9-mc modulation and ofdm
TRANSCRIPT
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9. Multi Carrier Modulation and OFDM
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ifsymbol duration >>time spreadthen there is almost no InterSymbol Interference (ISI).
1 0 time
channel
1 0
phase still recognizable
ST
Problem with this: Low Data Rate!!!
Single Carrier Modulation in Flat Fading Channels
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this corresponds to Flat Fading
Frequency Frequency
channel
ST/1
Flat Freq. Response
Frequency
in the Frequency Domain
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ifsymbol duration ~time spreadthen there is considerable InterSymbol Interference (ISI).
1 0
time
channel
? ?
phase not recognizable
Single Carrier Modulation in Frequency Selective Channels
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In MC modulation each MC symbol is defined on a time interval and it contains a
block of data
gT bT
Symbol
T
data interval
t
guard interval
. .time
OFDM Symbol
data datadatadata
data
MAXgT X" MAX channel time spreadwith
Structure of Multi Carrier Modulation
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. .
the guardtimeislong
enough,so the multipath inoneblockdoesnotaffect the
nextblock
Data BlockData Block
TX RX
We leave a guard time
between blocks to allowmultipath
gT
Guard Time
bT
SymbolT
data+guard
Guard Time
. .
_
TX
RX
NO Inter Block Interference!
gT
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!
{!
(!2
20
2)(
FN
FN
k
k
k
tFkj
kectxT
data!kc
offsetfrequencysubcarrier!(Fk
SymbolTtee0
Baseband Complex Signal:
MC Signal
Transmitted Signal:
_ a)(Re)( 2 txets tFj CT!frequencycarrierCF
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Orthogonal Subcarriers and OFDM
gT
bT data intervalt
guard interval
bTF
1
!(
{
!!!
(
N
NNN
k
kdte
T
dtee
T
bb
k
Tt
t
Ftkj
b
Tt
t
tFjtFj
b if0
if111 0
0
0
0
)(222 TTT
Choose:
Orthogonality:
FCF
F(
FkFF Ck (!
FN F(
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Let
be the sampling frequency;
be the number of data samples in each symbol;
the subcarriers spacing
Then:
SF
NFTNF SS //1 !!(
!
!
!!
( 2
2
)(2
2
)(2 211)(
F
F
N
F
F
sFF
N
Nk
Lnjk
k
N
Nk
Lnkj
kS ec
N
ec
N
nTxTT 1,..,0 ! NLn
FNN"
with the guard time.Sg TLT v!
OFDM symbols in discrete time
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Summary OFDM Symbol
SS
FT /1!
t0 gT
L
bT
FNN"
Sampling Interval
guard data
TIME:
NFF S /!(
F
N
FN SF
2
Freq spacing
FREQUENCY:
2/SF2/SF
N
FN SF
2
0
# samples
# subcarriers
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OFDM Symbol and FFT
_ a][][1
11
1][
1
0
1
2
)(2
1
2
2
2
22
2
kXIFFTekXN
ec
N
ec
N
ecN
Lnx
N
k
njk
Nk
nkNj
k
N
k
njk
k
N
Nk
njkk
N
F
N
F
N
F
F
N
!
!
!
!
!!
!
!
T
TT
T
otherwise,0][
2/,...,1,][
2/,...,1,][
!
!!
!!
kX
NkckNX
NkckX
Fk
Fk
Where:positive subcarriers
negative subcarriers
unused subcarriers
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OFDM Demodulator
_ a
21
0
21
0
[ ] [ ]* [ ]1
[ ]* [ ]
1 [ ] [ ] [ ] [ ]
N j knN
k
N j knN
k
y n L h n x n L
h n X k eN
H kX k e IFFT H kX k
N
T
T
!
!
!
!
! !
_ a]1[],...,[][][ ! NLyLyFFTkXkH
with_ a[ ] [0],..., [ 1],0,..., 0H k FFT h h L! 1,...,0 ! Nk
See each block:
n
0 1L 1 NL
No InterBlock Interference
][ny
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Overall Structure of OFDM Comms System
-
!
]1[
]1[]0[
NX
XX
X/
IFFT +CP P/S
][nh
FFT -CP S/P
N NLN
LN
LN
LN NN
W
NXNH
XH
XH
Y
-
!
]1[]1[
]1[]1[
]0[]0[
/
][nw
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OFDM as Parallel Flat Fading Channels
Significance: a Freq. Selective Channel becomes NFlat Fading
Channels
OFDM
Mod
OFDM
Demod/ /
)(tx ( )y t
Frequency
Selective
channel
]0[mX
[ 1]mX N/
[0]mY
[ 1]mY N/
/
]0[mX [0]mY
[ 1]mY N
( )w t
]0[H
[0]m
W
[ 1]mX N [ 1]H N
[ 1]m
W N/ /
NFlat
Fading
Channels
( )h t
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OFDM Parameters
Summarize basic OFDM Parameters:
sampling rate in Hz
N length of Data Field in number of samples
L length of Cyclic Prefix in number of samples
total number of Data Subcarriers
SF
F
N Ne
N
/St T
data
Ltime
SFF/0
data
/F
N N
frequency
guard guard guard
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IEEE 802.11a:
Frequency Bands: 5.150-5.350 GHz and 5.725-5.825 GHz (12 channels)
Modulation OFDM
Range: 100m
IEEE 802.11g
Frequency Bands: 2.412-2.472GHz
Modulation: OFDM
Range: 300m
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Channel Parameters: FCC
Example: the Unlicensed Band 5GHz U-NII (Unlicensed National
Information Infrastructure)
4 channels in the range 5.725-5.825GHz
8 channels in the range 5.15-5.35GHz
)(MHzF5150 5350
MHz30 MHz3020MHz
5180 5200
.
5300 5320
CF
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Channel Parameters: Example IEEE802.11
In terms of a Transmitter Spectrum Mask (Sec. 17.3.9.2 inIEEE Std 802.11a-1999)
CF99 1111 2020 3030
dB0
20dB
28dB
40dB
)(MHzF
Typical Signal
Spectrum
Typical BW~16 MHz
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In either case:
MHzFS 20! Sampling frequency
64!N
16!L
FFT size
Cyclic Prefix
64!N16!N
64 / 20 3.2 secbT Q! !16 / 20 0.8 sec
gT Q! !
DATACP
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Sub-carriers: (48 data + 4 pilots) + (12 nulls) = 64
Pilots at: -21, -7, 7, 21
01
26
38
63
/
/
/
NULL
NULL
0
63
/
/
/
/
Frequency Time
1c
26c
26c
1c
0x
63x
IFFT
52!FN 64!N
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k2638 64 26
20 /64 312.5 F MHz kHz( ! !
( ) F MHz
8.1258.125
CARRIERF
)(MHzF
MHz25.16
DATA
Frequencies:
sTMHz /120 !
163 Subcarriersindex
10CARRIER
F 10CARRIERF
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Overall Implementation (IEEE 802.11a with 16QAM).
1. Map encoded data into blocks of192bits and 48 symbols:
data EncodeInterleave
010011010101
Buffer
(192 bits)
1110
0111
1000
1101
4x48=192 bits
Map to
16QAM
48
4
+1+j3
-1+j
+3-j3
+1-j
a"
48
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Overall Implementation (IEEE 802.11a with 16QAM).
2. Map each block of48 symbols into 64 samples
[ ]mX k
+1+j3
-3-j
+3-j3
+1-j
/
01
2627
6427 /
/
6426 /
[0]mx
IFFT
0
12
63
62
time domainfrequency domain
null
null
24 data
2 pilots
24 data
2 pilots
/
..
k1 2626
641
1
[ ]m
a " [ ]m
x n
1:48!" 0:63k ! 0:63n !
[1]mx
[62]mx[63]mx
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Constraints on OFDM Symbol Duration:
to minimize CP overhead
1 /MAXMAX g b D
T T FX
sec10 6 sec10 3 roughly!!!
Frequency Spread
Time Spread
),( FSXF
X
kHzFMAXD
indoorsec5010
outdoorsec101
nMAX
MAX
}
}
X
QX
for channel Time Invariant
Channel Parameters: Physical
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Summary of OFDM and Channel Parameters
Channel:
1. Max Time S pread sec
2. Doppler S pread Hz
3. Bandwidth Hz
4. Channel S pacing Hz
OFDM (design parameters):
1. Sampling Frequency
2. Cyclic Prefix
3. FFT size (power of2)
4. Number of Carriers
MAXX
MAXDF
BW
SF
SF
integerMAX S L FXu
4 / integerMAXS D
L N F F e
? A/ integerF S N N BW F ! v
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Channel:
1. Max Time Spread
2. Doppler Spread
3. Bandwidth
4. Channel Spacing
OFDM (design parameters):
1. Sampling Frequency
2. Cyclic Prefix
3. FFT size (power of2)
4. Number of Carriers
0.5 secMAXX Q!50
MAXDF Hz!
16BW MHz!
20SF MHz!
20SF MHz!
16 0.5 20 10L ! " v !664 20 10 / 50 integerN! v
? A52 64 16 / 20 integerFN ! ! v
Example: IEEE802.11a
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According to the applications, we define three AreaNetworks:
Personal Area Network (PAN), for communications within a few meters. This is the typicalBluetooth or Zigbee application between between personal devices such as your cell phone,
desktop, earpiece and so on;
Local Area Network (LAN), for communications up 300 meters. Access points at the
airport, coffee shops, wireless networking at home. Typical standard is IEEE802.11 (WiFi) or
HyperLan in Europe. It is implemented by access points, but it does not support mobility;
Wide Area Network (WAN), for cellular communications, implemented by towers. Mobilityis fully supported, so you can move from one cell to the next without interruption. Currently it
is implemented by Spread Spectrum Technology via CDMA, CDMA-2000,TD-SCDMA,
EDGE and so on. The current technology, 3G, supports voice and data on separate networks.
For(not so) future developments, 4G technology will be supporting both data and voice on the
same network and the standard IEEE802.16 (WiMax) seems to be very likely
Applications: various Area Networks
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