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TRANSCRIPT
Nagoya Institute of Technology
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’09.03.19
Nagoya Institute of Technology
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•––
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••
••• OFDM• SC-FDE (single carrier-FDE) OFDM
PAPR•
Nagoya Institute of Technology
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••
••• OFDM• SC-FDE (single carrier-FDE) OFDM
PAPR•
Nagoya Institute of Technology
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•
••
•
•
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10kbps 2Mbps 10Mbps 100Mbps
Mobility
2G
GSMPDCPHS
3G
WCDMAcdma2000
4G
BWA
WLANIEEE802.11b
WLANIEEE802.11g, n
1Gbps
6
2011 2013
Nagoya Institute of Technology
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•
• Hz•
•
•
AWGN
)/1(log 2 NSBC bit/sec
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••
••• OFDM• SC-FDE (single carrier-FDE) OFDM
PAPR•
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•••
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•–
•–
•–
•
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•–
•– RF
•
s/p
QPSK mappingda
ta
LPF
LPF
cos/2
BPF PAchannel
LNA BPF
cos/2
LPF
LPF
p/s
QPSK de-
mapping
data
AWGN
transmitter channel receiver
s(t)
n(t)
r(t)
I
Q
I
Q
s/p
QPSK mappingd
ata
LPFchannel
LPFp/s
QPSK de-
mapping
dat
a
AWGN
transmitter channel receiver
s(t)
n(t)
r(t)
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• h( , t)–– t
• H(f, t)•
n(t)
s(t) r(t)
h( ,t)
( ) ( , ) ( ) ( )r t h t s t n t
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0 1 2 3 4
recei
ved
pow
er
(dB
)
delay time ( s)
13
h( , t)
•
0 1 2 3 4
recei
ved
pow
er
(dB
)
delay time ( s)
h( , 0)
h( , 1)
n(t)
s(t) r(t)
h( ,t)
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••
••• OFDM• SC-FDE (single carrier-FDE) OFDM
PAPR•
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•
• Jakes
•
( , ) ( ) ( )h t c t t
0 1 2 3 4
rece
ived
pow
er
(dB
)
delay time ( s)
c(t) (t)
n
v m/s
(vcos n)/Hz
m
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• cos(2 f0t)+cos(2 {f0+ f}t)
•• |c(t)|
-2
-1
0
1
2
-10 -8 -6 -4 -2 0 2 4 6 8 10
1.E-02
1.E-01
1.E+00
1.E+01
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
ampl
itude
t sec
f0=1, f=0.075
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• or
•
•
( ) ( ) ( ) ( )r t c t s t n tn(t)
s(t) r(t)
c(t)
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•– c(t)– NLOS (non-line-of-sight)
–•
– c(t)– LOS (line-of-sight)
2
2 2( ) exp2
r rf r22
r
2 2
02 2 2( ) exp2
r r a arf r I0I
a
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1.E-03
1.E-02
1.E-01
1.E+00
1.E+01
0 0.2 0.4 0.6 0.8 1
am
plit
ude
time sec
fdTs=0.001
fdTs=0.005
fdTs=0.01
-1
-0.5
0
0.5
1
0 0.2 0.4 0.6 0.8 1
phase
/ p
i
time sec
fdTs=0.001
fdTs=0.005
fdTs=0.01
19
•
• fd
0d
vffc
fd Hz v m/sf0 Hz c
Ts=0.001 secTs
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• r(t)
•
serial to parallel
QPSK mapping
LPF
LPFdecisionparallel to serial
data
dataAWGN
Rayleigh fading
channel equalization
channel estimation
pilot symbol
insertion
without consideration at this time
r(k)
c(k)
s(k)
r(k)^
n0(k)
( ) ( ) ( ) ( )r t c t s t n t
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•
• c(t)•
– ZF
– MMSE
c(t) C(f) LPF
( ) ( )( ) ( )( ) ( )
r k n kr k s kc k c k
*
2 22
( )( ) ( )( ) ( )
c kr k r kc k E s k
( ) ( ) ( ) ( )r k c k s k n k
( )s k( )r k
( )n kˆ( )r k
( )c k
2
k
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•
•
1.E-06
1.E-05
1.E-04
1.E-03
1.E-02
1.E-01
1.E+00
0 10 20 30 40 50
BER
Avg. Eb/N0 dB
fdTs=0.001 w/ eq.
fdTs=0.001 w/o eq.
fdTs=0.01 w/ eq.
fdTs=0.01 w/o eq.
theory
Ts=0.001, QPSKZF
fdTs
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••
••• OFDM• SC-FDE (single carrier-FDE) OFDM
PAPR•
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•
•
•
( , ) ( )H f t H f
0 Ts
h1
h0
h2 h3 h4 h5h6 h7 h8 h9
9Ts2Ts ………
1 dB
|h(t, )|[dB]
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•– Ts
0 1 2 3 4
recei
ved
pow
er
(dB
)
delay time ( s)
0 4
Ts= 4 s
trans. rate = 250 Kbps
recei
ved
pow
er (dB
)
delay time ( s) 0 1 2 3 4
rece
ived
pow
er (dB
)
delay time ( s)
Ts= 0.26 s
trans. rate = 3.84 Mbps
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H(f)
•
1.E-03
1.E-02
1.E-01
1.E+00
-500 -400 -300 -200 -100 0 100 200 300 400 500
ampl
itud
e
f Hz
H (L=1)1.E-03
1.E-02
1.E-01
1.E+00
1.E+01
-500 -400 -300 -200 -100 0 100 200 300 400 500
am
plit
ude
f Hz
H (L=10, 10dB decayed)
1.E-03
1.E-02
1.E-01
1.E+00
1.E+01
-500 -400 -300 -200 -100 0 100 200 300 400 500
am
plit
ude
f Hz
H (L=10, 1dB decayed)
( )H f
( )h0 Ts
h1
h0
h2 h3 h4 h5h6 h7 h8 h9
9Ts2Ts ………
1 dB
|h(t, )|[dB]
0 Ts 2Ts ………
|h(t, )|[dB]
0
|h(t, )|[dB]
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•H(f)
•
•
•
1
10 0 0
( )( ) ( )ˆ( ) ( )L
l
l
h s k lr k n kr k s kh h h
27
1
0( ) ( ) ( )
L
ll
r k h s k l n k hl=
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FDE: frequency domain equalization
•
•– ZF
– MMSE
•
)()1()1()()( 110 knLkshkshkshkr L2 2 ( 1 )
0 1 1( ) ( ) ( )
( ) ( ) ( )
s sn T N n L T NLR n h h e h e S n N n
H n S n N n
( ) ( )( ) ( )( ) ( )
R n N nR n S nH n H n
*
2 22
( )( ) ( )( ) ( )
H nR n R nH n E S n
Nagoya Institute of Technology
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••
••• OFDM• SC-FDE (single carrier-FDE) OFDM
PAPR•
Nagoya Institute of Technology
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(orthogonal frequency division multiplexing)•
serial to parallel
QPSK mapping
IFFT
decisionparallel to serial
data
dataAWGN
S/P
P/S r(k)
s(k)
R(n)
n(k)
channel
h(k)
S(n)
FFTFDE
R(n)^
channel estimation
pilot symbol
insertion
guard interval insertion
guard intervalremoval
LAN WiMAX
Nagoya Institute of Technology
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•
-1-0.8-0.6-0.4-0.2
00.20.40.60.8
1
0 0.02 0.04 0.06 0.08 0.1 0.12
I-cha
nnel
t sec
1.E-05
1.E-04
1.E-03
1.E-02
1.E-01
1.E+00
1.E+01
-4000 -3000 -2000 -1000 0 1000 2000 3000 4000
ampl
itude
f Hz
Ts=0.001 sec, K=64
QPSK
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•–––
•– peak to average
power ratio
–
–
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•
•– Ts– Ts T
Ts sec0 Ts sec
1
0 1T=KTs sec
KOFDM1
1
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KOFDM1
OFDM
•ISI: inter-symbol interference
• GI: guard interval
KOFDM1
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•
•• i.i.d independently and identically distributed
–••
0 Ts
h1
h0
h2h3 h4
h5 h6 h7 h8 h9
2Ts ………
|h(t, )|[dB]
Nagoya Institute of Technology
36•
1.E-05
1.E-04
1.E-03
1.E-02
1.E-01
1.E+00
0 5 10 15 20 25 30 35
BER
Avg. Eb/N0 dB
L=1 L=2
L=4 L=8
L=10 L=16
theory
Ts=0.001 sec, K=64T=0.064 sec
QPSK OFDMGI =T/8=8Ts
L TsZF
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•
•
•
20 1
2 ( 1) /1
( ) ( ) ( ) ( ) ( )
( ) ( ) ( )
s
s
nT N
j n L T NL
R n h n S n h n S n e
h n S n e N n
0 Ts
h1
h0
h2h3 h4
h5 h6 h7 h8 h9
2Ts ………
|h(t, )|[dB]
0 1 1( ) ( ) ( ) ( 1) ( 1) ( 1) ( 1) ( )Lr k h k s k h k s k h k L s k L n k
p28
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••
••• OFDM• SC-FDE (single carrier-FDE) OFDM
PAPR•
Nagoya Institute of Technology
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single carrier-• cyclic
prefix
•
serial to parallel
QPSK mapping
decisionparallel to serial
data
dataAWGN
IFFTr(k)
s(k)
R(n)
n(k)
channel
h(k)
FFTFDEr(k)^
channel estimation
pilot symbol
insertion
cyclic prefix
insertion
cyclic prefix
removal
Nagoya Institute of Technology
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•–
–
–
1.E-05
1.E-04
1.E-03
1.E-02
1.E-01
1.E+00
0 5 10 15 20 25 30 35
BER
Avg. Eb/N0 dB
OFDM
QPSK-SC Ts=0.001 sec, K=64T=0.064 sec
QPSKZF
Ts=0.001 sec, K=64
MMSE
10.5 dB
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••
1.E-05
1.E-04
1.E-03
1.E-02
1.E-01
1.E+00
1.E+01
-4000 -3000 -2000 -1000 0 1000 2000 3000 4000
ampl
itude
f Hz
OFDM
QPSK-SC root-roll-off 0.5QPSK-SC non-LPF
Ts=0.001 sec, K=64T=0.064 sec
QPSK
Ts=0.001 sec, K=64
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peak to average power ratio
1.0E-03
1.0E-02
1.0E-01
1.0E+00
2 4 6 8 10 12
CC
DF
PAPR (dB)
QPSK-SC
OFDMTs=0.001 sec, K=64T=0.064 sec
QPSK
Ts=0.001 sec, K=64
root-Nyquist LPF, =0.5
•
CCDF: complementary cumulative distribution function
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OFDM-FDE SC-FDE
•• 43
OFDM-FDE
×
SC-FDE sinc
Nagoya Institute of Technology
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••
••• OFDM• SC-FDE (single carrier-FDE) OFDM
PAPR•
Nagoya Institute of Technology
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•– Box-Muller
••
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.5 1 1.5 2 2.5 3amplitude
pro
babilit
y de
nsity
funct
ion
amp_n
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
-1 -0.5 0 0.5 1radian / pi
pro
babilit
y d
ens
ity func
tion
rad_n
Nagoya Institute of Technology
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•
•
• K Tss
s
0 T sec
N
0 N/(2T) Hz
N
-N/(2T)
, sN sK T KT
2 2s s
s sfT T
Nagoya Institute of Technology
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• 2 Eb/N0 dB
•BnTs=1
2
2QPSK 02
b
n s
EC S A kN N B T N
0
20.1 ( / dB)2 10
2bE NA
k
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•
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••
–––
•–
–
–
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