Ilmenau. STEPHAN, G. Photos. September Message to:

Control for a Double-Arc Positioner for Bi-static RCS Measurements
EMS Research Group – Fraunhofer IIS and TU Ilmenau Wireless Distribution Systems / Digital Broadcasting SE/3 - IME Alexandre Buscher, Hugo Oliveira, Gerd Sommerkorn, Matthias Röding Ilmenau, Fachgebiet Hochfrequenz- und Mikrowellentechnik

Outline DVT Motivation Overview Proposed Set-up Next Steps
Time Schedule EMT

Motivation http://www.digitaltrends.comcool-techflock-drone-safety

Motivation Obtainment small objects full RCS profile
Favour drone’s identification Support Public Security Organisms decisions Research and academical purposes

Time Schedule EMT

Overview EMITTER Project sketch: DUT RECEIVER

Overview Project sketch:

Time Schedule EMT

Proposed Set-up

Proposed Set-up http://www.ime.eb.br NUC BeagleBone Black Raspberry PI
NUC BeagleBone Black Raspberry PI Arduino Model NUC5i5MYHE Rev A5 3 Model B DUE Size 4"x4''x2'' 3.4"x2.1" 3.37"x2.1" 3.99''x2.1 Processor Intel Core i5 ARM Cortex-A8 ARM11 AT91SAM3X8E Clock Speed 2300 MHz 700 MHz 1200 MHz 84 MHz Flash 32 GB ¹ 4 GB + Micro SD 4 GB SD Card ³ 512 KB RAM 1 GB ² 256 MB 1 GB 96 KB CAN Interface Cost € 66.54 € 41.60 € 19.97 € Additional costs 14.99 ¹ € 2 84.00 € Can Cape 3.50 € ³ 13.00 € Can Shield Total: € € 45.10 € 53.16 €

Proposed Set-up

Outline Motivation Next Steps Proposed Set-up Next steps Time Schedule

Next Steps Implementation of a functional SOAP interface for the servomotor controller, taking advantage of FORTE’s position controller experience; Upgrade to REST; Calibration of logical inputs with the references (when assembled); Addition of security routines and physical emergency stops; Development of a GUI.

Outline Motivation Overview Proposed Set-up Next steps Time Schedule

Time Schedule Data Achievement 27 Out
Implementation of functional REST Interface 11 Nov Calibration of logical interface with the real positions 25 Nov Implementation of safety routines and physical emergency stops 15 Dez Implementation of GUI *Accompanying the assembly of the equipment

THANK YOU EMS Research Group – Fraunhofer IIS and TU Ilmenau Wireless Distribution Systems / Digital Broadcasting SE/3 - IME Alexandre Buscher, Hugo Oliveira, Gerd Sommerkorn, Matthias Röding Ilmenau, Fachgebiet Hochfrequenz- und Mikrowellentechnik

Userspace Networking Framework Comparison for Packet Capture and Transmission
SE/8 - IME Bruno Worm, Mario Lorenz Ilmenau,

Outline Motivation Objectives Frameworks Progress Next Steps Schedule
References EMT

Motivation Standard kernel based capture techniques aren’t suited for achieving line rate capture on high-performance interfaces (e.g. 10Gbps ethernet), since copying packages from kernel to userspace results into high overhead. In order to avoid it, several methods for accessing the NIC directly from userspace have been proposed in the last years. Our goal is to evaluate, from a set of possible aproaches, the one that fits us best and develop a capture/playback application. EMT

Motivation Motivation
Available at EMT

References EMT

Objectives Tasks: Research available userspace networking approaches, making a theorical comparison of them. Develop capture applications with the chosen frameworks and compare them with benchmarks. Develop applications for playing back into the interfaces the captured packages. EMT

References EMT

Frameworks PF_RING PF_RING ZC (Zero Copy) Netmap DPDK
Solarflare OpenOnload Myricom Sniffer10G EMT

Frameworks [*] All NICs supported without Zero Copy features Framework
License NIC’s OS PF_RING Open All Linux PF_RING ZC Proprietary Intel/All* Netmap FreeBSD, Linux DPDK Intel OpenOnload Solarflare Sniffer10G Myricom FreeBSD, Linus, Windows [*] All NICs supported without Zero Copy features

References EMT

Progress Bibliographic review of UIO frameworks and study of the framework’s API Development of raw package capture applications using PF_RING, PF_RING ZC and Netmap. EMT

References EMT

Next Steps Refine the package capture applications for PF_RING ZC and Netmap, including multi-threads scenarios for polling packages Develop capture applications for DPDK Creating benchmark scenarios at FORTE server Develop playback application and benchmark scenario for the framework with the best results Documentation for the developed applications Final report EMT

References EMT

Schedule October 7th Development of package capture applications
Date Activity October 7th Development of package capture applications October 14th Benchmarks for the package capture applications October 21th Result’s analysis and adjustments for capture applications November 18th Development of package playback applications November 25th Benchmarks for the package playback applications December 9th Documentation and final report EMT

References EMT

References L. Rizzo. Netmap webpage. Available at ntop. PF_RING webpage. Available at ntop. PF_RING ZC webpage. Available at DPDK webpage. Available at Solarflare. OpenOnload webpage. Available at Myricom. Sniffer10G details page. Available at L. Rizzo.Revisiting Network I/O APIs: The netmap Framework T. Barbette, C. Soldani, L. Mathy.“Fast Userspace Packet Processing” EMT

THANK YOU Ilmenau, 23.09.2016 www.tu-ilmenau.de/hmt SE/8- IME
Bruno Worm, Mario Lorenz Ilmenau,

Smart Grids – Power Quality in Low Voltage Grids
EMS Research Group – Fraunhofer IIS and TU Ilmenau Wireless Distribution Systems / Digital Broadcasting SE/3 - IME Hugo Oliveira, Thomas Hühn Ilmenau, Fachgebiet Hochfrequenz- und Mikrowellentechnik

Outline DVT Motivation Overview Achievements Next Steps Time Schedule
Bibliography EMT

Motivation 2 1 3 [1] [2] [3]

Motivation Small energy producer management Power quality analysis
Optimize energy distribution Ensure grid security Economical purposes

Bibliography EMT

Overview Production is adjusted to demand
Production is done when it’s possible Control production/distribution since it can cause damages to the grid Grid wasn’t designed to support bi-direcional flow Avoid fluctuations on frequency and voltage (Un)Plug the small producer of the grid

Overview Known Final Goal Grid Topology Data: - Voltage - Harmonics
- Frequency Data Processing Control System that manage the grid and the influence of small energy producer

Grid Behavior Understanding
Overview RMS Voltage First 5 Harmonics Frequency Grid Behavior Understanding Data Processing

Bibliography EMT

Achievements Bibliografic review Identify grid imperfections
Grid disorders Causes Correlate those imperfections with the parameters

Achievements Grid disorders Frequency Components Harmonics / Frequency
Voltage sag Voltage swell Undervoltage Overvoltage Oscillatory transients Harmonic Distorcion RMS Voltage RMS Voltage Frequency Components Harmonics / Frequency

Achievements Grid disorders Causes Remote systems faults
Motor starting or load variations Load/capacitor Switching Nonlinear loads or resonance system

Outline Motivation Next Steps Proposed Model Next steps Time Schedule
Bibliography

Next Steps Access data Start to process the data Start to correlate the data with the grid behavior Understand grid behavior Correlate them to disorders or induvidual production Find patterns that allow recognize individual producers Propose model Submit Paper Propose control algorithm

Outline Motivation Overview Proposed Model Next steps Time Schedule
Bibliography

Time Schedule Data Achievement 3 Out Acces/start to process data
Understand grid behavior 19 Nov Find patterns and correlate the data to disorders or individual producer 5 Dez Submit paper * From 5/12 until the end: develop control algorithm

Outline Motivation Overview Proposed Model Next steps Time Schedule
Bibliography

Bibliography [1] G. Bucci, E. Fiorucci and C. Landi “Digital Measurement Station for Power Quality Analysis in Distributed Environments” Vol. 52, IEEE, February, [2] P. K. Bash, B. K. Panigrahi and G. Panda “Power Quality Analysis Using S-Transform” Vol. 18, IEEE, April, [3] L. N. Huyhn “Structuring the ICT evaluation in the low-voltage grid” Technical University of Berlin, Berlin. [4] S. Bolognani, N. Bof, D. Michelotti, R. Muraro and L. Schenato “Identification of power distribution network topology via voltage correlation analysis” 52nd IEEE, December, [5] A. Woyte, V. V. Thong, R. Belmans and J. Nijs “Voltage Fluctuations on Distribution Level Introduced by Photovoltaic Systems” Vol. 21, March, 2006.

THANK YOU EMS Research Group – Fraunhofer IIS and TU Ilmenau Wireless Distribution Systems / Digital Broadcasting SE/3 - IME Hugo Oliveira, Thomas Hühn Ilmenau, Fachgebiet Hochfrequenz- und Mikrowellentechnik

Delay Estimation Using Antennas Array in GNSS Systems
EMS Research Group – Fraunhofer IIS and TU Ilmenau Wireless Distribution Systems / Digital Broadcasting LASP – UnB Laboratory of Array Signal Processing SE/3 - IME Alexandre Serio Buscher, Mateus Zanatta, Caio Garcez, João Paulo C. L. Da Costa, Markus Landmann, Christopher Schirmer Ilmenau, Fachgebiet Hochfrequenz- und Mikrowellentechnik

Outline DVT Motivation State of the art Proposed work Next Steps
Chronogram EMT

Motivation SISO Model s η - PRN Code; - Navigation Data - DoA (θ)
- Doppler Error - Code Phase - SNR - PRN Code - Navigation Data 𝜃 x

Motivation 𝒙=𝒔+𝜼 SISO Model s η - PRN Code; - Navigation Data
- DoA (θ) - Doppler Error - Code Phase - SNR - PRN Code - Navigation Data 𝒙=𝒔+𝜼 𝜃 x

Motivation SISO Model - PRN Code; - Navigation Data - DoA ( 𝜃 𝑖,𝑙,𝑘 )
- Doppler Error - Code Phase - SNR - SIR - Delay NLOS LOS 𝜃 𝑖 NLOS 𝜃 𝑖 𝜃 𝑖 𝜃 𝑖 NLOS

Motivation - 𝑘 PRN Codes; - 𝑘 Navigation Data - Multipath components
- 𝜃 𝑙,𝑘 DoA - 𝑒 𝑙,𝑘 Doppler Errors - 𝑝 𝑙,𝑘 Code Phases - 𝜏 𝑙,𝑘 Delays - 𝑘 SNR - 𝐿 𝑘 SIR Motivation η S X M antennas

Motivation 𝑿=𝑨𝑺+𝜼 - 𝑘 PRN Codes; - 𝑘 Navigation Data
- Multipath components - 𝜃 𝑙,𝑘 DoA - 𝑒 𝑙,𝑘 Doppler Errors - 𝑝 𝑙,𝑘 Code Phases - 𝜏 𝑙,𝑘 Delays - 𝑘 SNR - 𝐿 𝑘 SIR Motivation η S Multiuser SIMO Model 𝑿=𝑨𝑺+𝜼 X A – steering matrix Based on arrays characteristics M antennas

Motivation 𝑿=𝑨𝑺+𝜼 Receiver - 𝑘 PRN Codes; - 𝑘 Navigation Data
- Multipath components - 𝜃 𝑙,𝑘 DoA - 𝑒 𝑙,𝑘 Doppler Errors - 𝑝 𝑙,𝑘 Code Phases - 𝜏 𝑙,𝑘 Delays - 𝑘 SNR - 𝐿 𝑘 SIR Estimation Decodification Processing

Chronogram EMT

State of the art GALANT – Galileo Antenna – DLR [1]
Combined vector tracking loops and array processing* *STAP – Space-time adaptive processing; *SFAP – Space-frequency adaptive processing; Beamforming techniques; [1]

State of the art GALANT – Galileo Antenna – DLR [1] STAP SFAP X 𝑿 𝑷𝒊𝒏𝒗
Power inversion MLE - Low compl. - Eliminates high energy, low correlated interference signals 𝑾 𝑷𝒊𝒏𝒗

2) Beamforming – Eigenbeamforming or MMSE 2.1 Eigenbeamforming – blind adaptive method a) Eigendecomposition of array post-correlation spatial covariance 𝑹 𝑝𝑜𝑠𝑡 b) 𝒘 𝐵𝐹 beam forming weight array vector set with 𝒖 1 eigenvector corresponding to the largest eigenvalue λ 1 .  Don’t need locking techniques 2.2 MMSE beamforming a) 𝒘 𝐵𝐹 = arg 𝑚𝑖𝑛 𝐸 𝒘 𝐵𝐹 𝐻 𝒔 𝑐𝑜𝑟𝑟 −𝑑 2  Phase lock needed 3) Robust tracking – VDFLL Architecture  Extended error state Kalman filter

3) Robust tracking – VDFLL Architecture  Extended error state Kalman filter

Chronogram EMT

Proposed work GPS Signal Simulator - Full parameters control; - Confrontation of processed data; - Sounding of models capabilities and limitations; GNSS AA-SDR - Book’s code AASP upgrade [2], [3]; - Confrontation of processed data with generated ones; - Incorporation of RFI mitigation techniques; 1) PRN (Gold Code); 2) DoA 3) Code Phase; 4) Doppler Error (desirable); 5) SNR; 6) Number of NLOS componentes; 7) SIR (of NLOS components); 8) Delay estimation; 9) Channel Noise addition;

RFI Mitigation Techniques
Proposed work RFI Mitigation Techniques ESPRIT; FBA; SPS; Multiuser SIMO Model Multiuser SIMO Model GPS Signal Generator SISO Model AAP Techniques EADF Testbed

Experimental Data Collection
Proposed work AAP Techniques EADF 3D Array Beam Pattern Experimental Data Collection

Experimental Data Collection
Proposed work AAP Techniques EADF Effective Aperture Distribution Function 3D Array Beam Pattern EADF Storage Efficient representation of the polarimentric antenna response High data compression – reduced sample number needed Independent of antenna geometry – real description DFT Frequency domain information Experimental Data Collection

Chronogram EMT

Next Steps Finish satellite signal generator suitable to book’s code, according to current work and validate it; Upgrade code for Antenna Array processing. Upgrade code with RFI mitigation techniques;

Chronogram EMT

Chronogram Date Achievment 07 Out Signal Simulator 14 Out
ESPRIT processing SPS processing FBA processing 21 Out EADF processing 13 Nov 1st revision of article 20 Nov WSA 2017 paper submission

Bibliography [1] M. Cuntz, A. Konovaltsev and M. Meurer
“Concepts, Development, and Validation of Multiantenna GNSS Receivers for Resilient Navigation,” 14 p., IEEE, May 2016. [2] Kai Borre et al. “A software-defined GPS and Galileo Receiver – Applied and Numerical Harmonic Analysis,” 175 p., Birkhäuser, Boston, 2007. [3] Darius Plaušinaitis “Matlab GNSS SDR Updates,” - March Accessed Sep 13, 2016. [4] M. Landmann and G. Del Galdo “Efficient Antenna Description for MIMO Channel Modelling and Estimation” Accessed Aug 21, 2016. [5] E. C. de C. Loureiro “Estimação de atrasos e direção de chegada em receptores GNSS baseados em arranjos de antenas,” Universidade de Brasília, Brasília-DF, 2015.

THANK YOU EMS Research Group – Fraunhofer IIS and TU Ilmenau Wireless Distribution Systems / Digital Broadcasting LASP – UnB Laboratory of Array Signal Processing SE/3 - IME Alexandre Serio Buscher, Mateus Zanatta, Caio Garcez, João Paulo C. L. Da Costa, Markus Landmann, Christopher Schirmer Ilmenau, Fachgebiet Hochfrequenz- und Mikrowellentechnik

Development of 3D GNSS full polarimetric and antenna array based channel models for GNSS receivers
EMS Research Group – Fraunhofer IIS and TU Ilmenau Wireless Distribution Systems / Digital Broadcasting LASP – UnB Laboratory of Array Signal Processing SE/3 - IME Romulo Braga, Daniel Valle, João Paulo C. L. Da Costa, Markus Landmann, Christopher Schirmer Ilmenau, Fachgebiet Hochfrequenz- und Mikrowellentechnik

Outline DVT Motivation State of the art Next Steps Proposed Model
Chronogram Bibliography EMT

Motivation Military applications
Localization in real-time fishing ships to guarantee the sustainable management of fishing resources Trucks tracking in real-time to determine status of the load Precision farming applications

Outline Motivation State of the art Next Steps Proposed Model
Chronogram Bibliography

State of the art A polarimetric line-of-sight channel model for MIMO satellite communications – Model 1 A rural channel model for Satellite Navigation Applications – Model 2 Characterisation of the Sattelite-to-indoor propagation channel – Model 3

State of the art A polarimetric line-of-sight channel model for MIMO satellite communications – Model 1 Scenario: A satellite transmitting using a triad antenna (three half-wavelength dipoles oriented in the , , and axes) to a terminal that also has a triad antenna (three half-wavelength dipoles oriented in the , , and axes, which is , , and relative to the ground). Parameters: - azimuth at the satellite to the terminal - elevation at the satellite to the terminal - angle between the satellite and the terminal considering the center of the earth - Ricean factor - Power - dipole gain as a function of the azimuth and elevation to the antenna orientation - The radio wavelength - The separation of the satellite ( ) and the terminal ( )

State of the art Schematic
Figure 1: Satellite geometry

State of the art Schematic
Figure 2: Satellite Field of View

State of the art A rural channel model for satellite navigation applications – Model 2 Scenario: Land Mobile System (LMS) in a rural setting. Models the attenuation and scattering effect for a signal impinging on a vehicle-mounted receiver passing through a road in an “alley” formed by trees on each side. Parameters: - Attenuation of LOS from trasmitter due to tree canopies - Specific attenuation - Length - Volume - Antenna gain - Delay - Scatterers’ amplitude - Component weight of the scattered components scattering

State of the art Characterisation of the Sattelite-to-indoor propagation channel – Model 3 Scenario: A satellite transmits a signal which a receiver in an indoor environment receives said signal. Propagation is modeled as being affected by high entry losses and the creation of echoes from reflection and diffraction in the environment. Echoes are modeled as occurring in clusters. Parameters: - Entry loss - Elevation - No. of [echo] clusters - Power density - Average delay - Amplitude of each echo - Angle of arrival

State of the art Comparative table of models 1 X 2 3 Model
Angle of arrival Polarization Time delay Amplitude Multipath Distance 1 X 2 3

Next Steps Propose models with more realistic structure
Generate the parameters of proposed models Upgrade model with dense multipath components, full polarimetric and tensors Implement and test the proposed models Analyze the results Submit a paper to a conference

Proposed Model Polarimetric LOS and clustered NLOS Channel Model
Polarimetric MIMO system: Where is a vector of received signals, represents a complex channel matrix, is a symbol vector, , and is AWGN. Complex fading channel as composition of average LOS component and variable scattered NLOS component Where is the Ricean -factor

Proposed Model Polarimetric LOS and clustered NLOS Channel Mode Where:

Proposed Model Polarimetric LOS and clustered NLOS Channel Model
For the NLOS component, we can replace the satellite transmitter gain with a complex gain and using the extended Saleh-Valenzuela where the scattered NLOS component appears in ``clusters'‘ In is the cluster number and is the NLOS component within cluster . and are the direction of propagation of the scattered component.

Proposed Model Polarimetric LOS and clustered NLOS Channel Model 1 X 2
Angle of arrival Polarization Time delay Amplitude Multipath Distance 1 X 2 3 Proposed

Chronogram Until September, 23: bibliographic review of state-of-art channel models, propose model with more realistic structure Until September, 30: bibliographic review of generation of parameters. Generate the parameters of proposed model Until October, 14: implement proposed model, test and analyze results. Until October, 21: adjust the model failures, implement, test and analyze results. Until November, 18: Write two page paper to submit for WSA 2016 Until December, 09: Write four page paper to be submitted to a conference

Bibliography N. Lawrence, L. M. Davis and D. Haley, “A polarimetric line-of-sight channel model for MIMO satellite communications”. Communications Theory Workshop (AusCTW), 2013 Australian, Adelaide, SA, 2013, pp F. Perez-Fontan et al., “Characterisation of the Satellite-to-Indoor Propagation Channel” th Advanced Satellite Mobile Systems, Bologna, 2008, pp T. Jost, W. Wang, U. C. Fiebig and F. Pérez-Fontán “A Wideband Satellite-to-Indoor Channel Model for Navigation Applications”, IEEE Transactions on Antennas and Propagation, vol. 62, no. 10, pp , Oct

Bibliography R. Heddergott and P. E. Leuthold, “An extension of stochastic radio channel modeling considering propagation environments with clustered multipath components”, IEEE Transactions on Antennas and Propagation, vol. 51, no. 8, pp , Aug C. A. Hofmann, R. T. Schwarz and A. Knopp, “Measurements and Modeling of the UHF Satellite Channel for Animal Tracking Systems”, IEEE ICC 2015 SAC - Satellite and Space Communications}, 2015. C. A. Hofmann, R. T. Schwarz and A. Knopp, “Measurement and modeling of the UHF satellite channel for animal tracking systems”, 2015 IEEE International Conference on Communications (ICC)}, London, 2015, pp

THANK YOU EMS Research Group – Fraunhofer IIS and TU Ilmenau Wireless Distribution Systems / Digital Broadcasting LASP – UnB Laboratory of Array Signal Processing SE/3 - IME Romulo Braga, Daniel Valle, João Paulo C. L. Da Costa, Markus Landmann, Christopher Schirmer Ilmenau, Fachgebiet Hochfrequenz- und Mikrowellentechnik

Implementation of Algorithms for Fast Linear Transformations

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