wireless channel modelocw.snu.ac.kr/sites/default/files/note/10340.pdf · 2018. 1. 30. · path...
TRANSCRIPT
![Page 1: Wireless Channel Modelocw.snu.ac.kr/sites/default/files/NOTE/10340.pdf · 2018. 1. 30. · Path loss as a function of distance: − sometimes simple model can captures the essence](https://reader035.vdocuments.mx/reader035/viewer/2022071402/60f2a5427f35f00cd73c1ce4/html5/thumbnails/1.jpg)
Wireless Channel Model
Wha Sook Jeon Mobile Computing and Communication Lab.
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Mobile Computing and Communication Lab. 1
Radio Channel (1)
Signal Fading − large-scale component: Path Loss − medium-scale slow varying component:
Shadowing − small-scale fast varying component:
Multipath fading
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Mobile Computing and Communication Lab. 2
Radio Channel (2)
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Mobile Computing and Communication Lab. 3
LOS Path vs. NLOS Path
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Mobile Computing and Communication Lab. 4
Path Loss & Shadowing
Path Loss − caused by dissipation of the power radiated by the
transmitter − depends on the distance between transmitter and receiver
Shadowing − caused by obstacles between the transmitter and receiver
that absorb power.
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Mobile Computing and Communication Lab. 5
Multipath fading
short-term fluctuation of the received signal caused by multipath propagation
when mobile is moving Fading becomes fast as a mobile moves faster delay-power profile (delay spread)
Average power (dB)
Delay
Narrowband fading
Wideband fading
Rayleigh distribution
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Mobile Computing and Communication Lab. 6
Channel Model
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Mobile Computing and Communication Lab. 7
Simplified Pass Loss Model
Path loss as a function of distance: − sometimes simple model can captures the essence of signal propagation
without resorting to complicated path loss models. − Free-space, two-ray, Hata, COST extension to Hata are all of the same form − K : constant which depends on antenna characteristics and the average channel
attenuation ■ Free space path gain at distance d0 assuming omni-directional antennas ■ Empirical measurements at d0
− d0: reference distance ■ generally valid only at d> d0
■ d0 : 1-10m (indoor), 10-100m (outdoor) − : path loss exponent
■ at higher frequencies tend to be higher and at higher antenna heights tend to be lower
γ
= ddKPP tr
0
γ
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Mobile Computing and Communication Lab. 8
Empirical Path Loss Models
Piecewise Linear Model
Indoor Attenuation Factors − partition loss
− floor loss − the building penetration loss − It is difficult to find generic
models
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Mobile Computing and Communication Lab. 9
Shadowing (1) Statistical models
− The transmitted signal experiences random variation due to blockage from objects in the signal path and changes in reflecting surfaces and scattering objects.
Log-normal shadowing − Ratio of transmit-to-receive power is a random variable
with a log-normal distribution
− Distribution of (the dB value of ) is Gaussian with mean and standard deviation
tr PP /=ψ
−−= 2
210
2)log10(
exp2
10ln/10)(dB
dB
dB
pψ
ψ
ψ σµψ
ψσπψ
dBψ ψdBψµ
dBψσ
−−= 2
2
2)(
exp2
1)(dB
dB
dB
dBdBp
ψ
ψ
ψ σµψ
σπψ
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Mobile Computing and Communication Lab. 10
Shadowing (2)
constant.n attenuatioan is where,)( ααdeds −=∑= it dd
ti ddt eeds αα −− =∑=)(
Justification for the Gaussian model as the distribution of − when shadowing is dominated by the attenuation from blocking object − attenuation of a signal as traveling through an obstacle with depth d
■ − attenuation of a signal as it propagates through the region
■ − dt : Gussian r.v. (by the Central Limit Theorem) − : Gussian r.v.
Decorrelation distance:
− the distance at which autocovariance equals 1/e of its maximum value − on the order of the size of the blocking objects or clusters of objects
)(log10 tds
dBψ
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Mobile Computing and Communication Lab. 11
Combined Path Loss and Shadowing
Combined model − average dB path loss: the path loss model − shadow fading with mean of 0 dB: variations about the path loss
Simplified path loss with log-normal shadowing −
− : a Guassian r.v. with mean zero and variance dBψ
dBt
r
ddKdB
PP ψγ +−=
01010 log10log10)(
dBψσ
Pr/Pt
(dB)
log d
Very slow
Slow 10logK
γ10−
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Mobile Computing and Communication Lab. 12
Outage Probability
under the path loss and shadowing − : the minimum received power level − outage probability:
■ the probability that the received power at a given distance d falls below
■ ■ for the combined path loss and shadowing (at slide 23)
minP
minP
),( min dPpout
))((),( minmin PdPpdPp rout <=
−+−−=<
dB
ddKPPQPdPp tr
ψσγ )/(log10log10(1))(( 01010min
min
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Mobile Computing and Communication Lab. 13
Multipath Multipath fading
− Constructive and destructive addition of different multipath components introduced by a channel
Time-varying channel impulse response − If a single pulse is transmitted over a multipath channel, the received
signal appears as a pulse train
− A multipath channel is modeled by a channel impulse response. Characteristic of the multipath channel
− time delay spread ■ Time delay between the arrivals of the first received signal component
and the last received component associated with a single transmitted pulse − time-varying nature due to moving
Narrowband fading model Wideband fading model
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Mobile Computing and Communication Lab. 14
Example of Multipath
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Mobile Computing and Communication Lab. 15
Multipath Component (1)
Nonresolvable components: these are combined into a single component.
Resolvable components: if the delay difference between two components significantly exceeds the inverse signal bandwidth
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Mobile Computing and Communication Lab. 16
Multipath Component (2)
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Mobile Computing and Communication Lab. 17
Doppler Shift
When the transmitter is moving, the received signal has a Doppler shift
Doppler effect is on the order of 100 Hz for typical vehicle speed (75km/hr) and frequencies (about 1GHz)
DD
D
f
vt
f
πφ
θλ
φπ
2
cos21
=
=∆∆
=
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Mobile Computing and Communication Lab. 18
Time-varying Channel Impulse Response Equivalent lowpass time-varying channel impulse response at time t to an
impulse at time :
− N(t): the number of multipath components − For the nth component
■ : delay ■ : phase shift - ■ : Doppler phase shift ■ : amplitude
Time-invariant channel:
)()(
0n
jN
nn
nec ττδατ φ −= −
=∑
τ−t ))(()(),( )()(
0tettc n
tjn
tN
nn ττδατ φ −= −
=∑
)(tnτ
nDφnDncn tft φτπφ −= )(2)(
)(tnα
)(tnφ
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Mobile Computing and Communication Lab. 19
Transmit & Receive Signal Models (1)
Complex baseband representation − The transmitted or received signals are actually real sinusoids − The complex representations are used to facilitate analysis
Transmitted signal − −
■ complex baseband signal with in-phase component sI(t) and quadrature component sQ(t)
{ } )2sin()()2cos()( )(Re)( 2 tftstftsetuts cQcItfj c πππ −==
)()()( tsjtstu QI +=
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Mobile Computing and Communication Lab. 20
Transmit & Receive Signal Models (2) Transmitted signal
− Received signal
−
−
−=
−−=
−−=
−=
∑
∑ ∫
∫ ∑
∫
=
−
=
∞
∞−
−
∞
∞=
−
∞
∞−
tfjN(t)
nn
tjn
tfjN(t)
nn
tjn
tfj
-
N(t)
nn
tjn
tfj
cn
cn
cn
c
ettuet
edtutet
edtutet
edtutctr
πφ
πφ
πφ
π
τα
ττττδα
ττττδα
τττ
2
0
)(
2
0
)(
2
0
)(
2
))(()(Re
)())(()(Re
)())(()(Re
)(),(Re)(
{ }tfj cetuts π2)(Re)( =
−= −
=∑ tfj
ntj
tN
nn
cn ettuettr πφ τα 2)()(
0))(()(Re)(
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Narrowband Fading Model
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Mobile Computing and Communication Lab. 22
Narrowband Fading Model (1)
Narrowband fading assumption − Delay spread: − The LOS and all multipath components are typically nonresolvable.
Received Signal − −
In order to characterize the random scale factor caused by the
multipath, u(t)=1 − Transmitted signal: − Received signal:
BTm1<<
ii tutu ττ allfor )()( ≈−
= −
=∑ )(
)(
0
2 )()(Re)( tjtN
nn
tfj nc etetutr φπ α
channel characteristic
{ } tfets ctfj c ππ 2cosRe)( 2 ==
tftrtftreettr cQcItfjtj
tN
nn
cn ππα πφ 2sin)(2cos)( )(Re)( 2)()(
0+=
= −
=∑
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Mobile Computing and Communication Lab. 23
Narrowband Fading Model (2)
Received Signal −
− in-phase component:
− quadrature component:
rI(t) and rQ(t) can be approximated as Gaussian random
processes − if N(t) is large, and and are independent for different
components. − when for small N(t) each ray has a Rayleigh distributed envelope
and uniform phase − rI(t) and rQ(t) are independent Gaussian process with the same
autocorrelation , a mean of zero, and a crosscorrelation of zero
)(cos)()()(
0tttr n
tN
nnI φα∑
=
=
tftrtftrtr cQcI ππ 2sin)(2cos)()( +=
)(sin)()()(
0tttr n
tN
nnQ φα∑
=
=
)(tnα )(tnφ
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Mobile Computing and Communication Lab. 24
Autocorrelation and Cross Correlation (1) Assumption
− There is no dominant LOS component − The amplitude, multipath delay and Doppler frequency shift are
changing slowly enough to be considered constant over the time interval of interest
■ ■
− is uniform distributed on [-π, π] ■ this is reasonable because is large and hence can go through a
360o rotation for a small change The received signal r(t) is zero-mean Gaussian process
− − −
nn DDnnnn ftftt ≈≈≈ )(,)(,)( τταα
)(tnφ
tfft nDncn πτπφ 22)( −=
0)](cosE[ ][E)]([E n ==∑ ttr nn
I φα
cfnτ
)0)]()([E ( =trtr QI
0)]([E =tr
0)](E[sin ][E)]([E n ==∑ ttr nn
Q φα
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Mobile Computing and Communication Lab. 25
Autocorrelation and Cross Correlation (2)
Autocorrelation
−
■
■
− A uniform scattering environment assumption ■ The channel consists of many scatters densely packed with respect to angle ■
− Each component has the same received power: −
Nnnn πθθ 2=∆=
NPrn 2][E 2 =α
)sin(2 )()2cos()()]()([E)( , tftAtftAttrtrtA crrcrr QII∆∆−∆∆=∆+=∆ ππ
∆
=∆+=∆ ∑ nnn
IIrtvttrtrtA
Iθ
λπα cos2cos][E5.0)]()([E)( 2
∆
−=∆+=∆ ∑ nnn
QIrrtvttrtrtA
QIθ
λπα cos2sin][E5.0)]()([E)( 2
,
θθλπ
π∆
∆
∆=∆ ∑
=
ntvPtAN
n
rrI
cos2cos2
)(1
v
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Mobile Computing and Communication Lab. 26
Autocorrelation and Cross Correlation (3)
)2cos()()( tftAtA crr I∆∆=∆ π
)2(
cos2cos2
)(
0
2
0
tfJP
dtvPtA
Dr
rrI
∆=
∆
=∆ ∫π
θθλπ
ππ
0
cos2sin2
)(2
0,
=
∆
=∆ ∫ θθλπ
ππ
dtvPtA rrr QI
0 , →∆∞→ θN
λ4.0 4.0 =∆⇒=∆ tvtfD
Antenna spacing of 0.4λ: the signal decorrelates over a distance of 0.4λ
θπ
θθπdee
jxJ jnjx
nncos2
021)( ∫=
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Mobile Computing and Communication Lab. 27
Power Spectral Density
)]2([)(
)]()([25.)(
0 τπ Dr
crcrr
fPJfS
ffSffSfS
I
II
F=
++−=
fc+fD fc
Sr(f)
fc-fD
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Mobile Computing and Communication Lab. 28
Envelope and Power Distributions without LOS
Signal envelope − − rI and rQ are Gaussian random variables with mean zero and
variance − z(t) is Rayleigh distributed
■
Power
− − The received signal power is exponentially distributed with mean
■
2σ
)()()()( 22 trtrtrtz QI +==
0 ,)( 2
2
22 ≥=
−zezzp
z
Zσ
σ
0 x,2
1)( 2
22
2 ≥=−
σ
σ
x
Z exp
22 )()( trtz =22σ
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Mobile Computing and Communication Lab. 29
Signal Envelope over Channel having a LOS
Signal envelope − The received signal equals the superposition of a LOS component
and a complex Gaussian component − The signal envelope z(t) has a Rician distribution.
Average received power − − Fading parameter :
■ K = 0: Rayleigh fading ■ K = ∞: no fading (only a LOS component) ■ the smaller K, the severer fading
0 ,)( 202
)(
22
22
≥
=
+−
zzsIezzpsz
Z σσσ
22
0
2 2)( σ+== ∫∞
sdxxpxP Zr
LOS component power
NLOS component power
* I0: the modified Bessel function
2
2
2σsK =
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Mobile Computing and Communication Lab. 30
Nakagami Fading Channel
Nakagami fading distribution − More general fading distribution whose parameters (m) can be
adjusted to fit a variety of empirical measurements
− m = 1: Rayleigh fading − m = ∞: no fading − : approximately Rician fading
5.0 ,)(
2)(2
12
≥Γ
=−−
mePm
zmzp rPmz
mr
mm
Z
)12()1( 2 ++= KKm
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Wideband Fading
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Mobile Computing and Communication Lab. 32
Intersymbol Interference
Narrowband fading: delay spread
- There is little interference with a subsequently transmitted pulse.
Wideband fading:
- The resolvable multipath components interfere with subsequently transmitted pulses: intersymbol interference (ISI)
1τ 2τuB121 >>−ττ
TTm >>
TTm <<
Two multipath components with delay and are resolvable if
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Mobile Computing and Communication Lab. 33
Autocorrelation: Time Domain
Equivalent lowpass time-varying channel impulse response at time t to an impulse at time − : a complex zero-mean Gaussian random process
The statistical characterization of is determined by its autocorrelation function
For the WSS channel, the autocorrelation is independent of t. −
For the WSS channel with uncorrelated scattering − The channel response associated with a multipath component of delay
is uncorrelated with the response associated with a component of a different delay because they are caused by different scatters.
−
))(()(),( )()(
0tettc n
tjtN
nn
n ττδατ φ −= −
=∑
τ−t
),( tc τ)],(),(E[),,,( 21
*21 ttctcttAc ∆+=∆ ττττ
)],(),(E[),,( 21*
21 ttctctAc ∆+=∆ ττττ
1τ
12 ττ ≠
),()(),()],(),(E[ 21121* tAtAttctc cc ∆=−∆=∆+ τττδτττ )( 12 τττ ==
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Mobile Computing and Communication Lab. 34
Autocorrelation: Frequency Domain
Characteristics of the time-varying multipath channel at time t − in time domain: − in frequency domain:
■ A complex zero-mean Gaussian process ■ is completely characterized by its autocorrelation.
Autocorrelation of −
− the WSS channel:
−
),( tc τττ τπ detctfC fj∫
∞
∞−
−= 2),(),(
),( tfC),( tfC
)],(),(E[),,,( 21*
21 ttfCtfCttffAC ∆+=∆)],(),(E[),,( 21
*21 ttfCtfCtffAC ∆+=∆
[ ]
),(
),(
),(
),(),(E
),(),(E),,(
2
)(2
2122
21*
22
2-12
1-
*21
12
2211
2211
tfA
detA
detA
ddeettctc
dettcdetctffA
C
fjc
ffjc
fjfj
fjfjC
∆∆=
∆=
∆=
∆+=
∆+=∆
∆−∞
∞−
−−∞
∞−
−−∞
∞−
∞
∞−
−∞
∞
∞
∞
∫∫∫ ∫
∫∫
ττ
ττ
ττττ
ττττ
τπ
τπ
τπτπ
τπτπ
ττ τπ deAfA fjcC
∆−∞
∞−∫=∆ 2)()(0=∆t
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Mobile Computing and Communication Lab. 35
Power Delay Profile Power delay profile
− − Average power associated with a given multipath delay
Delay spread − Average delay spread:
− rms delay spread:
− the delay associated with a given multipath component is weighted by its relative power
The delay spread of the channel is roughly by the time delay T where − : the system experiences significant ISI − : ISI can be negligible
)0 when ),(( )],(),(E[)( * =∆∆= ttAtctcA cc τττττ
∫∫
∞
∞
=
0
0
)(
)(
ττ
τττµ
dA
dA
c
cTm
∫∫
∞
∞−
=
0
0
2
)(
)()(
ττ
ττµτσ
dA
dA
c
cTT
m
m
Relative power
TAc ≥≈ ττ for 0)()10(
mm TsTs TT σσ <<<)10(
mm TsTs TT σσ >>>
symbol period
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Mobile Computing and Communication Lab. 36
Coherence Bandwidth (1)
− describes the autocorrelation of the time-varying multipath channel in
frequency domain (coherence) Coherence bandwidth of the channel
− − By the Fourier transform relationship between
Flat fading and frequency selective fading − signal bandwidth: B − Flat fading:
■ − Frequency selective fading:
■
cCc BffAB ≥∆≈∆ allfor 0)(such that
)],(),(E[)( * tffCtfCfAC ∆+=∆
)( and )( τcC AfA ∆
TffATA Cc 1for 0)( then ,for 0)( if >∆≈∆>≈ ττmT
ck
TB σ=≈ 1
cBB <<ISI negligible 11 ⇒≈>>≈
mTcs BBT σ
ISIt significan 11 ⇒≈<<≈mTcs BBT σ
cBB >>
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Mobile Computing and Communication Lab. 37
Coherence Bandwidth (2)
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Mobile Computing and Communication Lab. 38
Coherence Time and Doppler Power Spectrum (1)
Time variation of the channel which arise from transmitter or receiver motion cause a Doppler shift
− describe the autocorrelation of the channel at a frequency over the time
(channel coherence over the time)
Coherence time −
Doppler power spectrum − − ρ : Doppler shift − Sc(ρ): the PSD of the received signal as a function of ρ
Doppler Spread: BD
− the range of ρ such that
)],(),(E[)( * ttfCtfCtAC ∆+=∆
cCc TttAT ≥∆≈∆ for 0)(such that
tdetAS tjCC ∆∆= ∫
∞
∞−
∆− πρρ 2)()(
0)( >ρCS
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Mobile Computing and Communication Lab. 39
Coherence Time and Doppler Power Spectrum (2)
Relationship between the coherence time and the Doppler spread − By the Fourier transform relationship between
If the transmitter and reflector are stationary and the receiver is moving with velocity v − − Remind that in the narrowband fading model the signal decorrelates over the time
of 0.4/fD
− In general,
In summary,
cCcC TSTttA 1for 0)( then ,for 0)( if >≈>∆≈∆ ρρ
)( and )( ρCC StA ∆
cD TB 1≈
DD fvB =≤ λMaximum Doppler shift
).( of shape on the depends where, ρCcD SkTkB ≈
Dc
Tc BTB
m
1 , 1 ≈≈ σ