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D1 - 18/03/2004
A tapped Delay Line Model of Multipath Channel for CDMA
Systems March 15th-16th
COST 289 Meeting
Stefan Wendt
France Télécom R&DD2 - 18/03/2004
Outline
s Introduction
s Existing methods to obtain an equivalent model
s Equivalent channel model
s Advantages - Limitations
s Conclusion
France Télécom R&DD3 - 18/03/2004
Introduction
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Need of an equivalent channel model• Real channel models (Pedestrian, Indoor…) have paths delays that are
not multiple of the chip period Tc
• Simulations, therefore, need several samples per chip
• Aim: Equivalent channel
• Equivalence criterium:
signal after the channel or at the output of the Rake receiver
• Avantages: 1 sample per chip and one can discard the filters’ influence
)τ()('); τ(' cn
n nTthth −= ∑ δ
Channel Coding Spreading
Impulse forming
filter
Multipath Channel
RX
filter
De-spreading/
Correlations
Channel decoding
)ττ()(); τ(1
0i
L
ii thth −= ∑
−
=
δ
France Télécom R&DD5 - 18/03/2004
Existing methods
France Télécom R&DD6 - 18/03/2004
Former works
• J. G. Proakis [1]: equivalence at the channel output
• Filter u(t) is band limited
• Fechtel [2]: equivalence at the channel output• Projection to basis {u(t-nTc)}n :
• Mutually dependant paths
• The number of coefficients (paths) is large
)( )('τ);(':Channel
)τsinc()()(' :Paths1
0
ci
i
c
iL
nni
iTthth
iT
thth
−=
−=
∑
∑∞
−∞=
−
=
τδ
)( )('τ);(':Channel
)( )()(' :Paths1
0
ci
i
cn
L
nni
iTthth
iTgthth
−=
−=
∑
∑∞
−∞=
−
=
τδ
τ
France Télécom R&DD7 - 18/03/2004
Equivalent channel model
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Chip equivalent channel (1)• Assumptions : channel perfectly known, perfect spreading, WCDMA
• Output of the Rake receiver:
• Characteristic function of the energy
• G: Autocorrelation matrix of the filters, C: covariance matrix of the channel taps• D is the diagonal matrix of CG
kk
kThkThwhere
L
i
L
jjisjsisk bsgkThkThEs
tsLskkkk
+
−=
−==
−
=
−
=∑∑ )()()( ˆ
)](),...,([
1
0
1
0
*
10*
444444 3444444 21hGhhγ
ττ
)det()det() DIGCI jν1
jν1(ν
LLγk −=−=ψ
France Télécom R&DD9 - 18/03/2004
Chip equivalent channel (2)• Definition of the equivalent channel
• Average powers of the paths: values of the diagonal of D
• Same performance for an uncoded system
• Placing the paths at multiples of Tc there’s no influence of the filters.
• Let’s consider γk’=h’
k*.h’
k with h’k a vector with L Gaussian processes of the
diagonal matrix D
• We proved the equality of the two processes γk and γk’
same performance after decoding channel is equivalent
{ } 1L0ii−='γ
')'()( kk0
skkk
0
sk dpNE 'QdpN
E QBER γγγγγγ∫∫
=
=
),...,( et ),...,(où
pp k
1k101k10
==
=∀
−− '','',
)'()(
γγγγγγγγ
γγ
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Simulation results• 12.2 kbps Service UMTS mode FDD: Spreading factor 64, convolutional code 1/3
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Simulation results• 12.2 kbps Service UMTS mode FDD: Spreading factor 64, convolutional code 1/3
France Télécom R&DD12 - 18/03/2004
Comparisonof different strategies
when a path is not multiple of Tc
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Comparison
Tc
A
tTc/2
B
Tct
Tc/2
A+nB(1-n)B
Performance after Rake changes
Delay spread changes
Performance after Rake changes
Delay spread changes
Energy
tTcTc/2
AB
TcTc/2t
A’B’
Performance after Rake is the same
Delay spread changes
France Télécom R&DD14 - 18/03/2004
Tc
A
tTc/2
B+C
Performance after Rake changes
Delay spread changesComparison
Energy
tTcTc/2
AB C
Performance after Rake changes
Delay spread changes
tTcTc/2
A+nB(1-n)B+(1-m)C+mC
Performance after Rake is the same Delay spread changes but third path can be neglected
TcTc/2 2Tct
A’B’ C’
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Advantages – Limitationsof the proposed
equivalent channel
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Annotations
• Avantages• The paths are mutually independant, i.e uncorrelated
• Reduction of the number of paths is possible
• Comparison between channel models
• Limitations• Inter-Symbol-Interference and Inter-Path-Interference(residual correlation) are
different
310-31.88
290-26.14
170-17.99
110-10.0
50-2.99
00.0
τi (ns)(dB)
ITU Indoor-A
1300-81.9
1040-58.48
790-37.67
520-25.74
260-12.54
00.0
τi (ns)(dB)
Equivalent channel
410-22.8
190-19.2
110-9.7
00.0
τi (ns)(dB)
ITU Pedestrian-A
790-33.88
520-22.7
260-12.67
00.0
τi (ns)(dB)
Equivalent channel
iγ iγiγiγ
France Télécom R&DD17 - 18/03/2004
Conclusions
• Chip equivalent model for WCDMA systems
• mutually independant paths
• Reduction of the number of paths possible
• ISI and IPI is neglected (true for spreading factor > 16)
• order and exact place (at which multiple of Tc) of the paths are to be defined according to
needs
France Télécom R&DD18 - 18/03/2004
References
[1] “Digital Communications”, J.G. Proakis, McGraw-Hill, 1985.
[2] “A novel approach to modeling an efficient simulation of frequency selective
fading radio channels”, S. A. Fechtel, Proc. IEEE JSAC, vol.11, issue 3, April
1993.
[3] “Tapped delay line model of linear randomly time-variant WSSUS channel”, J.
Sykora, IEEE Electronic letters, Vol. 36, No. 19, Sept. 2000.
[4] “An Equivalent Multi-Path Channel Chip Model for CDMA Systems”, A. Saadani,
S. Wendt, P. Gelpi and D. Duponteil, accepted at ISCCSP 2004, Hammamet.
