Kỹ thuật Khử nhiễu tuần tự từng lớp (SIC) là phương pháp quan trọng trong NOMA

Signal losses due to three effects:
1. Large Scale:
due to distance
2. Medium Scale: due
to shadowing and
obstacles
3. Small Scale
Fading: due to
multipath

Wireless Channels
Several Effects:
• Path Loss due to dissipation of energy: it depends on distance only
• Shadowing due to obstacles such as buildings, trees, walls. Is caused by
reflection, scattering …
• Self-Interference due to Multipath.
transm
rec
P
P
10
log
10

1. Free-space loss
1.1 Path loss model
• Path loss formula
• Reference formula
• Decibel formula
5
Transmit
antenna Receive
antenna
d

1.2 Plane earth loss model (Two-ray Model)
6

0
0
10
log
10
}
{ L
d
d
L
E p 








 
Path loss
exponent
Reference distance
• indoor 1-10m
• outdoor 10-100m
Free space loss at reference
distance
10 0
log ( / )
d d
  0
p
E L L

10
1
10 0
10
2
10
20dB
10 Values for Exponent :
Free Space 2
Urban 2.7-3.5
Indoors (LOS) 1.6-1.8
Indoors(NLOS) 4-6

2. Medium Scale:
 Losses due to Buildings, Trees, Hills, Walls …
2.1 Log-distance Path loss models

2. Medium Scale:
 Log-normal shadowing (Log-normal distribution)
 
2
2
2
of Gaussian variable :
1 (ln )
( )
2
2
1 1
( ) exp( ) 1
2 2
2 2
( )
p p
z
p
r p
L E L
pdf
m
pdf e
x z
Q z dx erf
E L
P L Q



 

 





 

 
 
 
   
 
 
 
 

 
 
   
 
 


The Power Loss in dB is random:

2. Medium Scale:
 Log-normal shadowing

2. Medium Scale:
2.2 Log-normal shadowing

 Okumura model: Urban macrocells 1-100km, frequencies
0.15-1.5GHz, BS antenna 30-100m high
2.3 Empirical Models for Medium Scale Path Loss
2. Medium Scale:

• Okumura Model: Urban macrocells 1-100km, frequencies
0.15-1.5GHz, BS antenna 30-100m high

• Hata model: Similar to simplified Okumura model: urban
macrocells 1-100km, frequencies 0.15-1.5GHz, BS antenna
30-100m high
2. Medium Scale:

3. Small Scale Fading due to Multipath.
3.1 Spreading in Time: different paths have different lengths;
time
Transmit Receive
0
( ) ( )
x t t t

 
0
t
0
( ) ( ) ...
k k
y t h t t
 
    

1
 2
 3

0
t
2
1
3
8
100 10
sec
3 10
c
 
  

Example for 100m path difference we have a time delay

Typical values of channel time spread:
channel
0
( ) ( )
x t t t

 
1
 2
 MAX

0
t
0
t
1
Indoor 10 50 sec
Suburbs 2 10 2 sec
Urban 1 3 sec
Hilly 3-10 sec
n





 


 Transmit a narrowband pulse into the channel
 Measure replicas of the pulse that traverse different paths between
transmitter and receiver

Intersymbol Interference
Suppose that there are two paths.
The shorter path has length d1, the
longer path has length d2.
What is the difference in propagation
delay between the two paths?
3
0
1
2
Symbols
received
path 1
Received
signal
Symbols
received –
path 2

3
0
1
2

P t
( ) 0 t T

if
3
2








t T

( ) t 2 T


( )

if
3
2

 







t 2 T


( ) t 3 T


( )

if
3
2

 


2







t 3 T


if

Suppose we use differential phase shift keying to transmit 3 2 1 0
   
 
t
P
t
f
t
s c 
 
2
sin
3 2 1
0 1 2 3 4 5
1
0
1
1
1

f t
( )
5
0 t
0
?

0 0.5 1 1.5 2 2.5 3
1
0
1
1
1

f t
( )
f t
T
5







3
0 t
0 0.5 1 1.5 2 2.5 3
1
0
1
0.951
0.951

f t
( ) f t
T
5








2
3
0 t

Comparison of the BER for a fading
and non-fading channel

Chòm sao tin hiệu qua kênh
• Gaussian channel
• Rayleigh channel

Doppler effect
cos
2
d
v
f
t


 

 

' c d
f f f
 

3.2 Spreading in Frequency: motion causes frequency shift (Doppler)
time
time
Transmit Receive
Freq.
Doppler Shift
v
c
F
2
( ) c
j F t
T
x t X e 

 
2
( ) c
j F F t
R
y t Y e
 

for each path
c
F F


Put everything together
time
Transmit Receive
v
time
)
(t
x )
(t
y

Re{.}
t
F
j C
e 
2 t
F
j C
e 
2

)
(t
h
)
(t
gT
LPF
)
(t
gR
LPF
( )
x t
( )
y t
2 ( )( )
( )
( ) Re ( ) c
j F t
F
y t x t e
a t  
  

 
 
 
 
 


 
Each path has … …shift in time …
…shift in frequency …
… attenuation…
(this causes small scale time variations)
paths
channel

Statistical Models of Fading Channels
Several Reflectors:
Transmit
v
( )
x t
t ( )
y t
t
1

2



Statistical Models of Fading Channels
2 ( )( )
( ) Re ( )
c k
j F t
k
k
k
F
y t a e x t

 


  

 
 
  
 
 
 
 
 

 
v

( )
y t


average time delay
• each time delay
• each doppler shift
k
 


D
F F
 

cos( )
v 
 t
t

)
2 ( )( 2
2
( ) Re ( )
c k c
F
F j F j F t
j t
k
k
k
y t e e x t e
a  
 



  


 
 
  
 
 
 
 
  

 
 
2 ( )
2
( ) ( )
c k
j F F
j F t
k
k
r t a e e x t
  


  

 
 
 
 
  

 
Assume: bandwidth of signal <<
( ) ( )
k
x t x t 
  
… leading to this:
Some mathematical manipulation …




 




 

k

/
1
 
2
( ) Re ( ) c
j F t
y t r t e 

 
( ) ( ) ( )
r t c t x t 
 
  
with
 
2 ( )
2
( ) c k
j F F
j F t
k
k
c t a e e
  
   

  

 random, time varying

Complex Baseband Representation of Bandpass

Bandpass Signal – QPSK Modulation

39
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0 1 2 3 4 5

Rayleigh PDF
   

mean = 1.2533

41
Rayleigh Fading



















)
(
)
(
0
0
0
)
(
2
2
2
2
r
r
e
r
r
p
r


Rayleigh distribution has the probability density function (PDF) given by:
2
is the time average power of the received signal before envelope detection.
 is the rms value of the received voltage signal before envelope detection

time
v
time
)
(t
x )
(t
y
1

1( )
c t

( )
c t

N

( )
N
c t


( )
y t

)
(t
x
… can be modeled as:
delays
1


N

time time
time
Simulation homework

43
Simulation homework
Envelope of Modulated Signal
Under Rayleigh Fading Channel

Statistical Model for the time varying coefficients
 
2 ( )
2
1
( ) c k
M
j F F
j F t
k
k
c t a e e
 

   


  


random
is gaussian, zero mean, with:
( )
c t

 
*
0
( ) ( ) (2 )
D
E c t c t t P J F t

  
  
D C
v v
F F
c 
 
with the Doppler frequency shift.

Each coefficient is complex, gaussian, WSS with autocorrelation
 
*
0
( ) ( ) (2 )
D
E c t c t t P J F t

   
  
( )
c t

and PSD
  2
0
2 1
if | |
( ) (2 ) 1 ( / )
0 otherwise
D
D
D D
F F
F
S F FT J F t F F





   



with maximum Doppler frequency.
D
F
( )
S F
D
F F
This is called Jakes
spectrum.

Kỹ thuật Khử nhiễu tuần tự từng lớp (SIC) là phương pháp quan trọng trong NOMA

Kỹ thuật Khử nhiễu tuần tự từng lớp (SIC) là phương pháp quan trọng trong NOMA

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Kỹ thuật Khử nhiễu tuần tự từng lớp (SIC) là phương pháp quan trọng trong NOMA