Effect of Carrier Frequency Offset
on Channel Capacity
in Multi User OFDM-FDMA Systems
Martin Stemick and Hermann Rohling
Hamburg University of Technology
Institute of Telecommunications
Motivation
In frequency-selective radio channels, OFDM-FDMA provides
• high data rates
• high degree of adaptivity
Adaptive subcarrier allocation exploits Multi User Diversity:
|Hk|2
Subcarrier Allocation
Frequency
Institute of Telecommunications
Dipl.-Ing. M. Stemick
2
Cell Model
BS
10
|H|2[dB]
0
MT
-10
-20
user 1
-30
user 2
user 3
Single cell with N users at the
-40
0
4
8
12
Bandwidth [MHz]
16
same distance from base station
256 subcarriers
Downlink Situation
WSSUS Channel
Institute of Telecommunications
Dipl.-Ing. M. Stemick
20
3
Multi User Diversity and Blocksize
adapt. select.
QPSK, R=1/2, 16 users
random select.
0
0
10
10
-1
-1
10
BER
BER
10
-2
10
4.7dB
-3
-2
10
-3
10
10
7 dB
-4
10
-6
-4
-4
-2
0
2
SNR (dB)
4
6
8
blocksize 8
10
-6
-4
-2
0
2
SNR (dB)
4
6
8
subcarrierwise
→ Smaller blocksize yields higher diversity gain
Institute of Telecommunications
Dipl.-Ing. M. Stemick
4
Pure Multi User Diversity
adapt. select.
Subcarrierwise selection, QPSK, R=1/2
0
0
10
0
10
-1
10
-1
-1
10
-2
10
5dB
-3
10
10
BER
BER
10
BER
random select.
-2
10
6dB
-3
10
-2
10
-3
10
7 dB
-4
10
-6
-4
-2
0
2
SNR (dB)
4
6
4 users
8
10
-4
-6
-4
-4
-2
0
2
SNR (dB)
8 users
4
6
8
10
-6
-4
-2
0
2
SNR (dB)
4
6
8
16 users
Increasing number of users
→ Adaptive subcarrier allocation yields a high diversity gain
Institute of Telecommunications
Dipl.-Ing. M. Stemick
5
Cell Model in the Uplink
BS
Bandwidth at BS
MT
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)
Institute of Telecommunications
Dipl.-Ing. M. Stemick
6
Analytical Model for Intercarrier Interference
Received Signal at BS:
Yv   ,v H ,v X  ,v  N vICI  N vAWG
ICI noise N vICI depends on transmit symbols from all other users
ICI
→ Deterministic description of ICI noise N v quite complex
Since transmit symbols X  ,v can be modeled as random variables
ICI
→ Stochastic modeling of N v
Institute of Telecommunications
Dipl.-Ing. M. Stemick
7
Analytical Model for Intercarrier Interference
Stochastic assumptions:
• Modulation symbols are statistically independent random variables
E  X l ,k X i*, j   0
for l  j  k  j
• Transmit power is normalized

E X l ,k
2
 1
→ Therefore, we can apply the central limit theorem:

Institute of Telecommunications
2
ICI

(l , v)  E N
Dipl.-Ing. M. Stemick
ICI 2
l ,v

(ICI noise power)
8
Analytical Model for Intercarrier Interference
This leads to the following description of ICI influence:
N 1
2
 ICI
(l , v)   H l ,k
k 0
k v
L ,v
2
sin 2   fl  k  v  
  f
l
 k  v 
2
1 N 1 2  N  d 
 2

 
cos
d


f
 

N d 1 N 2
 N

SNRv 
L ,v H  ,v
Nu 1

l 0
Institute of Telecommunications
2
ICI
(ICI noise power)
(Rx power loss)
2
(Overall SNR)
2
(l , v)   AWG
(v )
Dipl.-Ing. M. Stemick
9
Example for Intercarrier Interference
user 0
user 1
| Receive-Amplitude |
δf0
Power Loss
Self-Interference
External Interference
f / f
0
Institute of Telecommunications
1
2
Dipl.-Ing. M. Stemick
3
4
5
10
Evaluation of CFO on Allocation Schemes
Considering various subcarrier allocation schemes
in multi user systems:
• Blockwise allocation (various blocksizes)
…
subcarriers
user 0
• Interleaved allocation
user 1
user N u  1
…
…
…
subcarriers
Institute of Telecommunications
Dipl.-Ing. M. Stemick
11
Evaluation of ICI Noise
Blockwise allocation: 2 users, 2 blocks, blocksize 128
 f1  0
 f 0  0.1
user 0
user 1
-10
user 0
user 1
-15
σ2ICI [dB]
-20
-25
-30
-35
-40
-45
0
Institute of Telecommunications
64
128
subcarriers
Dipl.-Ing. M. Stemick
192
256
12
Evaluation of ICI Noise
Blockwise / Interleaved allocation: 2 users, 16 blocks, blocksize 16
 f 0  0.1
user 0
…
-10
user 1
user 1
-15
σ2ICI [dB]
-20
-25
-30
user 0
-35
-40
-45
0
Institute of Telecommunications
64
128
subcarriers
Dipl.-Ing. M. Stemick
192
256
13
Evaluation of ICI Noise
• Blockwise allocation produces self-interference
• Interleaved allocation reduces self-interference but
increases external interference
The distribution of ICI noise in the system depends
very much on the subcarrier allocation scheme
Institute of Telecommunications
Dipl.-Ing. M. Stemick
14
Effect of CFO on Capacity
After evaluation of noise power for individual users, a measure
for the performance of a multi user system is needed
Using Shannon Capacity to quantify the effect of CFO
on the system performance:
Shannon Capacity of user l :
Cl 
Institute of Telecommunications
 log 1  SNR 
v of
user l
2
Dipl.-Ing. M. Stemick
v
[bits / OFDM-Sym.]
15
System Model
BS
• AWGN Channel
• WSSUS Channel
MT
Uplink Situation
System assumptions:
…
• 256 carriers, 16 users
• various allocation schemes
• random subcarrier assignment
Institute of Telecommunications
Dipl.-Ing. M. Stemick
…
…
…
subcarriers
16
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
Bits per OFDM-Symbol
56
55
54
53
52
51
50
49
0
Institute of Telecommunications
Blocksize 16
Blocksize 8
Blocksize 4
Blocksize 1
Interleaved
0.02
0.04
Dipl.-Ing. M. Stemick
f
0.06
0.08
0.1
17
Simulation Results (AWGN Channel)
Second Scenario:
• All users in the cell show consistent CFO of  f , except one
• Capacity of perfectly synchronized user is observed for
various allocation schemes
Bits per OFDM-Symbol
56
55
54
53
52
51
50
49
0
Institute of Telecommunications
Blocksize 16
Blocksize 8
Blocksize 4
Blocksize 1
Interleaved
0.02
0.04
Dipl.-Ing. M. Stemick
f
0.06
0.08
0.1
18
Comparison WSSUS
AWGN
Second Scenario in AWGN and WSSUS Environment:
56
Bits per OFDM-Symbol.
54
52
Blocksize 16
Blocksize 8
Blocksize 4
Blocksize 1
Interleaved
AWGN
WSSUS
50
48
46
44
42
0
Institute of Telecommunications
0.02
0.04
Dipl.-Ing. M. Stemick
f
0.06
0.08
0.1
19
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
20
Thank you for your attention
Institute of Telecommunications
Dipl.-Ing. M. Stemick
21
Results (wrong!!!)
56

Bits per OFDM-Sym.
55.5
55
54.5
54
53.5

53
0
Blocksize 16
Blocksize 8
Blocksize 4
Blocksize 1
Interleaved
0.02
0.04
0.06
0.08
0.1
f

one good user, all other unsynched, perf of good user.
Institute of Telecommunications
Dipl.-Ing. M. Stemick
22
Multi User Diversity and Blocksize
QPSK, R=1/2, 16 users
0
0
10
10
best.block.sel
adapt.sel
non.adapt.sel
-1
-1
10
BER
BER
10
-2
10
4.7dB
-3
best chan. sel
adapt.select
non.adapt.sel
-2
10
-3
10
10
7 dB
-4
10
-6
-4
-4
-2
0
2
SNR (dB)
4
6
8
blocksize 8
10
-6
-4
-2
0
2
SNR (dB)
4
6
8
subcarrierwise
→ Smaller blocksize yields higher diversity gain
Institute of Telecommunications
Dipl.-Ing. M. Stemick
23
Pure Multi User Diversity
best subc. select.
Subcarrierwise selection, QPSK, R=1/2
adapt. select.
random select.
0
0
10
best.subc.sel
adapt.sel
non.adapt.sel
-1
BER
-2
5dB
-3
best.subc.sel
adapt.sel
non.adapt.sel
10
10
10
10
-1
-2
10
6dB
-3
10
best chan. sel
adapt.select
non.adapt.sel
10
BER
-1
10
BER
0
10
-2
10
-3
10
7 dB
-4
10
-6
-4
-2
0
2
SNR (dB)
4
6
4 users
8
10
-4
-6
-4
-4
-2
0
2
SNR (dB)
8 users
4
6
8
10
-6
-4
-2
0
2
SNR (dB)
4
6
8
16 users
Increasing number of users
→ Adaptive subcarrier allocation yields a high diversity gain
Institute of Telecommunications
Dipl.-Ing. M. Stemick
24