Transcript lec3Wireless-CH

Wireless Propagation
Characteristics
Prof. Li Ping’an
Tel: )027-61282569
Email: [email protected]
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 for
 system planning, cell coverage
 link budget (what is the frequency reuse factor?)
• Shadowing is used for
 power control design
 2nd order interference and TX power analysis
 more detailed link budget and cell coverage
analysis
• Multipath fading is used for
 physical layer modem design --- coder, modulator,
interleaver, etc
Sky Wave Propagation
LOS Propagation
Line-of-Sight Equations
• Optical line of sight
d  3.57 h
• Effective, or radio, line of sight
d  3.57 h
d = distance between antenna and horizon (km)
h = antenna height (m)
K = adjustment factor to account for refraction,
rule of thumb K = 4/3
Line-of-Sight Equations
• Maximum distance between two antennas for
LOS propagation:

3.57 h1  h2

h1 = height of antenna one
h2 = height of antenna two
Free Space Loss
• Consider an Isotropic point source fed by a transmitter of Pt Watts
• The energy per unit area of the surface of the
sphere with radius d
Pt
4d 2
• Hence, at a distance d, an receive antenna with
effective aperture Ae obtain a total power
Pt Ae
Pr 
4d 2
Free Space Loss
• Define an antenna gain as
G
4Ae
2
• Hence, the received power :
Pt Gt Gr
Pr 
[4 (d /  )]2
The
wavelength
Free Space Loss
• Free space loss, ideal isotropic antenna

Pt 4d 
4fd 


2
Pr

c2
Pt = signal power at transmitting antenna
Pr = signal power at receiving antenna
 = carrier wavelength
d = propagation distance between antennas
c = speed of light (» 3 ´ 10 8 m/s)
where d and  are in the same units (e.g.,
meters)
2
2
Free Space Loss
• Free space loss equation can be recast:
Pt
 4d 
LdB  10 log  20 log 

Pr
  
 20 log    20 log d   21.98 dB
 4fd 
 20 log 
  20 log  f   20 log d   147.56 dB
 c 
Path Loss Exponent
n
 d 

PL(d )  
 d0 
PL(d )  PL( d 0 )  10n log d / d 0 
Environments
Urban area cellular radio
n
2.7 to 3.5
Shadowed urban cellular
radio
In building LoS
Obstructed in building
3 to 5
Obstructed in factory
2 to 3
1.6 to 1.8
4 to 6
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,s2)
where
 PLavg (dB) is obtained from the path loss model
 s is the standard deviation of X in dB
Small-scale fading: Multipath Rayleigh
Fading
Delay=D1
100km/hr
Delay=D2
TX an impulse
RX impulse response
D1 -D2
Small-scale channel
h (t ,  )
x(t )
y (t )
z (t )
n(t )
Time-varying and time-invariant
channel
h( )
t



y (t )   h(t , ) x(t   )d

h (t , ) 
L ( t ) 1
 (t ) (  (t ))
l 0
y(t ) 
l
l
L ( t ) 1
 (t )s(t   (t ))
l 0
l
l

y(t )   h( ) x(t   )d

L 1
h ( )    l (   l )
l 0
L 1
y (t )    l s (t   l )  n(t )
l 0
Why Convolution?

y(t )   h( ) x(t   )d

x(t) x(t-1)x(t-2)
x(t-1)h(1)
x(t-0)h(0)
x(t-4)h(4)
At time t
Time-frequency analysis of the
wireless channels
冲激响应
h( , t )
Ft
时延多普勒扩展
H ( , f d )
F
F
1
fd
F
F f1
时变传输函数
H ( f , t)
F f1
F fd1
多普勒扩展
H ( f , fd )
Ft
Time-Doppler couple
• Doppler frequency
shift (由运动中不同时
间相位变化引起)
  2
fd 
l


1 
2 t
2vt

cos 
  cos 
v
l

v
1
d
v
2
 1  t
 2  t
Delay-Frequency couple
• At any time, autocorrelation 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
1
v
2
Fourier -couples
自相关
功率谱
时间自相关
1
H (t )   H (d ) exp( jd t )dd
2
多普勒谱

H (d )   H (t ) exp(  jd t )dt

时延谱
频率自相关

H (f )   H ( ) exp(  j 2f )d


H ( )   H (f ) exp( j 2f )df

Coherent-Time: Fast/slow fading
Tc
h(t )  V0 , t  t0 
2
小尺度信道
1
Tc 
fm
H (t )
Tc
fm  
 Tc  

Tc  Ts : fast  fading
Coherent-Bandwidth:Flat fading
and frequency selective fading
H (f )
信道谱
Bc
f
s 2   2  ( ) 2

1
Bc 
5s 
n

 Sh ( )d
, n  
 S ( )d
h

窄带信号
宽带信号
s  
 Bc  
 Bc  Bs
frequency selective fading
Flat Rayleigh fading
a1
a2 a4
Time Delay Spread
a3 a5
a6a7
Symbol Period >>
Time Delay Spread
Equivalent
Model:
   ai e
j1 i
t
f
f
1
y(t) = 
x(t),
t t[0,T]
f
1
f
Rayleigh Fading (No Line of
Sight)
   Re( a e   )  j  Im( a e   )
j
j
1 i
i
1 i
i
By Central Limit Theorem
  I  j Q
 re j
f I , Q ( I ,  Q )  f I ( I ) f Q ( Q ) 
Independent zero mean
Gaussian
1
2s
2
e
  I 2  Q 2



2

2
s


1 r r 2 / 2s 2  Magnitude is Rayleigh
f R (r ,  )  f  ( ) f R (r ) 
e
2
2 s
Phase is Uniform
whe re     ,  , r  0,  
Flat Rayleigh fading channel
f I , Q ( I ,  Q ) : Independen t Gaussian w ith mean s 2
1
f  ( ) 
if   0,2  : Uniform Phase
2
r
r2
f R (r )  2 exp(  2 ) if r  0 : Rayleigh Amplitude
s
2s
1
p
f P ( p)  exp(  ) if p  0 : Exponentia l Channel Power Gain
Po
Po
whe re p  r 2 and Po = 2s 2 is mean channel power gain
Rician Distribution-with LoS
• N+1 paths with one
LoS
• The amplitude of the
received signal
• K factor
r  ( x  A) 2  y 2
Zero-means Gaussian
each with variance s 2
K  A / 2s
2
2
Rician Distribution
Zero-order modified Bessel function
Rician
Factor
Effects of Racian Factor K
Channel model：Flat fading
T-Signal
R-Signal
a
Rayleigh
Noise
y (t )   (t ) s (t )  n(t )
Channel Model: Frequency
selective fading
L 1
y (t )    l (t ) s (t   l )  n(t )
l 0