wireless propagation characteristics prof. li ping’an tel: )027-61282569 email:...
TRANSCRIPT
Mobile Commun. Environments
• Path loss
• Shadow
• Multi-path fading
• Time spread
• Doppler frequency shift (Doppler spread)
General 3-level Model
General 3-level Model
• Path loss model is used forsystem planning, cell coverage link budget (what is the frequency reuse factor?)
• Shadowing is used forpower control design2nd order interference and TX power analysismore detailed link budget and cell coverage
analysis
• Multipath fading is used forphysical layer modem design --- coder,
modulator, interleaver, etc
Sky Wave Propagation
LOS Propagation
Line-of-Sight Equations
• Optical line of sight
• Effective, or radio, line of sight
d = distance between antenna and horizon (km)h = antenna height (m)K = adjustment factor to account for refraction,
rule of thumb K = 4/3
hd 57.3
hd 57.3
Line-of-Sight Equations
• Maximum distance between two antennas for LOS propagation:
h1 = height of antenna oneh2 = height of antenna two
2157.3 hh
Free Space Loss
• Consider an Isotropic point source fed by a trans-mitter of Pt Watts
• The energy per unit area of the surface of the sphere with radius d
• Hence, at a distance d, an receive antenna with effective aperture Ae obtain a total power
24 d
APP etr
24 d
Pt
Free Space Loss
• Define an antenna gain as
• Hence, the received power :
2)]/(4[ dGGP
P rttr
2
4
eAG
The wavelength
Free Space Loss
• Free space loss, ideal isotropic antenna
Pt = signal power at transmitting antennaPr = signal power at receiving antenna = carrier wavelengthd = propagation distance between antennasc = speed of light (» 3 ´ 10 8 m/s)where d and are in the same units (e.g.,
meters)
2
2
2
2 44
c
fdd
P
P
r
t
Free Space Loss
• Free space loss equation can be recast:
d
P
PL
r
tdB
4log20log10
dB 98.21log20log20 d
dB 56.147log20log204
log20
dfc
fd
Path Loss Exponent
00
0
/log10)()(
)(
ddndPLdPL
d
ddPL
n
Environments n
Urban area cellular radio 2.7 to 3.5
Shadowed urban cellular radio
3 to 5
In building LoS 1.6 to 1.8
Obstructed in building 4 to 6
Obstructed in factory 2 to 3
Log-normal distribution
Shadowing Effects
• Variations around the median path loss line due to buildings, hills, trees, etc. Individual objects introduces random attenuation
of x dB.As the number of these x dB factors increases,
the combined effects becomes Gaussian (normal) distribution (by central limit theorem) in dB scale: “Lognormal”
• PL(dB) = PLavg (dB) + X where X is N(0,2) where PLavg (dB) is obtained from the path loss model is the standard deviation of X in dB
Small-scale fading: Multipath Rayleigh Fading
100km/hr
Delay=D1
Delay=D2
TX an impulseD1 -D2
RX impulse response
Small-scale channel
),( th)(tx )(ty )(tz
)(tn
Time-varying and time-invariant channel
))(()(),(1)(
0
ttth l
tL
ll
1)(
0
))(()()(tL
lll ttstty
)(h
t
dtxhty )()()(
)()(1
0l
L
llh
dtxthty
)(),()(
)()()(1
0
tntstyL
lll
Why Convolution?
dtxhty )()()(
x(t) x(t-1)x(t-2)
x(t-4)h(4)
x(t-0)h(0)
x(t-1)h(1)
At time t
Time-frequency analysis of the wireless channels
冲激响应),( th
时延多普勒扩展),( dfH
tF
1df
F时变传输函数
),( tfH
F1
fF
多普勒扩展
1fF
F
tF
1df
F
),( dffH
Time-Doppler couple
• Doppler frequency shift (由运动中不同时间相位变化引起 )
cos2 2 tvl
l
d
vv
12
t1t2
cos21 v
tdf
Delay-Frequency couple
• At any time, auto-correlation of frequency only affects the power of the signal as a function of delay
• 由于各径中心频率相同，如果时延扩展小，频率相关性强，相干合并功率大
• Power-delay spectrum
v
12
Fourier -couples
自相关 功率谱
时间自相关
频率自相关
dddHH dtjt
)exp()(2
1)(
多普勒谱
fdfjfHH
)2exp()()(
时延谱
tdtjt dHdH
)exp()()(
dfjf HH
)2exp()()(
Coherent-Time: Fast/slow fading
2,)( 00
cTttVth
mc fT
1
Tc
)( tH
小尺度信道
fadingfastTT
Tf
sc
cm
:
Coherent-Bandwidth:Flat fading and frequency selective fading
窄带信号 宽带信号
信道谱
51
cB
dS
dS
h
hn
n
)(
)(
,
)( 222
Bc
f
)( fH
fadingselectivefrequency
BBB scc
Flat Rayleigh fading
Symbol Period >> Time Delay Spread
Time Delay Spreada
a
a
a
aaa
t
Equivalent Model:
ff
1
ijiea
1
t
y(t) = x(t),
t[0,T]ff
1
Rayleigh Fading (No Line of Sight)
j
QI
ji
ji
re
j
eajea ii
)Im()Re( 11
By Central Limit Theorem
Independent zero mean Gaussian
,0,, re whe
2
1)()(),(
2
1)()(),(
22
2
22
2/2
2
2,
r
er
rffrf
efff
rRR
QIQI
QI
QIQI
Phase is Uniform
Magnitude is Rayleigh
Flat Rayleigh fading channel
gainpower channelmean is 2= and re whe
GainPower Channel lExponentia :0 if)exp(1
)(
AmplitudeRayleigh :0 if)2
exp()(
Phase Uniform:0,2 if2
1)(
mean ith Gaussian wt Independen :),(
2o
2
2
2
2
2,
Prp
pP
p
Ppf
rrr
rf
f
f
ooP
R
QIQI
Rician Distribution-with LoS
• N+1 paths with one LoS
• The amplitude of the received signal
• K factor 22 2/ AK
Zero-means Gaussianeach with variance 2
22)( yAxr
Rician Distribution
Rician Factor
Zero-order modified Bessel function
Effects of Racian Factor K
Channel model： Flat fading
T-Signal R-Signal
Rayleigh Noise
a
)()()()( tntstty
Channel Model: Frequency selective fading
)()()()(1
0
tntsttyL
lll
