An introduction to Bandwidth Allocation in OFDM

1. An introduction to Bandwidth Allocation in OFDM Presented by 96598002 嚴 雷 (Lei Yan)

2. Outline • References • Introduction to Bandwidth Allocation with contexts • Related algorithms for Bandwidth Allocation • Simulation • Conclusion

3. References [1] H. T. Cheng, W. Zhuang, “Joint Power-Frequency-Time Resource Allocation in Wireless Mesh Networks”, IEEE Network, January/Febuary, 2008, pp. 45-51 [2] C. Y. Wong et al., “Multiuser OFDM with Adaptive Subcarrier, Bit, andPower Allocation,” IEEE JSAC, vol. 17, no. 10, Oct. 1999, pp. 1747–58. [3] D. Kivanc and H. Liu, “Subcarrier Allocation and Power Control for OFDMA,” Proc. 34th Asilomar Conf. Sig., Sys. and Computers, 2000, pp. 147–51. [4] Didem Kivanc, Guoqing Li, and Hui Liu, “Computationally Efficient Bandwidth Allocation and Power Control for OFDMA”, IEEE Transctions on Wireless Communications, Vol. 2, NO. 6, November, 2003, pp. 1150-1158 [5] G. Song and Y. Li, “Utility-Based Resource Allocation and Scheduling inOFDM-Based Wireless Broadband Networks,” IEEE Commun. Mag., vol. 43,no. 12, Dec. 2005, pp. 127–34.

4. References (cont.) [6] Prof. H. P. Lin’s slides for OFDM, ftp://140.124.72.57 [7] Prof. Jung-Lang Yu’s slides for Spread Spectrum Communications, Ch6, 2005, pp. 2-3 [8] http://www.wikipedia.org/OFDM [9] http://www.wikipedia.org/OFDMA [10] S. Haykin, “Communication Systems 4ed., 2001”, Wiley&Sons [11] J. T. Yuan, Z. C. Lin, C. H. Guo, N. Z. Xiao, L. Yan, “Comparison of LMS-Based Algorithms in Adaptive Equalization”, EEFJU Workshop on Research and Development, 2005 [12] http://bbs.matwav.com/post/view?bid=28&id=199262&sty= 3&age=0&tpg=1&ppg=1#199262

5. An inspiration from Information Theory • Using Shannon’s Information Capacity theorem under Additive White Gaussian Noise (AWGN) condition, the channel capacity for signal equals Where: C = the maximum reliable transmission bandwidth B = channel bandwidth SNR = received signal-to-noise ratio =

6. An inspiration from Information Theory (cont.) • To enhance channel reliability, we have to enlarge the channel bandwidth or SNR (add power) at transmitter. • So the question is: What/How can we do for the power/bandwidth control at the right place, right time?

7. A brief to Orthogonal Frequency Division Multiplexing (OFDM) • Frequency: Base band in subcarriers • Goal: To overcome Intersymbol Interference (ISI) due to multipath delay fading • Method: Using guard intervals after data by zero-padding on time domain to cancel the multipath delay

8. A brief to OFDM (cont.) • The multipath propagation is shown below: • And the received signal is shown below:

9. A brief to OFDM (cont.) The Infrastructure of OFDM:

10. A brief to OFDM (cont.) A simplified flow for OFDM transmission/reception: Interfered by ISI

11. A brief to OFDM (cont.) • How guard interval works:

12. Delay u(n)=interfered data ＋ d(n) = data ＋ ISI Channel LMS Equalizer － y(n)=estimated d(n) AWGN e(n)=d(n)-y(n), the estimated error A brief to OFDM (cont.) • An alternative to canceling ISI: The Adaptive Least Mean-Square error (LMS) Equalizer at the receiving end ＋

13. A brief to OFDM (cont.) • Simulation steps for the LMS Equalizer: • Compute the error between the desired data and the interfered (ISI + AWGN) one 2. Put error into the weighted Equalizer with LMS algorithm recursively and then we can have a gradually minimized error (close to min. mean-square error)

14. A brief to OFDM (cont.) • The communication channel can be seen as a filter-like block diagram shown below: where or via Fourier Transform for any non-periodic signal a(t)

15. ISI+AWGN Channel C(f) Demodulator LMS Equalizer L(f) Receiving end A brief to OFDM (cont.) • Goal of the LMS algorithm: • The LMS Equalizer spectrum could vary all the time to satisfy Desired signal Transmitted signal

16. A brief to OFDM (cont.) Q: Why now the LMS Equalizers become no more popular than OFDM? A: Under large interferences like satellite signals, the LMS Equalizers need more weights, which adds complexity to design, but OFDM is free instead (using guard interval) Q: So, what are the LMS Equalizers used in the industry? A: FM/AM demodulator in your flash disk

17. A brief to OFDM (cont.) • Pros for OFDM: • No equalizer needed • Robustness against ISI • Cons for OFDM: • FFT consumes system resource much • Sensitive to subcarrier frequency offset

18. A brief to OFDM (cont.) • Ex: IEEE 802.11a specification: • Data rate: • 6, 9, 12, 18, 24, 36, 48, 54 Mbit/s, depending on SNR • User throughput (1500 byte packets): 5.3 (6), 18 (24), 24 (36), 32 (54), 6, 12, 24 Mbit/s mandatory • Transmission range: • 100m outdoor, 10m indoor • Frequency: • Free 5.15-5.25, 5.25-5.35, 5.725-5.825 GHz ISM-band • Security: • Limited, WEP insecure, SSID • Connection set-up time: • Connectionless/always on • Quality of Service: • Typ. best effort, no guarantees (same as all 802.11 products) • Manageability: • Limited (no automated key distribution, sym. Encryption) • Applications: IEEE 802.11a/g/n modulator and antenna module for vehicle TV (ex: 民視飛來訊),…etc

19. A brief to OFDMA • OFDMA = OFDM + FDMA • The spectrum of OFDMA:

20. Goal of Bandwidth Allocation • Step1-Resource Allocation : Find the averaged number of subcarrier needed for each user • Step2-Subcarrier Allocation: According to the outcome from step1, the system “borrow” subcarriers from users that are sufficient of rate requirements to those who are insufficient.

21. Goal of Bandwidth Allocation (cont.) • Water filling method can divide power to all subcarriers into the same level

22. Goal of Bandwidth Allocation (cont.) • Q: Why does adding subcarriers work for improving SNR? • A: By the formula of channel capacity represented for one subcarrier below, adding more carriers (B.W) to user can also have the SNR risen, which spares the additional power for rising the SNR • Key: As the number of subcarrier rises, the total channel capacity will increase, and so as the total SNR.

23. A brief of Bandwidth Allocation • The communication channel can be seen as a filter-like block diagram shown below: where or via Fourier Transform for any non-periodic signal a(t)

24. A brief of Bandwidth Allocation (cont.) • The channel gain for h(t) equals: or Generally speaking, the channel gain is unpredictable since the channel varies all the time, so if we want to adjust the received power, then we have to change the input power first.

25. Bandwidth Allocation in multiuser OFDM • In multiuser case, we have to do power and subcarrieer allocation in order to flexibly serve users with reasonable quality

26. Bandwidth Allocation in multiuser OFDM (cont.) • A more clearer graph below:

27. Bandwidth Allocation in multiuser OFDM (cont.) • [2] adopt the summary previously announced in power control: • Where: = the transmitted power, allocated to the nth subcarrier by kth user • = the received power, allocated to the nth subcarrier by kth user • = the channel gain, allocated to the nth subcarrier by kth user • = the number of bits of the kth user assigned to the nth subcarrier

28. Bandwidth Allocation in multiuser OFDM (cont.) Steps for resource allocation: [2] tends to minimize power in the view of bits: • To have the min. power each subcarrier subject to the min. transmission rate • Using Lagrangian optimization to get the optimal bits, , to minimize power for all users given the same Quality of Service (QoS).

29. Resource Allocation in multiuser OFDM (cont.) • The transmitted power is shown as below: • Where is the weight to minimize power for kth user and nth subcarrier such that

30. Resource Allocation in multiuser OFDM (cont.) • [3], the alternative does the same thing but in the view of min. total transmission rate and number of subcarriers with the same definition of , , , and the channel gain • Subject to

31. Bandwidth Allocation in multiuser OFDM (cont.) • The Bandwidth Assignment Based on SNR (BABS) algorithm finds the optimal number of subcarriers per user

32. Subcarrier Allocation in multiuser OFDM • Rate Craving Greedy Algorithm dynamically balances subcarriers fairly (目標為平均分配頻寬)

33. Subcarrier Allocation in multiuser OFDM (cont.) • How the RCG works:

34. Subcarrier Allocation in multiuser OFDM (cont.) • To lower complexity of RCG, the Amplitude Craving Greedy (ACG) Algorithm has lowered complexity from to

35. Subcarrier Allocation in multiuser OFDM (cont.) • Comparison of complexity:

36. Subcarrier Allocation in multiuser OFDM (cont.) • Simulation parameters and channels

37. Subcarrier Allocation in multiuser OFDM (cont.) • Compare Power/Rate with/without water filling:

38. Subcarrier Allocation in multiuser OFDM (cont.) • Compare CPU time with/without water filling:

39. Subcarrier Allocation in multiuser OFDM (cont.) • Summary: 1. ACG reduces complexity but has more power transmitted than RCG 2. BABS+ACG, BABS+RCG, and TDMA perform well than Lagrange Relaxation 3. With water filing, all algorithms reduce the Power/Rate needed a few

40. Conclusion • OFDM is so far the optimal solution to cancel ISI • To provide users acceptable bandwidth without enhancing QoS in OFDM, bandwidth allocation algorithms are needed • As OFDM becomes more important since the adoption by WiMAX, bandwidth algorithms may become a hot topic

41. Thank You!!