A 3D channel modeling framework based on plane wave propagation assumption.

1. Spatial Channel Modeling Based on
Wave-field Representation
Pavel Loskot
University of Alberta, Edmonton, Alberta, Canada
June 14, 2002
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Presented in Finnish Wireless Communications Workshop, 2001, Tampere, Finland

2. Outline
How to apply electromagnetic (EM) theory to channel modeling in
communication signal processing ? i.e., signal wave
Overview of existing spatial channel models (literature)
A new approach to spatial channel modeling is suggested
A necessary EM theory background is discussed
The method illustrated on linear stochastic and geometrical channel
models

3. Why Spatial Channel Models ?
Conventional channel models (COST#207)
field-strength and signal delays only (tap-delay line)
omnidirectional Tx,Rx antennas
For multiple antennas (COST#259)
we may gain (some) access to spatial domain
need for more accurate (directional) channel model
(but backward compatibility with COST#207)
also useful to network planing and deployment
(macrocells, microcells, picocells in some frequency band)

4. Spatial Channel Models, Examples
1. [Hedddergott,Bernhard,Fleury, PIMRC’97]
time-invariant channel impulse response (CIR) for Rx antenna
at location with response
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; models delay, direction and
polarization
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2. [Blanz,Jung, TrCom’98]
time-variant CIR for Tx antenna response
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convolved with
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5. Spatial Channel Models, Examples (cont.)
3. [Fleury, TrIT’00]
relates input signal and received signal at location
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4. [Zwick,Fischer,Didascalou,Wiebeck, JSAC’00]
time-variant CIR through spatial impulse response
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6. Spatial Channel Models, Examples (cont.)
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radio channel CIR (antenna inclusive) with double directional CIR
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7. Representation of Wireless Transmission
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let us assume a global 3D-space, time and frequency coordinates
could be an electromagnetic wave
signal,wave system (channel)
when does or form a channel impulse response ?

8. System Model
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9. Antenna Representation
Electromagnetic wave
a function of time and space
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, i.e., a time-varying field
fields are invariant w.r.t. coordinate system
scalar or vector fields; given ( ) we know ( )
Transmit Antenna
radiating (source) field
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where
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Receive Antenna
observable field
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where
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is time-invariant infinite bandwidth antenna response

10. Wave Propagation
obstacles, atmosphere (rain, fog, smoke), noise and interference
(cosmic, atmospheric, industrial) EM energy absorbed, scattered
indoor, outdoor and deep-space different propagation conditions,
hence channel models with different accuracy (= prediction)
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Near-field
reactive and radiating field with very complex structure
Far-field
spherical wave

11. Maxwell Theory
every medium: permitivity
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, permeability
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conductivity ; e.g.,
raindrops, trees, walls (dielectric material), cars (conductive material)
Homogeneous medium
propagation along straight lines (at least locally)
Dispersive medium
Isotropic
energy flow along the direction of propagation ( , direction
independent)
Linear
, and are independent of applied field
Maxwell equations are linear and superpozition applies
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12. Plane Waves
monochromatic, time-harmonic plane wave with wave-vector
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good approximation for far-field and sufficiently short wavelengths
Complex Envelope (Phasor Representation)
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where
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for Doppler frequency
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13. Spatial Channel Model
radio channel = mapping from radiating field to observable field
spatial channel model
temporal channel model
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14. Linear Stochastic Model
let the linearity assumption holds and
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spatio-temporal channel impulse response
temporal channel impulse response
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15. Linear Geometrical Model
Geometrical Optics
high frequency approximation, diffraction neglected
asymptotic solution of field integrals (Maxwell equations)
approximation of the field by rays (= locally plane waves)
ray tracing asymptotically accure time-invariant channel impulse
response
approximation of radiating field by sum of plane-waves
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assume separate channels with attn.
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16. Combined Geometrical and Stochastic Model
[Molisch, VTC’02, ICC’02]
generic model to study wave propagation in MIMO systems
independent of antenna configuration (polarization)
random scatterers with given distribution
local scatterers around Tx, Rx antennas
far scatterers, clusterring
waveguiding and diffraction (keyhole effect)
Channel reciprocity (uplink/downlink)
direction of arrival and departure (DOA, DOD)
2D model: azimuth, 3D model: azimuth and elevation
delays, mean powers
plus comlex path gains in time-duplex systems

17. Conclusions
spatial channel modeling based on wave-fields was presented as an
attempt to bring EM theory into communication signal processing
it was demonstrated for the case of linear stochastic model and linear
geometrical model where plane-wave propagation is assumed
necessary but not sufficient conditions of radio channel linearity are
– far-field, isotropic and homogeneous medium, no diffraction
– but further investigation is still required
receiving antennas provide us with (some) knowledge on signal
distribution
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where is 3D-Fourier transform

18. References
[1] J. J. Blanz and P. Jung, “A flexibly configurable spatial model for
mobile radio channels,” IEEE Trans. Commun., vol. 46, no. 3, pp.
367–371, Mar. 1998.
[2] R. B. Ertel, P. Cardieri, K. W. Sowebry, T. S. Rappaport, and J. H.
Reed, “Overview of spatial channel models for antenna array
communication systems,” IEEE Per. Comm., vol. 5, no. 1, pp. 10–22,
Feb. 1998.
[3] B. H. Fleury, “First- and second-order characterization of direction
dispersion and space selectivity in the radio channel,” IEEE Trans.
Inform. Th., vol. 46, no. 6, pp. 2027–2044, Sept. 2000.
[4] T. Zwick, C. Fischer, D. Didascalou, and W. Wiesbeck, “A stochastic
spatial channel model based on wave-propagation modeling,” IEEE
J. Select. Areas Commun., vol. 18, no. 1, pp. 6–15, Jan. 2000.

19. References
[5] Z. Ji, B.-H. Li, H.-X. Wang, H.-Y. Chen, and T. K. Sarkar, “Efficient
ray-tracing methods for propagation prediction for indoor wireless
communications,” IEEE Ant. Prop., vol. 43, no. 2, pp. 41–49, Apr.
2001.
[6] A. F. Molisch, J. Laurila, K. Hugl, and E. Bonek, “Smart antennas
and mimo systems,” in Proc. VTC, 2002, Tutorial.
[7] A. F. Molisch, “A generic model for mimo wireless propagation
channels,” in Proc. ICC, 2002, vol. 1, pp. 277–282.
[8] M. Steinbauer, A. F. Molisch, and E. Bonek, “The double-directional
radio channel,” IEEE Ant. Prop., vol. 43, no. 4, pp. 51–63, Aug.
2001.