Resource Allocation for Mobile Multiuser Orthogonal Frequency Division Multiplexing Systems

1. Resource Allocation for Mobile Multiuser Orthogonal Frequency Division Multiplexing Systems Prof. Brian L. Evans Embedded Signal Processing Laboratory Dept. of Electrical and Computer Engineering The University of Texas at Austin July 5, 2006 bevans@ece.utexas.edu Featuring work by PhD students Zukang Shen (now at TI) and Ian WongCollaboration with Prof. Jeffrey G. Andrews and Prof. Robert W. Heath

2. Outline • Introduction • Resource allocation in wireless systems • Multiuser OFDM (MU-OFDM) • Resource allocation in MU-OFDM • MU-OFDM resource allocation with proportional rates • Near-optimal solution • Low-complexity solution • Real-time implementation • OFDM channel state information prediction • Comparison of algorithms • High-resolution joint estimation and prediction • Multiuser OFDM resource allocation using predicted channel state information 2

3. frequency code/spatial user 4 user 5 user 6 user 1 user 2 user 3 time Resource Allocation in Wireless Systems • Wireless local area networks (WLAN) 54--108 Mbps • Metropolitan area networks (WiMAX) ~10--100 Mbps • Limited resources shared by multiple users • Transmit power • Frequency bandwidth • Transmission time • Code resource • Spatial antennas • Resource allocation impacts • Power consumption • User throughput • System latency 3

4. channel magnitude subcarrier frequency Bandwidth Orthogonal Frequency Division Multiplexing • Adopted by many wireless communication standards • IEEE 802.11a/g WLAN • Digital Video Broadcasting – Terrestrial and Handheld • Broadband channel divided into narrowband subchannels • Multipath resistant • Receiver equalization simpler than single-carrier systems • Uses static time or frequency division multiple access OFDM Baseband Spectrum 4

5. User 1 User 2 frequency Base Station User K (Subcarrier and power allocation) Multiuser OFDM • Orthogonal frequency division multiple access (OFDMA) • Adopted by IEEE 802.16a/d/e standards • 802.16e: 1536 data subchannels with up to 40 users / sector • Users may transmit on different subcarriers at same time • Inherits advantages of OFDM • Exploits diversity among users . . . 5

6. Exploiting Multiuser Diversity • Downlink multiuser OFDM • Users share subchannels and basestation transmit power • Users only decode their own data 6

7. : user k’s capacity (bits/s/Hz) as continuous function for single cell Multiuser OFDM Resource Allocation 7

8. Outline • Introduction • Resource allocation in wireless systems • Multiuser-OFDM (MU-OFDM) • Resource allocation in MU-OFDM • MU-OFDM resource allocation with proportional rates • Near-optimal solution • Low-complexity solution • Real-time implementation • OFDM channel state information prediction • Comparison of algorithms • High-resolution joint estimation and prediction • Multiuser OFDM resource allocation using predicted channel state information 8

9. MU-OFDM with Proportional Rates • Objective: Sum capacity • Constraints • Total transmit power • No subchannel shared by multiple users • Proportional rate constraints • Advantages • Allows different service privileges and different pricing 9

10. Two-Step Near-Optimal Solution • Subchannel allocation step • Greedy algorithm – allow user with leastallocated capacity/proportionality to choosebest subcarrier [Rhee & Cioffi, 2000] • Modified to incorporate proportional rates • Computational complexity O(K N log N) • Power allocation step [Shen, Andrews & Evans, 2005] • Exact solution given a subcarrier allocation • General case • Solution to set of K non-linear equations in K unknowns • Newton-Raphson methods are O(n K) where n is no. of iterations • Special case: High channel-to-noise ratio • Solution finds a root of a polynomial with O(n K) complexity • Typically 10 iterations in simulation K - # users N - # subchannels n - # iterations 10

11. 10 8 7 4 Lower Complexity Solution • In practical scenarios, rough proportionality is acceptable • Key ideas to simplify Shen’s approach[Wong, Shen, Andrews & Evans, 2004] • Relax strict proportionality constraint • Require predetermined number of subchannelsto be assigned to simplify power allocation • Power allocation • Solution to sparse set of linear equations • Computational complexity O(K) • Advantages [Wong, Shen, Andrews & Evans, 2004] • Waives high channel-to-noise ratio assumption of Shen’s method • Achieves higher capacity with lower complexity vs. Shen’s method • Maintains acceptable proportionality of user data rates Example 11

12. Simulation Parameters 12

13. Total Capacity Comparison N = 64 subchannels SNR = 38 dB SNR Gap = 3.3 dB Based on 10000 channel realizations Proportions assigned randomly from {4,2,1} with probabilities[0.2, 0.3, 0.5] Wong’s Method Shen’s Method 13

14. Proportionality Comparison Based on the 16-user case, 10000 channel realizations per user Normalized rate proportions for three classes of users using proportions {4, 2, 1} Proportions Wong’s Method Shen’s Method 14

15. Real-time Software Prototype LabVIEW 7.0 LabVIEW handles the interface between Matlab and the DSP and automates allocation tests. TMS320C6701 Digital Signal Processor (DSP) Matlab 6.5 Matlab generates a frequency-selective Rayleigh channel for each user. The DSP receives Channel State Information and performs resource allocation algorithm. 15

16. Computational Complexity 22% average improvement Code developed in floating point C Run on 133 MHzTI TMS320C6701 DSP EVM board 16

17. Memory Usage * All values are in bytes 17

18. Performance Comparison Summary 18

19. Outline • Introduction • Resource allocation in wireless systems • Multiuser-OFDM (MU-OFDM) • Resource Allocation in MU-OFDM • MU-OFDM resource allocation with proportional rates • Near-optimal solution • Low-complexity solution • Real-time implementation • OFDM channel state information prediction • Comparison of algorithms • High-resolution joint estimation and prediction • Multiuser OFDM resource allocation using predicted channel state information 19

20.  Back haul t= Internet t=0 Delayed Channel State Information mobile t=0: Mobile estimates channel and feeds this back to base station t=: Base station receives estimates, adapts transmission based on these Higher BER Lower bits/s/Hz Channel mismatch [Souryal & Pickholtz, 2001] 20

21. h(n-p) h(n-) h(n+) ? h(n) … Prediction of Wireless Channels • Use current and previous channel estimates to predict future channel response • Overcome feedback delay • Adaptation based on predicted channel response • Reduce amount of feedback • Predicted channel responsemay reduce how often directchannel feedback is provided 21

22. Pilot Subcarriers IFFT … … Data Subcarriers Time-domain channel taps Related Work • Prediction on each subcarrier [Forenza & Heath, 2002] • Each subcarrier treated as a narrowband autoregressive process[Duel-Hallen et al., 2000] • Prediction using pilot subcarriers [Sternad & Aronsson, 2003] • Used unbiased power prediction [Ekman, 2002] • Prediction on time-domain channel taps[Schafhuber & Matz, 2005] • Used adaptive prediction filters 22

23. OFDM Channel Prediction Comparison • Compared three approaches in unified framework[Wong, Forenza, Heath & Evans, 2004] • Analytical and numerical mean squared error comparison • All-subcarrier and pilot-subcarrier methods have similar mean squared error performance • Time-domain prediction performs much better than the two other frequency domain prediction methods • Complexity comparison • All-subcarrier > Pilot-subcarrier ¸ Time-domain 23

24. High-resolution OFDM Channel Prediction • Combined channel estimation and prediction[Wong & Evans, 2005] • Outperforms previous methods with similar order of computational complexity • Allows decoupling of computations between receiver and transmitter • High-resolution channel estimates available as aby-product of prediction algorithm 24

25. Deterministic Channel Model • Outdoor mobile macrocell scenario • Far-field scatterer (plane wave assumption) • Linear motion with constant velocity • Small time window (a few wavelengths) • Channel model • Used in modeling and simulation ofwireless channels [Jakes 1974] • Used in ray-tracing channelcharacterization [Rappaport 2002] n OFDM symbol indexk subchannel index 25

26. Prediction via 2-D Frequency Estimation • If we accurately estimate parameters in channel model, we could effectively extrapolate the fading process • Estimation and extrapolation period should be within time window where model parameters are stationary • Estimation of two-dimensional complex sinusoids in noise • Well studied in radar, sonar, and other array signal processing applications [Kay, 1988] • Many algorithms available, but are computationally intensive 26

27. Two-step 1-D Frequency Estimation • Typically, many propagation paths share the same resolvable time delay • We can thus break down the problem into two steps • Time-delay estimation • Doppler-frequency estimation 27

28. IEEE 802.16e Simulation 28

29. Mean-square Error vs. SNR Prediction 2  ahead ACRLB – Asymptotic Cramer-Rao Lower Bound CRLB – Cramer-Rao Lower Bound 29

30. Mean-square Error vs. Prediction Length SNR = 7.5 dB ACRLB – Asymptotic Cramer-Rao Lower Bound CRLB – Cramer-Rao Lower Bound 30

31. Performance Comparison Summary L - No. of paths M - No. of rays per path 31

32. MU-OFDM Resource Allocation with Predicted Channel State Infomation (Future) • Combine MU-OFDM resource allocation with long-range channel prediction • Using the statistics of the channel prediction error, we can stochastically adapt to the channel • Requires less channel feedback • More resilient to channel feedback delay • Improved overall throughput 32

33. Conclusion • Resource allocation for MU-OFDM with proportional rates • Allows tradeoff between sum capacity and user rate “fairness” to enable different service privileges and pricing • Derived efficient algorithms to achieve similar performance with lower complexity • Prototyped system in a DSP, showing its promise for real-time implementation • Channel prediction for OFDM systems • Overcomes the detrimental effect of feedback delay • Proposed high-performance OFDM channel prediction algorithms with similar complexity • Resource allocation using predicted channels is important for practical realization of resource allocation in MU-OFDM 33

34. Youssof Mortazavi Aditya Chopra Marcel Nassar Hamood Rehman Ian Wong Embedded Signal Processing Laboratory • Director: Prof. Brian L. Evans • http://www.ece.utexas.edu/~bevans/ • WiMAX (OFDM) related research • Algorithms for resource allocation in Multiuser OFDM • Algorithms for OFDM channel estimation and prediction • Key collaborators: Prof. Jeffrey Andrews and Prof. Robert Heath • Key graduate students: 34

35. Backup 35

36. Subchannel Allocation • Modified method of [Rhee et al., 2000], but we keep the assumption of equal power distribution on subchannels • Initialization (Enforce zero initial conditions)Set , for . Let • For to (Allocate best subchannel for each user) • Find satisfying for all • Let , and update • While (Iteratively give lowest rate user first choice) • Find satisfying for all • For the found , find satisfying for all • For the found and , Let , and update Back 36

37. Water-level subchannels Power Allocation for a Single User • Optimal power distribution for user • Order • Water-filling algorithm • How to find for 37

38. Power Allocation among Many Users • Use proportional rate and total power constraints • Solve nonlinear system of K equations: /iteration • Two special cases • Linear case: , closed-form solution • High channel-to-noise ratio: and where Back 38

39. Comparison with Optimal Solution Back 39

40. Comparison with Max-Min Capacity 40

41. Comparison with Max Sum Capacity 41

42. Summary of Shen’s Contribution • Adaptive resource allocation in multiuser OFDM systems • Maximize sum capacity • Enforce proportional user data rates • Low complexity near-optimal resource allocation algorithm • Subchannel allocation assuming equal power on all subchannels • Optimal power distribution for a single user • Optimal power distribution among many users with proportionality • Advantages • Evaluate tradeoff between sum capacity and user data rate fairness • Fill the gap of max sum capacity and max-min capacity • Achieve flexible data rate distribution among users • Allow different service privileges and pricing 42

43. Wong’s 4-Step Approach • Determine number of subcarriers Nkfor each user • Assign subcarriers to each user to give rough proportionality • Assign total power Pk for each user to maximize capacity • Assign the powers pk,n for each user’s subcarriers (waterfilling) O(K) O(KNlogN) O(K) O(N) 43

44. 10 8 7 4 Simple Example N = 4 subchannels K = 2 users Ptotal = 10 Desired proportionality among data rates 1 = 3/4 9 2 = 1/4 6 5 3 44

45. 10 8 7 4 1 2 3 4 Step 1: # of Subcarriers/User 1 = 3/4 9 2 = 1/4 6 5 3 N = 4 subchannels K = 2 users Ptotal = 10 45

46. 9 10 8 7 10 10 10 4 8 7 10 8 4 7 9 4 6 10 4 5 6 8 7 5 3 3 1 1 2 2 3 3 4 4 Step 2: Subcarrier Assignment Rk Rtot log2(1+2.5*10)=4.70 log2(1+2.5*8)=4.39 13.3 log2(1+2.5*7)=4.21 log2(1+2.5*9)=4.55 4.55 46

47. 10 10 8 9 7 1 2 3 4 Step 3: Power per user P1 = 7.66 P2 = 2.34 N = 4 subchannels; K = 2 users; Ptotal = 10 Back 47

48. 10 10 8 9 7 1 2 3 4 Step 4: Power per subcarrier • Waterfilling across subcarriers for each user P1 = 7.66 P2 = 2.34 p1,1= 2.58 p1,2= 2.55 p1,3= 2.53 p2,1= 2.34 Data Rates: R1 = log2(1 + 2.58*10) + log2(1 + 2.55*8) + log2(1 + 2.53*7) = 13.39008 R2 = log2(1+ 2.34*9) = 4.46336 Back 48

49. … f Df t Dt Pilot-based Transmission • Comb pilot pattern • Least-squares channel estimates 49

50. Prediction over all the subcarriers • Design prediction filter for each of the Nd data subcarriers • Mean-square error 50