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Optimal Spectrum Management

Optimal Spectrum Management. Contents. Optimal Spectrum Management Achieves maximum possible rates for modems within network Up to 300% rate gains over IW Crosstalk Precompensation Ginis’ QR Precompensator (requires modification of CPE) Row-wise diagonal dominance

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Optimal Spectrum Management

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  1. Optimal Spectrum Management Optimal Spectrum Management

  2. Contents • Optimal Spectrum Management • Achieves maximum possible rates for modems within network • Up to 300% rate gains over IW • Crosstalk Precompensation • Ginis’ QR Precompensator (requires modification of CPE) • Row-wise diagonal dominance • Linear Diagonalizing Precompensator (near optimal, no change of CPE) • Partial Cancellation • Distributing compute power across frequency • Large run-time complexity reduction Optimal Spectrum Management

  3. Optimal Spectrum Management • Joint work together with Wei Yu (Uni. of Toronto), Alcatel Bell • Goal: Characterise border of rate region • Find optimal operating points • Corresponding TX PSDs • In DSL channels equivalent to maximising weighted rate-sumtransmit spectra of user n:sn= [ s1n...sKn ] • 2 user example to simplify discussion ( > 2 users straight-forward) • Non-convex • Cannot use convex optimisation techniques! Optimal Spectrum Management

  4. Exhaustive Search • Limit skn to take d possible values e.g. • Granularity of PSD scale (e.g. 0.5 dB in DSM Report, T1E1.4/2003-018R6) • PSDs corresponding to exact bitloadings • (bmax + 1)N possible bitloading tuples (bk1,...,bkN ) • Each bitloading tuple has corresponding PSD tuple (sk1,...,skN ) • Easy to convert (bk1,...,bkN ) (sk1,...,skN ): O( N 3 ) complexity • d = bmax + 1 • Exhaustive search • sn has dK possible values • (s1, s2) has d2K possible values • Exhaustive search: O(d2K ) complexity • ADSL K = 256, VDSL K = 4096 Computationally Intractable! Optimal Spectrum Management

  5. Per-tone Solution • Consider original problem • Can be rewritten Optimal Spectrum Management

  6. Could be solved independently on each tone Objective • Exhaustive search O(dN) per tone -> O(KdN) • Computationally Tractable! Optimal Spectrum Management

  7. Constraints • But total power constraint couples optimisation between tones • What to do? Dual Decomposition! Optimal Spectrum Management

  8. Lagrangian Dual Decomposition • Standard technique in convex optimisation • Our work shows can also be applied to non-convex problems • Converts constrained opt. -> unconstrained opt. • Constraints naturally enforced by maximisation of Lagrangian Optimal Spectrum Management

  9. Objective Dual Decomposition • Standard technique in convex optimisation • Our work shows can also be applied to non-convex problems • Converts constrained opt. -> unconstrained opt. • Constraints naturally enforced by maximisation of Lagrangian Optimal Spectrum Management

  10. Total Power Constraints Dual Decomposition • Standard technique in convex optimisation • Our work shows can also be applied to non-convex problems • Converts constrained opt. -> unconstrained opt. • Constraints naturally enforced by maximisation of Lagrangian Optimal Spectrum Management

  11. KKT Conditions • Lagrangian multipliers l1, l2 chosen such that either • Then maximising Lagrangian is equivalent to constrained optimisation Optimal Spectrum Management

  12. Dual Decomposition Lagrangian can be decoupled across frequency The Big Picture Optimal Spectrum Management

  13. The Big Picture • Original problem • Non-convex optimisation with KN dimensions • O(dKN) • Computationally intractable Optimal Spectrum Management

  14. The Big Picture • Equivalent optimization • K decoupled non-convex optimisations with N dimensions each • O(KdN) • Computationally tractable! Optimal Spectrum Management

  15. Adjust total power of user 2 The OSM Algorithm Optimal Spectrum Management

  16. The OSM Algorithm Adjust total power of user 1 Optimal Spectrum Management

  17. The OSM Algorithm Adjust rate of user 1 Optimal Spectrum Management

  18. Performance • We compare performance of OSM against Iterative Waterfilling (IW) • CO distributed ADSL • Mix of CO/RT distributed ADSL • Upstream VDSL • Also include comparisons with techniques used in today’s modems • ADSL: Margin Adaptive (MA) mode • CO ADSLs TX flat PSD at -40 dBm/Hz • RT ADSLs TX flat PSD at -52 dBm/Hz • VDSL: Reference PSD method • Long lines at -60 dBm/Hz • Power back-off on short lines such that RX PSD = Ref. PSD • Simulation parameters: • 998 Bandplan – 26 AWG lines • 12.9 dB SNR-gap – TX power ADSL: 20.4 dBm, VDSL: 11.5 dBm • ANSI noise model A – Continuous bitloading (similar results with discrete) Optimal Spectrum Management

  19. ADSL - CO Distributed • Evaluated over a range of line lengths • Gains of IW typically 100-300% over MA • PSDs from IW virtually identical to those found with OSM • IW achieves same gains as OSM • IW effectively optimal • Found this to be case in general for all CO distributed ADSLs Iterative Waterfilling optimal for CO distributed ADSL Optimal Spectrum Management

  20. CO RT 3 km 3 km 4 km 1.5 MA IW OSM 1 CO ADSL (Mbps) 0.5 0 0 1 2 3 4 5 RT ADSL (Mbps) ADSL - CO/RT Mix • CO ADSL of 4km + RT ADSL of 3km • RT located 3km from CO • Leads to following rate regions Optimal Spectrum Management

  21. 1.5 MA IW OSM 1 CO ADSL (Mbps) 0.5 0 0 1 2 3 4 5 RT ADSL (Mbps) ADSL - CO/RT Mix • For example: Target rate of 1 Mbps on both lines Optimal Spectrum Management

  22. 1.5 MA IW OSM 1 CO ADSL (Mbps) 0.5 0 0 1 2 3 4 5 RT ADSL (Mbps) ADSL - CO/RT Mix • MA: Only achieves 0.5 Mbps on 4km Optimal Spectrum Management

  23. 1.5 MA IW OSM 1 CO ADSL (Mbps) 0.5 0 0 1 2 3 4 5 RT ADSL (Mbps) ADSL - CO/RT Mix • MA: Only achieves 0.5 Mbps on 4km • IW: Achieves 1 Mbps on both Optimal Spectrum Management

  24. 1.5 MA IW OSM 1 CO ADSL (Mbps) 0.5 0 0 1 2 3 4 5 RT ADSL (Mbps) ADSL - CO/RT Mix • MA: Only achieves 0.5 Mbps on 4km • IW: Achieves 1 Mbps on both • OSM: CO at 1 MbpsIncreases RT to 3.3 Mbps! (+230%) Optimal Spectrum Management

  25. ADSL - CO/RT Mix • Where do gains of OSM come from? Optimal Spectrum Management

  26. RT ADSL PSD -20 MA IW -30 OSM -40 PSD (dBm/Hz) -50 -60 -70 -80 0 0.2 0.4 0.6 0.8 1 Frequency (MHz) ADSL - CO/RT Mix • Examine RT ADSL PSD Optimal Spectrum Management

  27. RT ADSL PSD -20 MA IW -30 OSM -40 PSD (dBm/Hz) -50 -60 -70 -80 0 0.2 0.4 0.6 0.8 1 Frequency (MHz) ADSL - CO/RT Mix • Crosstalk coupling minimal at low frequencies Optimal Spectrum Management

  28. RT ADSL PSD -20 MA IW -30 OSM -40 PSD (dBm/Hz) -50 -60 -70 -80 0 0.2 0.4 0.6 0.8 1 Frequency (MHz) ADSL - CO/RT Mix • Crosstalk coupling minimal at low frequencies • RT ADSL can transmit at high PSD with little degradation to CO ADSL Optimal Spectrum Management

  29. CO ADSL PSD -20 MA IW -30 OSM -40 PSD (dBm/Hz) -50 -60 -70 -80 0 0.2 0.4 0.6 0.8 1 Frequency (MHz) ADSL - CO/RT Mix • Examine CO ADSL PSD Optimal Spectrum Management

  30. ADSL - CO/RT Mix • CO ADSL not active in high frequencies (large channel attenuation) CO ADSL PSD -20 MA IW -30 OSM -40 PSD (dBm/Hz) -50 -60 -70 -80 0 0.2 0.4 0.6 0.8 1 Frequency (MHz) Optimal Spectrum Management

  31. RT ADSL PSD -20 MA IW -30 OSM -40 PSD (dBm/Hz) -50 -60 -70 -80 0 0.2 0.4 0.6 0.8 1 Frequency (MHz) ADSL - CO/RT Mix • CO ADSL not active in high frequencies (large channel attenuation) • RT ADSL can transmit at high PSD with little degradation to CO ADSL Optimal Spectrum Management

  32. ADSL - CO/RT Mix • Where do gains of OSM come from? • RT ADSL can transmit in low frequencies with little degradation to CO ADSL • RT ADSL can transmit in high frequencies with little degradation to CO ADSL • Leads to improved performance over IW • For example: Target rate of 1 Mbps on both lines Optimal Spectrum Management

  33. ADSL - CO/RT Mix • Where do gains of OSM come from? • RT ADSL can transmit in low frequencies with little degradation to CO ADSL • RT ADSL can transmit in high frequencies with little degradation to CO ADSL • Leads to improved performance over IW • For example: Target rate of 1 Mbps on both lines • With MA 1 Mbps service not possible on both lines • Possible with IW • OSM increases RT rate to 3.3 Mbps (video capable!) Optimal Spectrum Management

  34. CO/ONU CP 600 m 4 4 900 m 7 6 5 4 900m (Mbps) 3 2 Ref. PSD IW 1 OSM 0 0 5 10 15 20 600m (Mbps) VDSL - Upstream • 4 x VDSL of 600m + 4 x VDSL of 900m • Leads to following rate regions Optimal Spectrum Management

  35. 900m PSD -30 Ref. PSD IW -40 OSM -50 -60 PSD (dBm/Hz) -70 -80 -90 -100 4 5 6 7 8 9 10 11 12 Frequency (MHz) VDSL - Upstream • Where do gains of OSM come from? Optimal Spectrum Management

  36. 900m PSD -30 Ref. PSD IW -40 OSM -50 -60 PSD (dBm/Hz) -70 -80 -90 -100 4 5 6 7 8 9 10 11 12 Frequency (MHz) VDSL - Upstream • Examine PSD on 900m lines Optimal Spectrum Management

  37. 900m PSD -30 Ref. PSD IW -40 OSM -50 -60 PSD (dBm/Hz) -70 -80 -90 -100 4 5 6 7 8 9 10 11 12 Frequency (MHz) VDSL - Upstream • 900m not active in 2nd US band (high attenuation) Optimal Spectrum Management

  38. 600m PSD -30 Ref. PSD IW -40 OSM -50 -60 PSD (dBm/Hz) -70 -80 -90 -100 4 5 6 7 8 9 10 11 12 Frequency (MHz) VDSL - Upstream • 900m not active in 2nd US band (high attenuation) • 600m can TX at high PSD with little degradation to 900m Optimal Spectrum Management

  39. VDSL - Upstream • Leads to improved performance over IW • For example: Target rate of 6 Mbps on 900m • Not possible with Ref. PSD • Possible with IW only by decreasing 600m to 4.5 Mbps • OSM allows 6 Mbps on 900m + enhanced 14 Mbps service on 600m (211% gain) • Enables high-speed services: Web-hosting, Virtual Private LAN Optimal Spectrum Management

  40. OSM - Conclusions • IW: Optimal for CO distributed ADSL • OSM: Large gains over IW in RT ADSL and VDSL • Based on Dual Decomposition method from Optimisation Theory • Gives maximum possible performance • Typical gains 200 - 300% • Exploits minimal crosstalk coupling at low freq. to boost near-end PSD • Exploits weak channel of far-end at high freq. to boost near-end PSD • More centralised than IW: Requires PSDs to be remotely set, not just rates • Higher complexity than IW • Ultimately may want to combine best aspects of OSM and IW • Goal: • Simple Algorithm (IW) • Semi-autonomous (IW) • Near-optimal performance (OSM) Optimal Spectrum Management

  41. DSM Evolution • Phase 1: CO Distributed ADSL • Most commonly deployed system today • IW optimal (DSM Level 1) • Large gains (100 - 300%) Right Now Optimal Spectrum Management

  42. DSM Evolution • Phase 1: CO Distributed ADSL • Most commonly deployed system today • IW optimal (DSM Level 1) • Large gains (100 - 300%) • Phase 2: RT Distributed ADSL + VDSL • Implement combination of OSM and IW (DSM Level 2) • Adds 200 - 300% on top of already spectacular gains of IW • Offer high-speed services (video, virtual private LAN, P2P filesharing) to maximum number of people Right Now Next 1-2 Years Optimal Spectrum Management

  43. DSM Evolution • Phase 1: CO Distributed ADSL • Most commonly deployed system today • IW optimal (DSM Level 1) • Large gains (100 - 300%) • Phase 2: RT Distributed ADSL + VDSL • Implement combination of OSM and IW (DSM Level 2) • Adds 200 - 300% on top of already spectacular gains of IW • Offer high-speed services (video, virtual private LAN, P2P filesharing) to maximum number of people • Phase 3: Vectored DSL • DSM Level 3 • 100 Mbps+ symmetric service Right Now Next 1-2 Years 3 – 5 years Optimal Spectrum Management

  44. DSM Evolution • Phase 1: CO Distributed ADSL • Most commonly deployed system today • IW optimal (DSM Level 1) • Large gains (100 - 300%) • Phase 2: RT Distributed ADSL + VDSL • Implement combination of OSM and IW (DSM Level 2) • Adds 200 - 300% on top of already spectacular gains of IW • Offer high-speed services (video, virtual private LAN, P2P filesharing) to maximum number of people • Phase 3: Vectored DSL • DSM Level 3 • 100 Mbps+ symmetric service • Phase 4: Fiber to the Home • Retirement? Right Now Next 1-2 Years 3 – 5 years 20 years? Optimal Spectrum Management

  45. Contents • Optimal Spectrum Management • Achieves maximum possible rates for modems within network • Up to 300% rate gains over IW • Crosstalk Precompensation • Ginis’ QR Precompensator (modification of CPE) • Row-wise diagonal dominance • Linear Diagonalizing Precompensator (no change of CPE) • Partial Cancellation • Distributing compute power across frequency • Large run-time complexity reduction Optimal Spectrum Management

  46. Requires modification of CPE! Crosstalk Precompensation • Joint work together with George Ginis (Texas Inst.), Alcatel Bell • In downstream (DS) TXs co-located • Facilitates crosstalk precompensation • Pre-distort TX signals such that: • Distortion and crosstalk annihilate • RXs see crosstalk free signal • Ginis’ QR Precoder • Multi-user version of Tomlinson-Harashima precoder • Removes all crosstalk • Large performance gains • Achieves close to theoretical capacity in DSL channels • Uses modulo operations at TX to ensure TX power not increased • Modulo operation at RX makes modulo at TX transparent Optimal Spectrum Management

  47. Crosstalk Precompensation • Modification of CPE • Highly undesirable • Legacy issues: Potentially millions of CPEs already (soon to be) in place • All owned an operated by different customers! • CPE / COE often manufactured by different vendors (interoperability issues) • Our Work: Diagonalizing Precompensator • Linear • Achieves close to theoretical capacity in DSL channels • No modification of CPE required • First look at optimal linear pre/post filtering (SVD) Optimal Spectrum Management

  48. Optimal Linear Pre/Post Filtering • SVD of channel matrix Hk • Pre-filter applied prior to TX • Post-filter applied after RX • Estimate of (scaled) transmitted symbol Optimal Spectrum Management

  49. Optimal Linear Pre/Post Filtering • Crosstalk perfectly removed • Pre-filter does not increase TX power • Post-filter does not cause noise enhancement • Achieves channel capacity • But application of Wk requires co-located RXs • Not the case since RXs at different CPs • Only usefull in bonded DSL Optimal Spectrum Management

  50. RWDD Row-wise Diagonal Dominance • Precompensation: TXs must be co-located • Co-located TXs Hkrow-wise diagonal dominant (RWDD) • Implies rows of Hk orthogonal • In terms of SVD Optimal Spectrum Management

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