Radio Propagation in Hallways and Streetsfor UHF Communications
Dana PorratAdvisor: Professor Donald Cox
Outline
• Propagation in cellular systems• The over-moded waveguide model• Comparison to measurements• Applications of the model
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
• Street canyon effects in cities have been measured many times
• Guiding by indoor hallways – shown by measurements
Guided Radiation
Motivation
• Insight into the propagation mechanism in hallways and streets
• Average predictions based on geometry, with reasonable detail and low complexity
Outline
• The multi-moded waveguide model• Comparison to measurements• Applications of the model
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
The Smooth Waveguidex
z
d
-d
1st 2nd
8th
The TEM mode
• Field components: Hy and Ex
• Present for 2D smooth waveguide• Not present for 3D rough
waveguide
The Rough Waveguide
x=f(z)
x=h(z)
D
s
Correlation Length
PerturbationVariance
x
z
d
-d
Dielectric Waveguide: D. Marcuse, 1970’s
Expansion in terms of the waveguide modes
are the amplitudes of the modes
Rough Walls
• The wave equation for the smooth guide:
• For the rough guide:
• After manipulation:
The Perturbation Approach
Fn(z)
The Perturbation Solution
hold the spectrum of f(z), h(z)
The Coupled Modes
The coupling coefficients among modes:
• 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
Coupled Power Equations
Loss of the nth mode Coupling from the nth mode into other modes
Coupling from other modes into the nth mode
Power Coupling Coefficients
The coupling coefficients:
Solution of the Coupled Eq
Solution:
The Steady State Solution
The steady state distribution has most of power in lowest order TE mode
Mode (n)
P [d
B]
• Development along hallway / street
• Initial conditions:• Small antenna • Junction
n
zPn
Dynamic Solutions
Junctions
Low order modes of the main hallway couple into high order modes of the side hallway
Side Hallway
Main Hallway
Floor and Ceiling
• Full 3D model is very complicated• Simplification: smooth perfectly
conducting floor and ceiling• Vertical and horizontal are
independent
Indoor Measurements
The Packard BasementPow
er
[dB
]
x [m]
y
[m]
Tx
1234
5
6
Hallway 1 Power
Simulation parameters: = 3, = 0.085 S/m s2 = 0.2 m2, D = 2 m
TE initial conditions
Pow
er
[dB
]
y [m]
The Packard BasementPow
er
[dB
]
x [m]
y
[m]
Tx
1234
5
6
Power Across Hallway 1
x [m]
Pow
er
[dB
]
4.4 m
12 m
The Packard BasementPow
er
[dB
]
x [m]
y
[m]
Tx
1234
5
6
Hallway 6 Power
Simulation parameters: = 3, = 0.085 S/m s2 = 0.2 m2, D = 2 m
Uniform initial conditions
Pow
er
[dB
]
y [m]
The Packard BasementPow
er
[dB
]
x [m]
y
[m]
Tx
1234
5
6
Hallway 6 and Rooms
Simulation parameters: = 3, = 0.085 S/m s2 = 0.2 m2, D = 2 m
Uniform initial conditions
Pow
er
[dB
]
y [m]
The Packard BasementPow
er
[dB
]
x [m]
y
[m]
Tx
1234
5
6
Hallway 5 and RoomsPow
er
[dB
]
x [m]
Simulation parameters: = 3, = 0.085 S/m s2 = 0.2 m2, D = 2 m
Uniform initial conditions
Ray TracingPow
er
[dB
]
x [m]
y
[m]
Ray Tracing – Hallway 3
Simulation parameters: = 3, = 0.085 S/m, s2 = 0.2 m2, D = 2 m,
Uniform initial conditions
Pow
er
[dB
]
y [m]
Ottawa Measurements
J. Whitteker, 1987
Queen St Measurements
Distance along Street [m]
Pow
er
[dB
]
Simulation parameters: = 2.6, = 0.27 S/m s2 = 0.3 m2, D = 30 m
TE initial conditions
Ottawa Measurements
J. Whitteker, 1987
Metcalf St Measurements
Distance along Street [m]
Pow
er
[dB
]
Simulation parameters: = 2.4, = 0.26 S/m, s2 = 0.2 m2, D = 10 m,
Uniform initial conditions
Ottawa Measurements
J. Whitteker, 1987
Wellington St
Measurements
Distance along Street [m]
Pow
er
[dB
]
Simulation parameters: = 2.9, = 0.26 S/m, s2 = 0.2 m2, D = 10 m,
Uniform initial conditions
Applications of the Model
• Channel Capacity
• Delay Spread
Channel CapacityThe channel becomes ‘narrow’ at large distances, all the paths become similar
Distance along Hallway [m]
Capaci
ty [
bps/
Hz]
Max: 84 bps/Hz12 x 15
Antennas
SNR =20 dB
P. Kyritsi, 2001
400 m
The Delay Profile
The group velocity v = c cosn k
n z
[sec]
Pow
er
[dB
]
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
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
Extra Slides
The Over-Moded Waveguide
• A single long waveguide
• A junction of waveguides