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Radio Propagation in Hallways and Streets for UHF Communications Dana Porrat Advisor: Professor Donald Cox

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Outline Propagation in cellular systems The over-moded waveguide model Comparison to measurements Applications of the model

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Propagation Models Ray tracing – requires a lot of detail and computation (Bell Labs, Bertoni, Rappaport) Power laws – give a very general picture, weakly linked to geometry Usage: Power levels – Coverage and Interference Other properties of link

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Street canyon effects in cities have been measured many times Guiding by indoor hallways – shown by measurements Guided Radiation

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Motivation Insight into the propagation mechanism in hallways and streets Average predictions based on geometry, with reasonable detail and low complexity

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Outline The multi-moded waveguide model Comparison to measurements Applications of the model

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Key Features The wavelength at 1 GHz is 30 cm – much smaller than hallways and streets Multi-moded waveguide The walls are not smooth Mode coupling

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The Smooth Waveguide x z d -d 1 st 2 nd 8 th

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The TEM mode Field components: H y and E x Present for 2D smooth waveguide Not present for 3D rough waveguide

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The Rough Waveguide x=f(z) x=h(z) D s Correlation Length Perturbation Variance x z d -d Dielectric Waveguide: D. Marcuse, 1970’s

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Expansion in terms of the waveguide modes are the amplitudes of the modes Rough Walls

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The wave equation for the smooth guide: For the rough guide: After manipulation: The Perturbation Approach

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Fn(z)

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The Perturbation Solution hold the spectrum of f(z), h(z)

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The Coupled Modes The coupling coefficients among modes:

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Air filled waveguide, homogeneous material, rough boundaries Two dimensional model Small roughness, compared to Coupling coefficients, has a Gaussian correlation with s, D Coupling between TE-TM modes behaves as single polarization coupling Assumptions

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Coupled Power Equations Loss of the nth mode Coupling from the nth mode into other modes Coupling from other modes into the nth mode

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Power Coupling Coefficients The coupling coefficients:

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Solution of the Coupled Eq Solution:

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The Steady State Solution The steady state distribution has most of power in lowest order TE mode Mode (n) P [dB]

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Development along hallway / street Initial conditions: Small antenna Junction n zP n Dynamic Solutions

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Junctions Low order modes of the main hallway couple into high order modes of the side hallway Side Hallway Main Hallway

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Floor and Ceiling Full 3D model is very complicated Simplification: smooth perfectly conducting floor and ceiling Vertical and horizontal are independent

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Indoor Measurements

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The Packard Basement Power [dB] x [m] y [m] Tx 1 2 3 4 5 6

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Hallway 1 Power Simulation parameters: = 3, = 0.085 S/m s 2 = 0.2 m 2, D = 2 m TE initial conditions Power [dB] y [m]

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The Packard Basement Power [dB] x [m] y [m] Tx 1 2 3 4 5 6

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Power Across Hallway 1 x [m] Power [dB] 4.4 m 12 m

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The Packard Basement Power [dB] x [m] y [m] Tx 1 2 3 4 5 6

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Hallway 6 Power Simulation parameters: = 3, = 0.085 S/m s 2 = 0.2 m 2, D = 2 m Uniform initial conditions Power [dB] y [m]

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The Packard Basement Power [dB] x [m] y [m] Tx 1 2 3 4 5 6

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Hallway 6 and Rooms Simulation parameters: = 3, = 0.085 S/m s 2 = 0.2 m 2, D = 2 m Uniform initial conditions Power [dB] y [m]

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The Packard Basement Power [dB] x [m] y [m] Tx 1 2 3 4 5 6

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Hallway 5 and Rooms Power [dB] x [m] Simulation parameters: = 3, = 0.085 S/m s 2 = 0.2 m 2, D = 2 m Uniform initial conditions

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Ray Tracing Power [dB] x [m] y [m]

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Ray Tracing – Hallway 3 Simulation parameters: = 3, = 0.085 S/m, s 2 = 0.2 m 2, D = 2 m, Uniform initial conditions Power [dB] y [m]

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Ottawa Measurements J. Whitteker, 1987

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Queen St Measurements Distance along Street [m] Power [dB] Simulation parameters: = 2.6, = 0.27 S/m s 2 = 0.3 m 2, D = 30 m TE initial conditions

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Ottawa Measurements J. Whitteker, 1987

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Metcalf St Measurements Distance along Street [m] Power [dB] Simulation parameters: = 2.4, = 0.26 S/m, s 2 = 0.2 m 2, D = 10 m, Uniform initial conditions

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Ottawa Measurements J. Whitteker, 1987

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Wellington St Measurements Distance along Street [m] Power [dB] Simulation parameters: = 2.9, = 0.26 S/m, s 2 = 0.2 m 2, D = 10 m, Uniform initial conditions

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Applications of the Model Channel Capacity Delay Spread

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Channel Capacity The channel becomes ‘narrow’ at large distances, all the paths become similar Distance along Hallway [m] Capacity [bps/Hz] Max: 84 bps/Hz 12 x 15 Antennas SNR = 20 dB P. Kyritsi, 2001

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400 m The Delay Profile The group velocity v = c cos n k n z [ sec] Power [dB]

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Contributions A new waveguide model for hallways and streets with reasonable geometric input. This low complexity model agrees with indoor and outdoor measurements and provides insight to observed phenomena Demonstration of guiding effects in indoor hallways A ‘Keyhole’ effect which limits capacity in long hallways and streets Insight into delay profiles from the multi- moded waveguide model

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Publications D. Porrat and D. C. Cox, UHF Propagation in Indoor Hallways. Submitted to the IEEE Transactions on Wireless Communications, June 2002 D. Porrat, P. Kyritsi and D. C. Cox, MIMO Capacity in Hallways and Adjacent Rooms. IEEE Globecom, November 17-21, 2002 D. Porrat and D. C. Cox, Microcell Coverage and Delay Spread Prediction Using Waveguide Theory. URSI General Assembly August 17-24 2002 D. Porrat and D. C. Cox, Delay Spread in Microcells Analysed with Waveguide Theory. IEEE 55th Vehicular Technology Conference 2002 Spring, May 6-9 D. Porrat and D. C. Cox, A Waveguide Model for UHF Propagation in Streets. The 11th Virginia Tech/MPRG Symposium on Wireless Personal Communications, June 6-8, 2001

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Extra Slides

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The Over - Moded Waveguide A single long waveguide A junction of waveguides

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