1 / 41

OFDMA Downlink Resource Allocation for Ergodic Capacity Maximization with Imperfect Channel Knowledge

OFDMA Downlink Resource Allocation for Ergodic Capacity Maximization with Imperfect Channel Knowledge. *Ian C. Wong and Brian L. Evans The University of Texas at Austin IEEE Globecom 2007 Washington, D.C. *Dr. Wong is now with Freescale Semiconductor, Austin, TX. User 1. frequency.

seda
Télécharger la présentation

OFDMA Downlink Resource Allocation for Ergodic Capacity Maximization with Imperfect Channel Knowledge

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. OFDMA Downlink Resource Allocation for Ergodic Capacity Maximization with Imperfect Channel Knowledge *Ian C. Wong and Brian L. Evans The University of Texas at Austin IEEE Globecom 2007 Washington, D.C. *Dr. Wong is now with Freescale Semiconductor, Austin, TX

  2. User 1 frequency Base Station User M (Subcarrier and power allocation) Orthogonal Frequency Division Multiple Access (OFDMA) • Used in IEEE 802.16d/e (now) and 3GPP-LTE (2009) • Multiple users assigned different subcarriers • Inherits advantages of OFDM • Granular exploitation of diversity among users through channel state information (CSI) feedback . . .

  3. OFDMA Resource Allocation • How do we allocate K datasubcarriers and total power P to M users to optimize some performance metric? • E.g. IEEE 802.16e: K = 1536, M¼40 / sector • Very active research area • Difficult discrete optimization problem (NP-complete [Song & Li, 2005]) • Brute force optimal solution: Search through MK subcarrier allocations and determine power allocation for each

  4. Related Work * Considered some form of temporal diversity by maximizing an exponentially windowed running average of the rate ** Independently developed a similar instantaneous continuous rate maximization algorithm *** Only for instantaneous continuous rate case, but was not shown in their papers

  5. Summary of Contributions

  6. Diagonal gain matrix Diagonal channel matrix Noise vector OFDMA Signal Model • Downlink OFDMA with K subcarriers and M users • Perfect time and frequency synchronization • Free of inter-symbol and inter-carrier interference • Received K-length vector for mth user at nth symbol

  7. Statistical Wireless Channel Model • Frequency-domain channel • Stationary and ergodic • Complex normal with correlated channel gains across subcarriers • Time-domain channel • Stationary and ergodic • Complex normal and independent across taps i and users m

  8. MMSE Channel Prediction Partial Channel State Information Model • Stationary and ergodic channel gains • MMSE channel prediction Conditional PDF of channel-to-noise ratio (CNR) – Non-central Chi-squared Predicted CNR: Normalized error variance:

  9. Continuous Rate Maximization:Partial CSI with Perfect CDI Nonlinear integer stochastic program • Maximize conditional expectation given the estimated CNR • Power allocation a function of predicted CNR • Parametric analysis is not required, thus

  10. 1-D Integral (> 50 iterations) Computational bottleneck 1-D Root-finding (<10 iterations) Dual Optimization Framework “Multi-level waterfilling on conditional expected CNR”

  11. Power Allocation Function Approximation • Use Gamma distribution to approximate the Non-central Chi-squared distribution [Stüber, 2002] • Approximately 300 times faster than numerical quadrature (tic-toc in Matlab)

  12. Conditional PDF Runtime O(MKI (Ip+Ic)) Predicted CNR O(1) O(MK) O(K) Optimal Resource Allocation – Ergodic Capacity given Partial CSI M – No. of users K – No. of subcarriers I – No. of line-search iterations Ip – No. of zero-finding iterations for power allocation function Ic – No. of function evaluations for numerical integration of expected capacity

  13. Simulation Parameters (3GPP-LTE) Channel Snapshot

  14. Two-User Capacity Region M – No. of users; K – No. of subcarriers I – No. of line-search iterations Ip – No. of zero-finding iterations for power allocation function Ic – No. of function evaluations for numerical integration of expected capacity

  15. Comparison with Previous Work * Considered some form of temporal diversity by maximizing an exponentially windowed running average of the rate ** Only for instantaneous continuous rate case, but was not shown in their papers

  16. Conclusion • Developed a framework for OFDMA downlink resource allocation • Based on dual optimization techniques • Negligible duality gaps with linear complexity • Ergodic capacity with imperfect CSI • Related work • Discrete rate • No CDI assumptions

  17. Relevant Journal Publications [J1] I. C. Wong and B. L. Evans, "Optimal Resource Allocation in OFDMA Systems with Imperfect Channel Knowledge,“ IEEE Trans. on Communications., submitted Oct. 1, 2006, resubmitted Feb. 13, 2007. [J2] I. C. Wong and B. L. Evans, "Optimal OFDMA Resource Allocation with Linear Complexity to Maximize Ergodic Rates," IEEE Trans. on Wireless Communications, accepted for publication. Relevant Conference Publications [C1] I. C. Wong and B. L. Evans, ``Optimal OFDMA Subcarrier, Rate, and Power Allocation for Ergodic Rates Maximization with Imperfect Channel Knowledge'', Proc. IEEE Int. Conf. on Acoustics, Speech, and Signal Proc., April 16-20, 2007, Honolulu, HI USA. [C2] I. C. Wong and B. L. Evans, ``Optimal OFDMA Resource Allocation with Linear Complexity to Maximize Ergodic Weighted Sum Capacity'', Proc. IEEE Int. Conf. on Acoustics, Speech, and Signal Proc., April 16-20, 2007, Honolulu, HI USA. [C3] I. C. Wong and B. L. Evans, ``Optimal Downlink OFDMA Subcarrier, Rate, and Power Allocation with Linear Complexity to Maximize Ergodic Weighted-Sum Rates'', Proc. IEEE Int. Global Communications Conf., November 26-30, 2007 Washington, DC USA, submitted Questions?

  18. Backup Slides • Notation • Related Work • Stoch. Prog. Models • C-Rate,P-CSI Dual objective • Instantaneous Rate • D-Rate,P-CSI Dual Objective • PDF of D-Rate Dual • Duality Gap • D-Rate,I-CSI Rate/power functions • Proportional Rates • Proportional Rates - adaptive • Summary of algorithms

  19. Notation Glossary

  20. Related Work • OFDMA resource allocation with perfect CSI • Ergodic sum rate maximizatoin [Jang, Lee, & Lee, 2002] • Weighted-sum rate maximization [Hoo, Halder, Tellado, & Cioffi, 2004] [Seong, Mohseni, & Cioffi, 2006] [Yu, Wang, & Giannakis, submitted] • Minimum rate maximization [Rhee & Cioffi, 2000] • Sum rate maximization with proportional rate constraints [Wong, Shen, Andrews, & Evans, 2004] [Shen, Andrews, & Evans, 2005] • Rate utility maximization [Song & Li, 2005] • Single-user systems with imperfect CSI • Single-carrier adaptive modulation [Goeckel, 1999] [Falahati, Svensson, Ekman, & Sternad, 2004] • Adaptive OFDM [Souryal & Pickholtz, 2001][Ye, Blum, & Cimini 2002][Yao & Giannakis, 2004] [Xia, Zhou, & Giannakis, 2004]

  21. Stochastic Programming Models [Ermoliev & Wets, 1988] • Non-anticipative • Decisions are made based only on the distribution of the random quantities • Also known as non-adaptive models • Anticipative • Decisions are made based on the distribution and the actual realization of the random quantities • Also known as adaptive models • 2-Stage recourse models • Non-anticipative decision for the 1st stage • Recourse actions for the second stage based on the realization of the random quantities

  22. C-Rate P-CSI Dual Objective Derivation Lagrangian: Dual objective Linearity of E[¢] Separability of objective Power a function of RV realization Exclusive subcarrier assignment m,k not independent but identically distributed across k

  23. Runtime CNR Realization O(IMK) O(1) O(1) M – No. of users K – No. of subcarriers I – No. of line-search iterations N – No. of function evaluations for integration O(K) Optimal Resource Allocation – Instantaneous Capacity with Perfect CSI

  24. Discrete Rate Perfect CSI Dual Optimization • Discrete rate function is discontinuous • Simple differentiation not feasible • Given , for all , we have • L candidate power allocation values • Optimal power allocation:

  25. PDF of Discrete Rate Dual • Derive the pdf of

  26. Performance Assessment - Duality Gap

  27. Duality Gap Illustration M=2 K=4

  28. Sum Power Discontinuity M=2 K=4

  29. BER/Power/Rate Functions • Impractical to impose instantaneous BER constraint when only partial CSI is available • Find power allocation function that fulfills the average BER constraint for each discrete rate level • Given the power allocation function for each rate level, the average rate can be computed • Derived closed-form expressions for average BER, power, and average rate functions

  30. Average rate function: Closed-form Average Rate and Power Power allocation function: Marcum-Q function

  31. Ergodic Sum Rate Maximization with Proportional Ergodic Rate Constraints Developed adaptive algorithm without CDI Ergodic Sum Capacity • Allows more definitive prioritization among users • Traces boundary of capacity region with specified ratio Average Power Constraint Proportionality Constants Ergodic Rate for User m

  32. Dual Optimization Framework • Reformulated as weighted-sum rate problem with properly chosen weights Multiplier for rate constraint Multiplier for power constraint “Multi-level waterfilling with max-dual user selection”

  33. Projected Subgradient Search Power constraint multiplier search Multiplier iterates Step sizes Derived pdfs for efficient 1-D Integrals Subgradients Projection Rate constraint multiplier vector search Per-user ergodic rate:

  34. Optimal Resource Allocation – Ergodic Proportional Rate with Perfect CSI Initialization PDF of CNR O(INM2) Runtime CNR Realization O(MK) O(MK) M – No. of users K – No. of subcarriers I– No. of subgradient search iterations N – No. of function evaluations for integration O(K)

  35. Adaptive Algorithms for Rate Maximization Without Channel Distribution Information (CDI) • Previous algorithms assumed perfect CDI • Distribution identification and parameter estimation required in practice • More suitable for offline processing • Adaptive algorithms without CDI • Low complexity and suitable for online processing • Based on stochastic approximation methods

  36. Averaging time constant Subgradient approximates Solving the Dual Problem Using Stochastic Approximation Projected subgradient iterations across time with subgradient averaging - Proved convergence to optimal multipliers with probability one Power constraint multiplier search Multiplier iterates Subgradient Averaging Step sizes Subgradients Projection Rate constraint multiplier vector search

  37. Subgradient Approximates “Instantaneous multi-level waterfilling with max-dual user selection”

  38. Optimal Resource Allocation- Ergodic Proportional Rate without CDI Weighted-sum, Discrete Rate and Partial CSI are special cases of this algorithm

  39. Two-User Capacity Region OFDMA Parameters (3GPP-LTE) 1 = 0.1-0.9 (0.1 increments) 2 = 1-1

  40. Evolution of the Iterates for 1=0.1 and 2 = 0.9 User Rates Rate constraint Multipliers  Power Power constraint Multipliers l

  41. Summary of the Resource Allocation Algorithms

More Related