Spatial Channel Modeling Based onWave-field Representation �

Pavel Loskot

University of Alberta, Edmonton, Alberta, Canada

June 14, 2002

�� Presented in Finnish Wireless Communications Workshop, 2001, Tampere, Finland

Outline

How to apply electromagnetic (EM) theory to channel modeling incommunication 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 channelmodels

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)

Spatial Channel Models, Examples

1. [Hedddergott,Bernhar d,Fleur y, PIMRC’97]time-invariant channel impulse response (CIR) for Rx antennaat location with response �� ; models delay, direction andpolarization

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2. [Blanz,J ung, TrCom’98]time-variant CIR for Tx antenna response � convolved withdirectional CIR distribution

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Spatial Channel Models, Examples (cont.)

3. [Fleur y, TrIT’00]relates input signal and received signal at location

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4. [Zwic k,Fisc her,Didascalou,Wiebec k, JSAC’00]time-variant CIR through spatial impulse response � ��

and Rx, Tx antenna responses �� �� , � � , respectively

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Spatial Channel Models, Examples (cont.)

5. [Steinbauer ,Molisc h,Bonek, Ant. Prop. Mag.’01]radio channel CIR (antenna inclusive) with double directional CIR

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propagation channel CIR

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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 ?

System Model

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Antenna Representation

Electr omagnetic wavea function of time and space � , i.e., a time-varying field

fields are invariant w.r.t. coordinate system

scalar or vector fields; given ( ) we know ( )

Transmit Antennaradiating (source) field

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where � is carrier field (hence, amplitude modulator)

Receive Antennaobservable field

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�� ��where �� is time-invariant infinite bandwidth antenna response

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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reactive and radiating field with very complex structureFar-field

spherical wave

Maxwell Theor y

every medium: permitivity ² , permeability ² conductivity ; e.g.,raindrops, trees, walls (dielectric material), cars (conductive material)

Homog eneous mediumpropagation along straight lines (at least locally)

Disper sive medium

Isotr opicenergy flow along the direction of propagation ( , directionindependent)

Linear, and are independent of applied field

Maxwell equations are linear and superpozition applies

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Plane Waves

monochromatic, time-harmonic plane wave with wave-vector

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good approximation for far-field and sufficiently short wavelengths

Comple x Envelope (Phasor Representation)��º »� ¹ �

where � is carrier frequency, wave-vector �� � , andis direction of propagation

for Doppler frequency ¶� �º »¼ º ½ � ¹ � �º »� ¼ º ½�

Spatial Channel Model

radio channel = mapping from radiating field to observable field

spatial channel model

temporal channel model

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Linear Stoc hastic Model

let the linearity assumption holds and

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spatio-temporal channel impulse response

temporal channel impulse response

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finally

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Linear Geometrical Model

Geometrical Opticshigh 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 impulseresponse

approximation of radiating field by sum of plane-waves

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assume separate channels with attn. � , delay � , shift � � ,

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Combined Geometrical and Stoc hastic Model

[Molisc h, 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 antennasfar scatterers, clusterringwaveguiding and diffraction (keyhole effect)

Channel recipr ocity (uplink/do wnlink)

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

Conc lusio ns

spatial channel modeling based on wave-fields was presented as anattempt to bring EM theory into communication signal processing

it was demonstrated for the case of linear stochastic model and lineargeometrical 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 signaldistribution

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where is 3D-Fourier transform

References

[1] J. J. Blanz and P. Jung, “A flexibly configurable spatial model formobile 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 arraycommunication systems,” IEEE Per. Comm., vol. 5, no. 1, pp. 10–22,Feb. 1998.

[3] B. H. Fleury, “First- and second-order characterization of directiondispersion 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 stochasticspatial channel model based on wave-propagation modeling,” IEEEJ. Select. Areas Commun., vol. 18, no. 1, pp. 6–15, Jan. 2000.

References

[5] Z. Ji, B.-H. Li, H.-X. Wang, H.-Y. Chen, and T. K. Sarkar, “Efficientray-tracing methods for propagation prediction for indoor wirelesscommunications,” IEEE Ant. Prop., vol. 43, no. 2, pp. 41–49, Apr.2001.

[6] A. F. Molisch, J. Laurila, K. Hugl, and E. Bonek, “Smart antennasand mimo systems,” in Proc. VTC, 2002, Tutorial.

[7] A. F. Molisch, “A generic model for mimo wireless propagationchannels,” in Proc. ICC, 2002, vol. 1, pp. 277–282.

[8] M. Steinbauer, A. F. Molisch, and E. Bonek, “The double-directionalradio channel,” IEEE Ant. Prop., vol. 43, no. 4, pp. 51–63, Aug.2001.