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9. Multi Carrier Modulation and OFDM. Frequency Spread. Time Spread. Transmission of Data Through Frequency Selective Time Varying Channels. We have seen a wireless channel is characterized by time spread and frequency spread. Single Carrier Modulation in Flat Fading Channels. - PowerPoint PPT Presentation
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9. Multi Carrier Modulation and OFDM
Transmission of Data Through Frequency Selective Time Varying Channels
We have seen a wireless channel is characterized by time spread and frequency spread.
Time Spread
Frequency Spread ),( FS
F
MEAN
MAXDF
RMSRMS
• if symbol duration >> time spread then there is almost no Inter Symbol Interference (ISI).
1 0 time
channel
1 0phase still recognizable
ST
Problem with this: Low Data Rate!!!
Single Carrier Modulation in Flat Fading Channels
• this corresponds to Flat Fading
Frequency Frequencychannel
ST/1Flat Freq. Response
Frequency
… in the Frequency Domain
• if symbol duration ~ time spread then there is considerable Inter Symbol Interference (ISI).
1 0time
channel
? ?phase not recognizable
Single Carrier Modulation in Frequency Selective Channels
One Solution: we need equalization
channel equalizer
1 0time
1 0time
Channel and Equalizer
Problems with equalization:• it might require training data (thus loss of bandwidth)• if blind, it can be expensive in terms computational effort• always a problem when the channel is time varying
• let symbol duration >> time spread so there is almost no Inter Symbol Interference (ISI);
• send a block of data using a number of carriers (Multi Carrier)
1 0
time channel
time
time
0
0
1
1
“symbol” “symbol”
The Multi Carrier Approach
Compare Single Carrier and Multi Carrier Modulation
Frequency Frequency
channel
0 1 0 1 1 1
Block of symbols
subcarriers
Each subcarrier sees a Flat Fading
Channel: Easy Demod
MC
Frequency
1
One symbol
Frequency
Flat Fading Channel: Easy Demod
SC
101 1
0 1 0 1 1 1
In MC modulation each “MC symbol” is defined on a time interval and it contains a block of data
gT bT
SymbolT
data interval
t
guard interval
time
OFDM Symbol
data datadatadata
data
MAXgT MAX channel time spreadwith
Structure of Multi Carrier Modulation
the “guard time” is long enough, so the multipath in one block does not affect the next block
Data BlockData Block
TX RX
We leave a “guard time” between blocks to allow multipath
gTGuard Time
bT
SymbolTdata+guard
Guard Time
TX
RX
NO Inter Block Interference!
gT
2
20
2)(FN
FN
k
kk
tFkjkectx
datakc
offsetfrequency subcarrierFk
SymbolTt 0
Baseband Complex Signal:
MC Signal
Transmitted Signal:
)(Re)( 2 txets tFj Cfrequencycarrier CF
“Orthogonal” Subcarriers and OFDM
gT bT data intervalt
guard interval
bTF 1
kk
dteT
dteeT
bb
k
Tt
t
Ftkj
b
Tt
t
tFjtFj
b if 0 if 111 0
0
0
0
)(222
Choose:
Orthogonality:
FCF
F
FkFF Ck
FN F
still orthogonal at the receiver!!!
bg
g
k
TT
T
tFj
bkk dtety
TFHc 2)(1
)(1
Orthogonality at the Receiver
)(tht0
0
transient response
bg TT
bgg TTtT
tFj ke 2
gT
bg TT
Transmitted subcarrier Channel
(LTI)
Received subcarrier
k
tFjk
kectx 2)( k
tFjkk
keFHcty 2)()(
bg TTt 0
steady state response
)()( thFTFH
t
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
Lnjkk
N
Nk
LnkjkS ec
Nec
NnTx
1,..,0 NLn
FNN
with the guard time.Sg TLT
OFDM symbols in discrete time
Summary OFDM Symbol
SS FT /1t0 gT
L
bT
FNN
Sampling Interval
guard data
TIME:
NFF S /
FNFN SF
2
Freq spacing
FREQUENCY:2/SF2/SF
NFN SF
2
0
# samples# subcarriers
OFDM Symbol and FFT
][][1
11
1][
1
0
1
2
)(2
1
2
2
2
22
2
kXIFFTekXN
ecN
ecN
ecN
Lnx
N
k
njk
Nk
nkNjk
N
k
njkk
N
Nk
njkk
N
F
N
F
N
F
F
N
otherwise ,0][2/,...,1 ,][
2/,...,1 ,][
kXNkckNX
NkckX
Fk
Fk
Where:positive subcarriers
negative subcarriers
unused subcarriers
][][ nNxnx
]1[]1[...
]1[]1[][]0[
NLxLx
NxxNxx
Guard Time with Cyclic Prefix (CP)
1,...,0],[]1[],...,[ NkkXIFFTNLxLx
N
0 L 1 NL
CP from the periodicity
IFFT{ X }CP
OFDM Demodulator
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 k X k e IFFT H k X kN
]1[],...,[][][ NLyLyFFTkXkH
with [ ] [0],..., [ 1],0,...,0H k FFT h h L 1,...,0 Nk
See each block:
n0 1L 1 NL
No Inter Block Interference
][ny
Overall Structure of OFDM Comms System
]1[
]1[]0[
NX
XX
X
IFFT +CP P/S
][nh
FFT -CP S/P
N N LN LN
LN
LN NN
W
NXNH
XHXH
Y
]1[]1[
]1[]1[]0[]0[
][nw
To recover the transmitted signal you need a very simple one gain equalization:
][][][][ kWkXkHkY
received transm. noise
channel
Use simple Wiener Filter:
][][
][][ˆ22
*
kYkH
kHkXW
Simple One Gain Equalization
OFDM as Parallel Flat Fading Channels
Significance: a Freq. Selective Channel becomes N Flat 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]mW
[ 1]mX N [ 1]H N
[ 1]mW N
N Flat Fading
Channels
( )h t
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
FN N
N/ St T
data
Ltime
SFF /0
data
/FN Nfrequency
guard guard guard
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
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
Channel Parameters: Example IEEE802.11
In terms of a Transmitter Spectrum Mask (Sec. 17.3.9.2 in IEEE Std 802.11a-1999)
CF 99 1111 2020 3030
dB0
20dB
28dB
40dB
)(MHzF
Typical Signal Spectrum
Typical BW~16 MHz
In either case:
MHzFS 20 Sampling frequency
64N16L
FFT sizeCyclic Prefix
64N16N64 / 20 3.2 secbT
16 / 20 0.8 secgT
DATACP
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
52FN 64N
k2638 64 26
20 / 64 312.5F MHz kHz
( )F MHz
8.1258.125
CARRIERF)(MHzF
MHz25.16
DATA
Frequencies:
sTMHz /120
163 Subcarriers index
10CARRIERF 10CARRIERF
Time Block:
sec2.3 FFTT
sec105064/ 9 FFTs TT
sec8.0 GT
sec0.4 FRAMET
time
Overall Implementation (IEEE 802.11a with 16QAM).
1. Map encoded data into blocks of 192 bits and 48 symbols:
data Encode Interleave
…010011010101…
Buffer (192 bits)
111001111000
…
1101
4x48=192 bits
Map to 16QAM
…48
4
+1+j3-1+j
+3-j3…
+1-j
a
48
Overall Implementation (IEEE 802.11a with 16QAM).
2. Map each block of 48 symbols into 64 samples
[ ]mX k
+1+j3…
-3-j+3-j3
…+1-j
01
2627
6427
6426
[0]mx
IFFT
012
6362
time domainfrequency domainnull
null
24 data 2 pilots
24 data 2 pilots
k1 2626
641
1
[ ]ma [ ]mx n1: 48 0 : 63k 0 : 63n
[1]mx
[62]mx[63]mx
Constraints on OFDM Symbol Duration:
to minimize CP overhead
1/MAXMAX g b DT T F
sec10 6 sec10 3 roughly!!!
Frequency Spread
Time Spread
),( FS F
kHzF
MAXD
indoor sec5010outdoor sec101
nMAX
MAX
for channel Time Invariant
Channel Parameters: Physical
Summary of OFDM and Channel Parameters
Channel:
1. Max Time Spread sec
2. Doppler Spread Hz
3. Bandwidth Hz
4. Channel Spacing Hz
OFDM (design parameters):
1. Sampling Frequency
2. Cyclic Prefix
3. FFT size (power of 2)
4. Number of Carriers
MAX
MAXDF
BW
SF
SF
integerMAX SL F
4 / integerMAXS DL N F F
/ integerF SN N BW F
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 of 2)
4. Number of Carriers
0.5 secMAX
50MAXDF Hz
16BW MHz
20SF MHz
20SF MHz
16 0.5 20 10L
664 20 10 / 50 integerN
52 64 16 / 20 integerFN
Example: IEEE802.11a
According to the applications, we define three “Area Networks”:
• Personal Area Network (PAN), for communications within a few meters. This is the typical Bluetooth 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. Mobility is 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
More Applications
1. WLAN (Wireless Local Area Network) standards and WiFi. In particular:• IEEE 802.11a in Europe and North America• HiperLAN /2 (High Performance LAN type 2) in Europe and North America• MMAC (Mobile Multimedia Access Communication) in Japan
2. WMAN (Wireless Metropolitan Network) and WiMax• IEEE 802.16
3. Digital Broadcasting• Digital Audio and Video Broadcasting (DAB, DVB) in Europe
4. Ultra Wide Band (UWB) Modulation• a very large bandwidth for a very short time.
5. Proposed for IEEE 802.20 (to come) for high mobility communications (cars, trains …)
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