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.