martin stemick and hermann rohling hamburg university of technology institute of telecommunications...
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Martin Stemick and Hermann Rohling
Hamburg University of Technology
Institute of Telecommunications
Effect of Carrier Frequency Offset Effect of Carrier Frequency Offset
on Channel Capacityon Channel Capacity
in Multi User OFDM-FDMA Systemsin Multi User OFDM-FDMA Systems
Institute of Telecommunications Dipl.-Ing. M. Stemick 2
Motivation
Frequency
|Hk|2
Subcarrier Allocation
In frequency-selective radio channels, OFDM-FDMA provides
• high data rates
• high degree of adaptivity
Adaptive subcarrier allocation exploits Multi User Diversity:
Institute of Telecommunications Dipl.-Ing. M. Stemick 3
Cell Model
Single cell with N users at the
same distance from base station
0 4 8 12 16 20-40
-30
-20
-10
0
10
Bandwidth [MHz]
|H|2 [
dB]
user 1
user 2
user 3
256 subcarriers
WSSUS ChannelDownlink Situation
BS
MT
Institute of Telecommunications Dipl.-Ing. M. Stemick 4
Multi User Diversity and Blocksize
-6 -4 -2 0 2 4 6 810
-4
10-3
10-2
10-1
100
SNR (dB)
BE
R
4.7dB
-6 -4 -2 0 2 4 6 810
-4
10-3
10-2
10-1
100
SNR (dB)
BE
R
7 dB
QPSK, R=1/2, 16 users
blocksize 8 subcarrierwise
→ Smaller blocksize yields higher diversity gain
random select.
adapt. select.
Institute of Telecommunications Dipl.-Ing. M. Stemick 5
Pure Multi User Diversity
-6 -4 -2 0 2 4 6 810
-4
10-3
10-2
10-1
100
SNR (dB)
BE
R
6dB
-6 -4 -2 0 2 4 6 810
-4
10-3
10-2
10-1
100
SNR (dB)
BE
R
7 dB
-6 -4 -2 0 2 4 6 810
-4
10-3
10-2
10-1
100
SNR (dB)
BE
R
5dB
Subcarrierwise selection, QPSK, R=1/2
→ Adaptive subcarrier allocation yields a high diversity gain
4 users 8 users 16 users
Increasing number of users
random select.
adapt. select.
Institute of Telecommunications Dipl.-Ing. M. Stemick 6
Cell Model in the Uplink
subcarriers
Uplink Situation:
• Signals of mobile terminals superimpose at base station
• Every MT shows individual Carrier Frequency Offset (CFO)
• Non-ideal synchronization leads to Intercarrier Interference (ICI)
BS
MT
Bandwidth at BS
Institute of Telecommunications Dipl.-Ing. M. Stemick 7
Analytical Model for Intercarrier Interference
Received Signal at BS:
, , ,ICI AWG
v v v v v vY H X N N
→ Stochastic modeling of
→ Deterministic description of ICI noise quite complexICIvN
ICI noise depends on transmit symbols from all other usersICIvN
Since transmit symbols can be modeled as random variables
ICIvN
,vX
Institute of Telecommunications Dipl.-Ing. M. Stemick 8
Analytical Model for Intercarrier Interference
Stochastic assumptions:
• Modulation symbols are statistically independent random variables
*, , 0l k i jE X X for l j k j
• Transmit power is normalized
2
, 1l kE X
→ Therefore, we can apply the central limit theorem:
22,( , ) ICI
ICI l vl v E N (ICI noise power)
Institute of Telecommunications Dipl.-Ing. M. Stemick 9
Analytical Model for Intercarrier Interference
2122
, 20
sin( , )
Nl
ICI l kk lk v
f k vl v H
f k v
1
, 21
21 2cos
N
vd
N dL d f
N N N
2
, ,
12 2
0
( , ) ( )u
v v
v N
ICI AWGl
L HSNR
l v v
This leads to the following description of ICI influence:
(ICI noise power)
(Rx power loss)
(Overall SNR)
Institute of Telecommunications Dipl.-Ing. M. Stemick 10
Example for Intercarrier Interference
/f f0 1 2 3 4 5
δf0
user 0
user 1
Power Loss
Self-Interference
External Interference
| Rec
eive
-Am
plitu
de |
Institute of Telecommunications Dipl.-Ing. M. Stemick 11
Evaluation of CFO on Allocation Schemes
…
… ……
user 0
user 1
user 1uN
Considering various subcarrier allocation schemes
in multi user systems:
• Blockwise allocation (various blocksizes)
• Interleaved allocation
subcarriers
subcarriers
Institute of Telecommunications Dipl.-Ing. M. Stemick 12
Evaluation of ICI Noise
0 0.1f
Blockwise allocation: 2 users, 2 blocks, blocksize 128
user 0 user 1
-45
-40
-35
-30
-25
-20
-15
-10
σ2 ICI [d
B]
0 64 128 192 256subcarriers
1 0f
user 0
user 1
Institute of Telecommunications Dipl.-Ing. M. Stemick 13
Evaluation of ICI Noise
-10
-15
-20
-25
-30
-35
-40
-45
σ2 ICI [d
B]
0 64 128 192 256
subcarriers
user 1
user 0
…user 0
user 1
Blockwise / Interleaved allocation: 2 users, 16 blocks, blocksize 16
0 0.1f
Institute of Telecommunications Dipl.-Ing. M. Stemick 14
Evaluation of ICI Noise
The distribution of ICI noise in the system depends
very much on the subcarrier allocation scheme
• Blockwise allocation produces self-interference
• Interleaved allocation reduces self-interference but
increases external interference
Institute of Telecommunications Dipl.-Ing. M. Stemick 15
Effect of CFO on Capacity
Using Shannon Capacity to quantify the effect of CFO
on the system performance:
2 of
user
log 1l vv
l
C SNR
Shannon Capacity of user l :
[bits / OFDM-Sym.]
After evaluation of noise power for individual users, a measure
for the performance of a multi user system is needed
Institute of Telecommunications Dipl.-Ing. M. Stemick 16
System Model
BS
MT
Uplink Situation
• AWGN Channel
• WSSUS Channel
System assumptions:
• 256 carriers, 16 users
• various allocation schemes
• random subcarrier assignment subcarriers
…
………
Institute of Telecommunications Dipl.-Ing. M. Stemick 17
Simulation Results (AWGN Channel)
First Scenario:
• All users in the cell are perfectly synchronized, except one
• Capacity of badly synchronized user is observed for
various allocation schemes
49
50
51
52
53
54
55
56
Bits
per
OF
DM
-Sym
bol
f0 0.02 0.04 0.06 0.08 0.1
Blocksize 16Blocksize 8Blocksize 4Blocksize 1Interleaved
Institute of Telecommunications Dipl.-Ing. M. Stemick 18
Simulation Results (AWGN Channel)
Second Scenario:
• All users in the cell show consistent CFO of , except one
• Capacity of perfectly synchronized user is observed for
various allocation schemes
f
Bits
per
OF
DM
-Sym
bol
0 0.02 0.04 0.06 0.08 0.149
50
51
52
53
54
55
56
f
Blocksize 16Blocksize 8Blocksize 4Blocksize 1Interleaved
Institute of Telecommunications Dipl.-Ing. M. Stemick 19
Comparison WSSUS AWGN
0 0.02 0.04 0.06 0.08 0.142
44
46
48
50
52
54
56B
its p
er O
FD
M-S
ymbo
l.
f
Blocksize 16Blocksize 8Blocksize 4Blocksize 1InterleavedAWGNWSSUS
Second Scenario in AWGN and WSSUS Environment:
Institute of Telecommunications Dipl.-Ing. M. Stemick 20
Summary & Conclusions
• Adaptive allocation yields high performance gains in the downlink
• In the uplink, interference due to non-ideal synchronization
must be considered
• Choice of allocation scheme influences interference distribution
and system performance
• This can be especially of interest in adaptive allocation schemes,
where interference is the main noise contribution
Institute of Telecommunications Dipl.-Ing. M. Stemick 21
Thank you for your attentionThank you for your attention
Institute of Telecommunications Dipl.-Ing. M. Stemick 22
Results (wrong!!!)
0 0.02 0.04 0.06 0.08 0.153
53.5
54
54.5
55
55.5
56
f
B
its p
er O
FD
M-S
ym.
Blocksize 16Blocksize 8Blocksize 4Blocksize 1Interleaved
one good user, all other unsynched, perf of good user.
Institute of Telecommunications Dipl.-Ing. M. Stemick 23
Multi User Diversity and Blocksize
-6 -4 -2 0 2 4 6 810
-4
10-3
10-2
10-1
100
SNR (dB)
BE
R
best.block.seladapt.selnon.adapt.sel
4.7dB
-6 -4 -2 0 2 4 6 810
-4
10-3
10-2
10-1
100
SNR (dB)
BE
R
best chan. seladapt.selectnon.adapt.sel
7 dB
QPSK, R=1/2, 16 users
blocksize 8 subcarrierwise
→ Smaller blocksize yields higher diversity gain
Institute of Telecommunications Dipl.-Ing. M. Stemick 24
Pure Multi User Diversity
-6 -4 -2 0 2 4 6 810
-4
10-3
10-2
10-1
100
SNR (dB)
BE
R
best.subc.seladapt.selnon.adapt.sel
6dB
-6 -4 -2 0 2 4 6 810
-4
10-3
10-2
10-1
100
SNR (dB)
BE
R
best chan. seladapt.selectnon.adapt.sel
7 dB
-6 -4 -2 0 2 4 6 810
-4
10-3
10-2
10-1
100
SNR (dB)
BE
R
best.subc.seladapt.selnon.adapt.sel
5dB
Subcarrierwise selection, QPSK, R=1/2
→ Adaptive subcarrier allocation yields a high diversity gain
4 users 8 users 16 users
Increasing number of users
random select.
adapt. select.
best subc. select.