1. Martin Stemick and Hermann Rohling Hamburg University of Technology Institute of Telecommunications Effect of Carrier Frequency Offset on Channel Capacity in Multi User OFDM-FDMA Systems

2. Institute of Telecommunications Dipl.-Ing. M. Stemick2 Motivation Frequency |H k | 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:

3. Institute of Telecommunications Dipl.-Ing. M. Stemick3 Cell Model Single cell with N users at the same distance from base station WSSUS ChannelDownlink Situation BS MT

4. Institute of Telecommunications Dipl.-Ing. M. Stemick4 Multi User Diversity and Blocksize -6-4-202468 10 -4 10 -3 10 -2 10 10 0 SNR (dB) BER 7 dB QPSK, R=1/2, 16 users blocksize 8subcarrierwise → Smaller blocksize yields higher diversity gain random select. adapt. select.

5. Institute of Telecommunications Dipl.-Ing. M. Stemick5 Pure Multi User Diversity Subcarrierwise selection, QPSK, R=1/2 → Adaptive subcarrier allocation yields a high diversity gain 4 users8 users 16 users Increasing number of users random select. adapt. select.

6. Institute of Telecommunications Dipl.-Ing. M. Stemick6 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

7. Institute of Telecommunications Dipl.-Ing. M. Stemick7 Analytical Model for Intercarrier Interference Received Signal at BS: → Stochastic modeling of → Deterministic description of ICI noise quite complex ICI noise depends on transmit symbols from all other users Since transmit symbols can be modeled as random variables

8. Institute of Telecommunications Dipl.-Ing. M. Stemick8 Analytical Model for Intercarrier Interference Stochastic assumptions: Modulation symbols are statistically independent random variables for Transmit power is normalized → Therefore, we can apply the central limit theorem: (ICI noise power)

9. Institute of Telecommunications Dipl.-Ing. M. Stemick9 Analytical Model for Intercarrier Interference This leads to the following description of ICI influence: (ICI noise power) (Rx power loss) (Overall SNR)

10. Institute of Telecommunications Dipl.-Ing. M. Stemick10 Example for Intercarrier Interference 0 12 3 4 5 δf0δf0 user 0 user 1 Power Loss Self-Interference External Interference | Receive-Amplitude |

11. Institute of Telecommunications Dipl.-Ing. M. Stemick11 Evaluation of CFO on Allocation Schemes … … … … user 0 user 1 user Considering various subcarrier allocation schemes in multi user systems: Blockwise allocation (various blocksizes) Interleaved allocation subcarriers

12. Institute of Telecommunications Dipl.-Ing. M. Stemick12 Evaluation of ICI Noise Blockwise allocation: 2 users, 2 blocks, blocksize 128 user 0 user 1

13. Institute of Telecommunications Dipl.-Ing. M. Stemick13 Evaluation of ICI Noise -10 -15 -20 -25 -30 -35 -40 -45 σ 2 ICI [dB] 0 64128 192 256 subcarriers user 1 user 0 … user 1 Blockwise / Interleaved allocation: 2 users, 16 blocks, blocksize 16

14. Institute of Telecommunications Dipl.-Ing. M. Stemick14 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

15. Institute of Telecommunications Dipl.-Ing. M. Stemick15 Effect of CFO on Capacity Using Shannon Capacity to quantify the effect of CFO on the system performance: 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

16. Institute of Telecommunications Dipl.-Ing. M. Stemick16 System Model BS MT Uplink Situation AWGN Channel WSSUS Channel System assumptions: 256 carriers, 16 users various allocation schemes random subcarrier assignment subcarriers … … ……

17. Institute of Telecommunications Dipl.-Ing. M. Stemick17 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 OFDM-Symbol 00.020.040.060.080.1 Blocksize 16 Blocksize 8 Blocksize 4 Blocksize 1 Interleaved

18. Institute of Telecommunications Dipl.-Ing. M. Stemick18 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 Bits per OFDM-Symbol 00.020.040.060.080.1 49 50 51 52 53 54 55 56 Blocksize 16 Blocksize 8 Blocksize 4 Blocksize 1 Interleaved

19. Institute of Telecommunications Dipl.-Ing. M. Stemick19 Comparison WSSUS AWGN Bits per OFDM-Symbol. Blocksize 16 Blocksize 8 Blocksize 4 Blocksize 1 Interleaved AWGN WSSUS Second Scenario in AWGN and WSSUS Environment:

20. Institute of Telecommunications Dipl.-Ing. M. Stemick20 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

21. Institute of Telecommunications Dipl.-Ing. M. Stemick21 Thank you for your attention

22. Institute of Telecommunications Dipl.-Ing. M. Stemick22 Results (wrong!!!) 00  0.02  0.04  0.06  0.08  0.1  53  53.5  54  54.5  55  55.5  56  ff  Bits per OFDM-Sym.    Blocksize 16  Blocksize 8  Blocksize 4  Blocksize 1  Interleaved one good user, all other unsynched, perf of good user.

23. Institute of Telecommunications Dipl.-Ing. M. Stemick23 Multi User Diversity and Blocksize QPSK, R=1/2, 16 users blocksize 8subcarrierwise → Smaller blocksize yields higher diversity gain

24. Institute of Telecommunications Dipl.-Ing. M. Stemick24 Pure Multi User Diversity Subcarrierwise selection, QPSK, R=1/2 → Adaptive subcarrier allocation yields a high diversity gain 4 users8 users 16 users Increasing number of users random select. adapt. select. best subc. select.