Example 1: Cognitive Radio Network (More Later) Radio-domain-aware wireless network J. Huang (Princeton University) Performance coupling: mutual interferences Physically distributed: devices learn and adapt to the environment Project: Smart Markets for Smart Radio (Northwestern, Motorola) A L T E L I O N A T Table to determine the current status of U.S. allocations. made to the Table of Frequency Allocations. Therefore, for complete information, users should consult the FCC and NTIA. As such, it does not completely reflect all aspects, i.e., footnotes and recent changes This chart is a graphic single-point-in-time portrayal of the Table of Frequency Allocations used by the Secondary Primary SERVICE ALLOCATION USAGE DESIGNATION ACTIVITY CODE RADIO SERVICES COLOR LEGEND THE RADIO SPECTRUM ALLOCATIONS FREQUENCY STATES UNITED C I N U M M O C E U N R A P E D S . . T & I A S N O M E N T O T R I M O F N A M F O C M E NON-GOVERNMENT EXCLUSIVE GOVERNMENT EXCLUSIVE FIXED SATELLITE FIXED SATELLITE EARTH EXPLORATION SATELLITE BROADCASTING BROADCASTING AMATEUR SATELLITE AMATEUR RADIONAVIGATION AERONAUTICAL MOBILE SATELLITE AERONAUTICAL MOBILE AERONAUTICAL O T I N S M N I D A I E N O I T A T R C R October 2003 Office of Spectrum Management National Telecommunications and Information Administration U.S. DEPARTMENT OF COMMERCE Mobile FIXED EXAMPLE 1st Capital with lower case letters Capital Letters DESCRIPTION MOBILE SATELLITE MOBILE SATELLITE METEOROLOGICAL AIDS METEOROLOGICAL RADIONAVIGATION MARITIME SATELLITE MARITIME MOBILE MARITIME MOBILE SATELLITE LAND MOBILE LAND MOBILE INTER-SATELLITE GOVERNMENT/NON-GOVERNMENT SHARED AND TIME SIGNAL SATELLITE STANDARD FREQUENCY AND TIME SIGNAL STANDARD FREQUENCY SPACE RESEARCH SPACE OPERATION SATELLITE RADIONAVIGATION RADIONAVIGATION RADIOLOCATION SATELLITE RADIOLOCATION SATELLITE RADIODETERMINATION RADIO ASTRONOMY Distributed Resource Allocation ** EXCEPT AERO MOBILE * EXCEPT AERO MOBILE (R) 30 GHz Frequency and Standard FIXED SATELLITE MOBILE 30.0 3 GHz MARITIME Radiolocation 3.0 300 MHz 300.0 30 MHz FIXED MOBILE 30.0 30.56 3 MHz AERONAUTICAL MOBILE (R) 3.025 3.0 300 kHz (RADIO BEACONS) RADIONAVIGATION (Radio Beacons) Radionavigation 300 3 kHz 3 Satellite (S-E) Time Signal (E-S) SATELLITE (E-S) 31.0 RADIONAVIGATION 3.1 FIXED SATELLITE MOBILE MOBILE FIXED LAND MOBILE (OR) AERONAUTICAL MARITIME Aeronautical Stand. Frequency and Time Signal Satellite (S-E) FIXED MOBILE 31.3 LOCATION RADIO- Radiolocation MOBILE 3.155 RADIO ASTRONOMY SPACE RESEARCH (Passive) EXPLORATION SAT. (Passive) EARTH 31.8 FIXED MOBILE 322.0 FIXED MOBILE 32.0 MOBILE* FIXED 3.230 325 RESEARCH (deep space) SPACE RADIONAVIGATION 32.0 3.3 AERONAUTICAL RADIONAVIGATION 328.6 LAND 33.0 location Radio- MOBILE** FIXED Radionavigation Maritime Aeronautical Mobile (RADIO BEACONS) RADIONAVIGATION AERONAUTICAL SPACE RES. RADIONAVIGATION INTER- SAT INTER-SATELLITE RADIONAVIGATION 32.3 LOCATION RADIO- Radiolocation Amateur 335.4 FIXED FIXED MOBILE (Radio Beacons) 335 RADIONAVIGATION 33.4 33.0 FIXED SATELLITE MOBILE MOBILE 34.0 AERONAUTICAL 3.4 RADIOLOCATION Radiolocation AERONAUTICAL RADIONAVIGATION RADIO- Radio- 3.5 FIXED MOBILE MOBILE (R) 3.5 36.0 AERO. RADIO- (Ground) RADIO- LOCATION FIXED SAT. location Radio- 3.6 RADIONAVIGATION SATELLITE MOBILE SATELLITE (E-S) 399.9 FIXED LAND 35.0 Aeronautical (RADIO BEACONS) RADIONAVIGATION AERONAUTICAL FIXED MOBILE SPACE RE. .(Passive) EARTH EXPL. SAT. (Passive) 37.0 NAV.(Ground) MOBILE** LOCATION FIXED SAT. (S-E) location FIXED 3.65 MET. AIDS STD. FREQ. & TIME SIGNAL SAT. (400.1 MHz) MOBILE. SPACE RES. Space Opn. MET. SAT. 400.15 400.05 MOBILE AMATEUR Mobile FIXED MOBILE SPACE (space-to-Earth) RESEARCH (S-E) 3.7 MET. AIDS (Radiosonde) (Radio- SPACE OPN. SAT. (S-E) MET-SAT. (S-E) (E-S) SAT. (E-S) EARTH EXPL Met-Satellite (S-E) Earth Expl. Satellite (E-S) Earth Expl Sat (S-E) 401.0 FIXED MOBILE 36.0 NOT ALLOCATED FIXED MOBILE SPACE RES. SATELLITE (S-E) FIXED 37.6 sonde) (Radiosonde) MET. AIDS (S-E) (E-S) MET-SAT. EARTH EXPL SAT. (E-S) Met-Satellite (E-S) (E-S) Earth Expl Sat (E-S) (E-S) 402.0 LAND MOBILE 37.0 MOBILE FIXED SAT. (S-E) FIXED 38.0 FIXED (S-E) SATELLITE FIXED METEOROLOGICAL AIDS (RADIOSONDE) 403.0 406.0 Radio Astronomy LAND MOBILE 37.5 38.0 FIXED-SATELLITE FIXED MOBILE 38.6 39.5 RADIO MOBILE SATELLITE (E-S) FIXED MOBILE 406.1 RADIO ASTRONOMY FIXED FIXED MOBILE MOBILE 39.0 38.25 FIXED 4.0 SATELLITE FIXED MOBILE SAT. FIXED MOBILE 40.0 ASTRONOMY FIXED MOBILE SPACE RESEARCH 410.0 ISM – 40.68 ± .02 MHz LAND MOBILE 40.0 MARITIME MOBILE 4.063 Aeronautical Mobile RADIONAVIGATION 415 405 DESIGNATIONS WAVELENGTH SAT FIXED MOBILE SAT. SPACE RES. (E-S) Sat (s - e) Expl. Earth EARTH EXPL SAT (E-S) 40.5 4.2 (S-S) 420.0 FIXED MOBILE MARITIME AERONAUTICAL MARITIME FREQUENCY ACTIVITIES SAT. BCST BROAD- CASTING (S-E) FX-SAT Fixed Mobile 41.0 AERONAUTICAL RADIOLOCATION Amateur MOBILE RADIONAVIGATION MOBILE 435 0 BAND FIXED MOBILE BROAD- CASTING SAT. BCST RADIONAVIGATION FIXED LAND MOBILE LAND MOBILE 454.0 450.0 42.0 Infra-sonics RADIO ASTRONOMY FIXED MOBILE* * SATELLITE (E-S) FIXED 42.5 4.4 FIXED LAND MOBILE LAND MOBILE 455.0 456.0 FIXED LAND MOBILE 4.438 Radionavigation VERY LOW FREQUENCY (VLF) FIXED SATELLITE (E-S) MOBILE 43.5 FIXED MOBILE 4.5 LAND MOBILE FIXED Meteorological Satellite (S-E) 460.0 462.5375 43.69 MOBILE* FIXED MOBILE MARITIME Aeronautical 10 Hz 3 x 10 7 m SATELLITE RADIONAV. SATELLITE (E-S) SAT (E-S). MOBILE MOBILE 45.5 SATELLITE (S-E) FIXED MOBILE FIXED LAND MOBILE LAND MOBILE FIXED 462.7375 467.5375 LAND AERONAUTICAL MOBILE (R) 4.7 4.65 RADIONAV.SAT. MOB. SAT(E-S) MOBILE FIXED 47.0 46.9 LAND MOBILE LAND MOBILE FIXED 467.7375 470.0 MOBILE AERONAUTICAL MOBILE (OR) 4.75 100 Hz 3 x 10 6 m AMATEUR AMATEUR SATELLITE F X 47.2 4.8 BROADCASTING FIXED MOBILE 46.6 47.0 MOBILE* FIXED 4.85 Audible Range FIXED MOBILE SAT(E-S) F X 48.2 FIXED MOBILE 4.94 LAND MOBILE FIXED (TV CHANNELS 14 - 20) MOBILE LAND FIXED MOBILE MOBILE (DISTRESS AND CALLING) 495 505 Sonics FIXED MOBILE EARTH SAT(E-S) 50.2 FIXED MOBILE** 4.99 512.0 49.6 STANDARD FREQ. AND TIME SIGNAL (5000 KHZ) Space Research 4.995 5.003 MARITIME MOBILE 510 1 kHz 3 x 10 5 m SPACE RESEARCH FI XED EXPLORATION SATELLITE MOBILE 50.4 RADIO ASTRONOMY AERONAUTICAL Space Research (Passive) 5.0 FIXED MOBILE 50.0 STANDARD FREQ. FIXED 5.060 5.005 MOBILE MARITIME AERONAUTICAL RADIONAVIGATION 9 3 kHz FIXED FIXED MOBILE SATELLITE (E-S) MOBILE SATELLITE (E-S) 51.4 AERO. RADIONAV. RADIONAVIGATION FIXED SAT (S-E) 5.15 (TV CHANNELS 21-36) AMATEUR MOBILE** FIXED (SHIPS ONLY) (RADIO BEACONS) 525 10 kHz 30,000 m EARTH SPACE 52.6 RADIOLOCATION Radiolocation 5.25 BROADCASTING MOBILE AERONAUTICAL (RADIO BEACONS) RADIONAVIGATION 535 AM Broadcast EXPLORATION SATELLITE (Passive) RESEARCH (Passive) AERONAUTICAL RADIONAV. RADIO- LOCATIO N location Radio- 5.35 54.0 5.45 RADIONAVIGATION Ultra-sonics FIXED SPACE MOBILE RES. INTER- SAT INTER- SAT SPACE EARTH EXPL-SAT (Passive) RES. EARTH-ES 54.25 55.78 RADIONAVIGATION MARITIME Radiolocation 5.46 5.47 AERONAUTICAL MOBILE (R) 100 kHz LF 3,000 m FIXED MOBILE SPACE RES. EARTH-ES EARTH INTER- SAT 57.0 56.9 RADIONAVIGATION MARITIME METEOROLOGICAL Radiolocation Radiolocation 5.6 AERONAUTICAL MOBILE (OR) 5.68 5.73 MF HF RES. S P A C E MOBILE FIXED SPACE INTER - SAT SAT. (Passive) EXPLORATION 58.2 ISM – 5.8 ± .075 GHz RADIONAVIGATION RADIOLOCATION AIDS Amateur 5.65 5.83 MOBILE* FIXED 5.90 THE RADIO SPECTRUM UNLICENSED DEVICES 59-64 GHz IS DESIGNATED FOR ISM – 61.25 ± .250 GHz MOBILE FIXED RESEARCH (Passive) EXPLORATION SAT. (Passive) EARTH 59.0 LOCATION RADIO- Amateur- sat (s-e) Amateur Amateur 5.85 LAND MOBILE RADIO ASTRONOMY 614.0 608.0 MOBILE* FIXED BROADCASTING 5.95 1 MHz 300 m EXPLORATION EARTH SAT. (Passive) FIXED MOBILE SPACE RES.. LOC. RADIO- INTER- SAT 59.3 MOBILE FIXED SAT(E-S) FIXED FIXED 5.925 (TV CHANNELS 2-4) BROADCASTING MAGNIFIED ABOVE FM Broadcast FIXED MOBILE RADIO- LOCATION INTER- SATELLITE FIXED SATELLITE (E-S) 6.425 TV BROADCASTING BROADCASTING 10 MHz 30 m MOBILE** FIXED INTER- 64.0 SATELLITE (E-S) FIXED MOBILE 6.525 6.2 14 EARTH SPACE INTER- SATELLITE 65.0 FIXED SATELLITE (S-E)(E-S) SATELLITE (E-S) FIXED FIXED 6.70 MARITIME MOBILE VHF UHF EXPLORATION SATELLITE RESEARCH FIXED MOBILE** SATELLITE 66.0 MOBILE SATELLITE (E-S) FIXED FIXED 6.875 6.525 MARITIME MOBILE 100 MHz 3 m NAVIGATION RADIO- SATELLITE SATELLITE MOBILE NAVIGATION RADIO MOBILE SATELLITE INTER- MOBILE MOBILE FIXED SAT (E-S) FIXED FIXED 7.075 7.025 698 AERONAUTICAL MOBILE (R) 6.685 FIXED Fixed P 71.0 7.125 FIXED MOBILE BROADCAST ISM – 6.78 ± .015 MHz AERONAUTICAL MOBILE (OR) 6.765 1 GHz L 30 cm FIXED 7.19 FIXED MOBILE BROADCAST 746 Mobile FIXED 7.0 S (E-S) SATELLITE FIXED SATELLITE (E-S) MOBILE FIXED MOBILE FIXED FIXED SPACE RESEARCH (E-S) 7.235 7.25 764 AMATEUR AMATEUR SATELLITE 7.1 Microwaves C SHF FIXED SATELLITE (S-E) FIXED SATELLITE (S-E) SATELLITE (S-E) FIXED MOBILE Fixed Mobile Satellite (S-E) 7.30 FIXED MOBILE 776 FIXED MOBILE 72.0 AMATEUR 7.3 10 GHz X 3 cm SATELLITE (S-E) FIXED SATELLITE (S-E) MET. FIXED Satellite (S-E) Mobile 7.45 FIXED MOBILE BROADCAST RADIO ASTRONOMY 73.0 Mobile Mobile FIXED FIXED BROADCASTING BROADCASTING 7.35 STANDARD FREQ. AND TIME SIGNAL (20 kHz) 19.95 Radar EHF SATELLITE (E-S) FIXED FIXED MOBILE 75.5 74.0 SATELLITE (S-E) FIXED FIXED Mobile Satellite (S-E) 7.55 7.75 FIXED MOBILE 794 AERONAUTICAL RADIONAVIGATION FIXED MOBILE 74.8 74.6 Mobile 20.05 100 GHz Radar Bands RADIOLOC. AMATEUR Amateur AMATEUR SATELLITE 76.0 FIXED 7.90 FIXED 806 FIXED FIXED MOBILE MOBILE 75.4 75.2 FIXED 300 GHz 0.3 cm RADIOLOC. RADIOLOC. Amateur AMATEUR Amateur Sat. AMATEUR SAT 77.0 77.5 SATELLITE (E-S) FIXED SATELLITE (E-S) MOBILE Fixed 8.025 LAND MOBILE LAND MOBILE 821 76.0 MARITIME MOBILE LOCATION RADIO- Amateur Amateur Satellite 78.0 SATELLITE (E-S) FIXED FIXED SATELLITE(S -E) EARTH EXPL. FIXED MET. Satellite (E-S) Mobile Mobile 8.175 LAND MOBILE AERONAUTICAL MOBILE FIXED 849 824 (TV CHANNELS 5-6) BROADCASTING FIXED F X I D E MARITIME MOBILE MARITIME MOBILE 8.1 8.195 1 THz Sub-Millimeter INFRARED 0.03 cm FIXED MOBILE 81.0 SAT. (S-E) EARTH EXPL. EARTH EXPL. SATELLITE (E-S) FIXED FIXED SATELLITE (E-S) Mobile Satellite (no airborne) Satellite (E-S) 8.215 LAND MOBILE LAND MOBILE FIXED 866 851 FIXED FIXED MOBILE SATELLITE (S-E) SATELLITE (S-E) 84.0 SATELLITE (S-E) FIXED SATELLITE (E-S) FIXED SPACE RESEARCH (S-E) (E-S)(no airborne) 8.4 LAND MOBILE AERONAUTICAL MOBILE FIXED 869 894 MARITIME MOBILE FIXED MOBILE BROAD- CASTING BROAD- CASTING SPACE RESEARCH (S-E) (deep space only) FIXED 8.45 8.5 ISM – 915.0 ± 13 MHz LAND MOBILE MOBILE FIXED FIXED 901901 896 10 13 Hz Infrared 3 x 10 5 Å SATELLITE 86.0 AERONAUTICAL RADIOLOCATION Radiolocation 9.0 RADIOLOCATION Amateur 902 8.815 ASTRONOMY RADIO SPACE RESEARCH (Passive) SATELLITE (Passive) EXPLORATION EARTH RADIONAVIGATION MARITIME RADIONAVIGATION Radiolocation Radiolocation 9.2 FIXED 929 928 88.0 AERONAUTICAL MOBILE (R) AERONAUTICAL MOBILE (OR) 8.965 30 10 14 Hz Visible VISIBLE 3 x 10 4 Å RADIONAVIGATION Meteorological Aids Radiolocation 9.5 9.3 MOBILE LAND MOBILE FIXED FIXED 931 930 FIXED 9.040 FIXED MOBILE RADIO- FIXED SATELLITE 92.0 LAND MOBILE FIXED FIXED 932 935 FIXED BROADCASTING 9.4 (AM RADIO) BROADCASTING LOCATION (E-S) 95.0 RADIOLOCATION Radiolocation LAND MOBILE LAND MOBILE FIXED FIXED 940 941 (FM RADIO) BROADCASTING 9.5 10 15 Hz 3 x 10 3 Å MOBILE SATELLITE MOBILE NAVIGATION SATELLITE RADIO- NAVIGATION RADIO- location Radio- RADIO- Radiolocation Amateur 10.0 FIXED FIXED 960 944 BROADCASTING Ultraviolet ULTRAVIOLET Radiolocation LOCATION Amateur Amateur Satellite 10.45 STANDARD FREQ. AND TIME SIGNAL (10,000 kHz) FIXED 9.995 9.9 30 3 x 10 2 Å EARTH EXPL. SATELLITE (Passive) SPACE RESEARCH (Passive) 100.0 RADIOLOCATION FIXED 10.55 10.5 RADIONAVIGATION AERONAUTICAL STANDARD FREQ. AERONAUTICAL MOBILE (R) Space Research 10.003 10.005 10 16 Hz FIXED FIXED SATELLITE 102.0 SPACE RESEARCH (Passive) EARTH EXPL. SAT. (Passive) ASTRONOMY RADIO FIXED 10.6 AMATEUR 10.15 10.1 (S-E) 105.0 RADIO ASTRONOMY RESEARCH (Passive) SPACE SATELLITE (Passive) EARTH EXPL. 10.68 10.7 Mobile* FIXED MARITIME MOBILE 10 17 Hz 3 x 10Å ASTRONOMY EXPLORATION SATELLITE RADIONAVIGATION 108.0 FIXED X-RAY RADIO (Passive) RESEARCH SPACE (Passive) SATELLITE EARTH FIXED (S-E) FIXED RADIONAVIGATION 1215 AERONAUTICAL 11.175 11.7 SATELLITE (S-E) RADIOLOCATION 1240 AERONAUTICAL MOBILE (R) AERONAUTICAL MOBILE (OR) 11.275 11.4 10 18 Hz Gamma-ray 3Å 116.0 Mobile ** SATELLITE FIXED RADIOLOCATION Amateur FIXED FIXED BROADCASTING 11.6 11.65 X-ray ISM – 122.5 ± .500 GHz FIXED MOBILE INTER- SATELLITE RESEARCH SPACE EARTH EXPL SAT. (S-E) AERONAUTICAL 1300 AERONAUTICAL 117.975 BROADCASTING 10 19 Hz 3 x 10 -1 Å FIXED MO- INTER- SPACE (Passive) E A R T H Amatuer (Passive) 119.98 12.2 RADIONAVIGATION Radiolocation 1350 MOBILE (R) 121.9375 FIXED BROADCASTING 12.05 12.10 GAMMA-RAY BILE SAT. INTER- RES. SPACE EXPL . SAT EARTH 120.02 BROADCASTING SATELLITE FIXED FIXED FIXED MOBILE ** MOBILE RADIOLOCATION FIXED-SAT (E-S) 1390 1392 AERONAUTICAL MOBILE AERONAUTICAL MOBILE 123.5875 123.0875 FIXED 12.23 FIXED MOBILE SATELLITE (Passive) RESEARCH EXPL SAT. (Passive) 126.0 12.7 MOBILE ** LAND MOBILE FIXED 1400 1395 AERONAUTICAL MOBILE MARITIME 10 20 Hz 3 x 10 -2 Å MOBILE LOCATION SATELLITE SATELLITE (E-S) FIXED MOBILE FIXED 12.75 RADIO ASTRONOMY LAND MOBILE EARTH EXPL SAT (Passive) Fixed (TLM) SPA CE RESEARCH ( Passive) 1429.5 1427 MOBILE (R) 128.8125 AERONAUTICAL MOBILE (OR) 13.2 13.26 FIXED RADIO- INTER- RESEARCH (S-E) (Deep Space) SPACE FIXED SATELLITE (E-S) MOBILE FIXED LAND MOBILE (TLM) FIXED (TLM) 1430 AERONAUTICAL MOBILE (R) 132.0125 ISM – 13.560 ± .007 MHz AERONAUTICAL MOBILE (R) RADIO ASTRONOMY 13.41 13.36 3 x 10 -3 Å 134.0 AERONAUTICAL RADIONAV. Standard RADIO- Space Research (E-S) Radio- 13.25 13.4 FIXED-SAT (S-E) FIXED** FIXED (TLM) MOBILE LAND MOBILE (TLM) 1435 1432 AERONAUTICAL MOBILE (R) AERONAUTICAL MOBILE (R) 136.0 FIXED FIXED BROADCASTING Mobile* 13.57 13.6 10 21 Hz MOBILE SATELLITE MOBILE RADIO- NAVIGATION SATELLITE RADIO- NAVIGATION location Radio- Research Time Signal Freq. and Space RADIO- LOCATION FIXED location Radio- 13.75 MOBILE (AERONAUTICAL TELEMETERING) Mobile ** MOBILE SAT. 1525 MOB. SAT. (S-E) SPACE RES. (S-E) SPACE OPN. (S-E) MET. SAT. (S-E) 137.025 137.0 FIXED BROADCASTING BROADCASTING Mobile* 13.8 13.87 STANDARD FREQ. AND TIME SIGNAL (60 kHz) 59 61 Satellite (E-S) Space Research NAVIGATION RADIO LOCATION SAT.(E-S ) SAT. (E-S) FIXED Land Mobile Satellite (E-S) location 14.0 (Space to Earth) MARITIME MOBILE SAT. (Space to Earth) MOBILE SAT. (Space to Earth) (Aero. TLM) Mobile 1530 1535 MOB. SAT. (S-E) Mob. Sat. (S-E) Mob. Sat. (S-E) SPACE RES. (S-E) SPACE RES. (S-E) SPACE RES. (S-E) SPACE OPN. (S-E) SPACE OPN. (S-E) SPACE OPN. (S-E) MET. SAT. (S-E) MET. SAT. (S-E) MET. SAT. (S-E) 137.825 138.0 137.175 AMATEUR FIXED AMATEUR SATELLITE 14.0 14.25 MOBILE MARITIME 10 22 Hz 3 x 10 -4 Å AMATEUR AMATEUR SATELLITE 142.0 144.0 Mobile** FIXED Land Mobile 14.2 MARITIME MOBILE SATELLITE (space to Earth) MOBILE SATELLITE (S-E) MOBILE SATELLITE (S-E) 1544 FIXED MOBILE AMATEUR 14.35 FIXED Cosmic-ray COSMIC-RAY LOCATION RADIO- Amateur Amateur Satellite 149.0 SATELLITE (E-S) FIXED Satellite (E-S) Land Mobile 14.4 AERONAUTICAL MOBILE SATELLITE (R) (space to Earth) Mobile Satellite (S- E) 1545 1549.5 AMATEUR AMATEUR AMATEUR SATELLITE 144.0 148.0 146.0 FIXED Mobile* 14.990 FIXED MOBILE SATELLITE (S-E) FIXED 150.0 Fixed Fixed Mobile Mobile SAT. (E-S) FX SAT.(E-S) L M Sat(E-S) Satellite (E-S) 14.5 14.47 AERONAUTICAL MOBILE SATELLITE (R) AERONAUTICAL MOBILE SATELLITE (R) (space to Earth) (space to Earth) (Space to Earth) MOBILE SATELLITE 1558.5 MOBILE SATELLITE (E-S) RADIONAV-SATELLITE FIXED MOBILE SATELLITE (E-S) MOBILE 150.05 149.9 STANDARD FREQ. AND TIME SIGNAL (15,000 kHz) STANDARD FREQ. Space Research 15.005 70 10 23 Hz 3 x 10 -5 Å FIXED SATELLITE (S-E) FIXED MOBILE EXPL. SAT. EARTH (Passive) SPACE RES. (Passive) 151.0 MOBILE FIXED Fixed Mobile Space Research Space Research 14.7145 15.1365 AERO. RADIONAVIGATION AERONAUTICAL RADIONAVIGATION RADIO DET. SAT. (E-S) RADIONAV. SATELLITE (Space to Earth) 1610 1559 FIXED FIXED LAND MOBILE MOBILE 152.855 150.8 AERONAUTICAL MOBILE (OR) 15.10 15.010 TRAVELERS INFORMATION STATIONS (G) AT 1610 kHz Radiolocation MARITIME MOBILE SATELLITE FIXED Mobile Space Research 15.35 AERO. RADIONAV. AERO. RADIONAV. RADIO DET. SAT. (E-S) RADIO DET. SAT. (E-S) MOBILE SAT. (E-S) MOBILE SAT. (E-S) MOBILESAT(E-S) Mobile Sat. (S-E) RADIO ASTRONOMY 1613.8 1610.6 LAND MOBILE BROADCASTING 15.6 FIXED 10 24 Hz 3 x 10 -6 Å FIXED (S-E) FIXED RADIO ASTRONOMY AERONAUTICAL RADIONAVIGATION SPACE RESEARCH (Passive) EARTH EXPL. SAT. (Passive) 15.4 1626.5 FIXED LAND MOBILE 156.2475 154.0 FIXED FIXED BROADCASTING 15.8 AERO RADIONAV FIXED SAT (E-S) 15.63 15.43 MOBILE SATELLITE (E-S) MARITIME MOBILE MARITIME MOBILE 157.1875 157.0375 16.36 3 x 10 -7 Å EXPLORATION SATELLITE (Passive) EARTH ASTRONOMY RADIO SPACE RES. (Passive) 164.0 AERONAUTICAL RADIONAVIGATION RADIOLOCATION Radiolocation 15.7 16.6 RADIO ASTRONOMY MOBILE SAT. (E-S) 1660.5 1660 MARITIME MOBILE FIXED MARITIME MOBILE LAND MOBILE LAND MOBILE 161.575 157.45 MARITIME MOBILE BROADCASTING 1615 1605 10 25 Hz FIXED MOBILE 168.0 170.0 RADIOLOCATION RADIOLOCATION Space Res.(act.) Radiolocation Radiolocation 17.1 RADIO ASTRONOMY RADIO ASTRONOMY SPACE RESEARCH (Passive) METEOROLOGICAL 1668.4 MARITIME MOBILE LAND MOBILE LAND MOBILE 161.625 161.775 MOBILE 17.41 BROADCASTING RADIONAVIGATION 90 FIXED MOBILE SATELLITE INTER- 174.5 BCST SAT. Earth Expl Sat Space Res. FX SAT (E-S) RADIOLOC. Radiolocation Radioloc. 17.2 17.3 MOBILE** AIDS (RADIOSONDE) FIXED 1670 FIXED MOBILE 162.0125 FIXED FIXED BROADCASTING 17.55 17.48 FIXED MOBILE SPACE (Passive) RESEARCH SATELLITE INTER- SAT. (Passive) EXPLORATION EARTH 176.5 FIXED SATELLITE (E-S) FIXED 17.7 17.8 SATELLITE (s-E) METEOROLOGICAL METEOROLOGICAL AIDS (Radiosonde) 1675 1700 BROADCASTING 17.9 1705 FIXED MOBILE SATELLITE INTER- SPACE RES. FIXED SATELLITE (S-E) FIXED SATELLITE (S-E) FX SAT (S-E) EARTH EXPL. SAT. FIXED 18.3 18.6 MET. SAT. (s-E) FIXED Fixed FIXED Land Mobile 173.2 173.4 AERONAUTICAL MOBILE (R) AERONAUTICAL MOBILE (OR) FIXED 17.97 18.03 RADIO- LOCATION MOBILE FIXED RADIO ASTRONOMY SPACE RESEARCH (Passive) EXPLORATION SATELLITE (Passive) EARTH 182.0 FIXED SATELLITE (S-E) 19.3 18.8 FIXED MOBILE 1710 FIXED MOBILE 174.0 AMATEUR SATELLITE Mobile AMATEUR FIXED 18.068 18.168 1800 110 FIXED MOBILE SATELLITE INTER- 185.0 FIXED SATELLITE (S-E) FIXED SATELLITE (S-E) MOBILE SAT. (S-E) FIXED 19.7 FIXED MOBILE 1850 1755 FIXED MARITIME MOBILE BROADCASTING 18.9 18.78 MOBILE MARITIME Radiolocation 190.0 FX SAT (S-E) MOBILE SATELLITE (S-E) FX SAT (S-E) MOBILE SAT (S-E) 20.2 20.1 FIXED MOBILE (TV CHANNELS 7-13) MARITIME MOBILE FIXED 19.02 19.68 AMATEUR FIXED MOBILE SATELLITE MOBILE RADIO- NAVIGATION SATELLITE NAVIGATION RADIO- SPACE RES. STD FREQ. & TIME FIXED FIXED MOBILE EARTH EXPL. SAT. 21.4 21.2 MOBILE SATELLITE (E-S) 2000 BROADCASTING STAND. FREQ. & TIME SIG . FIXED Space Research 19.990 19.80 1900 FIXED FIXED MOBILE** MOBILE 22.21 22.0 FIXED MOBILE 2020 STANDARD FREQ. STANDARD FREQUENCY & TIME SIG NAL (20,000 KHZ) Space Research 19.995 20.005 20.010 RADIOLOCATION 130 FIXED MOBILE SPACE RES. (Passive) EXPLORATION SAT. EARTH (Passive) 200.0 SPACE RES. RAD.AST MOBILE** FIXED EARTH EXPL. SAT. 22.5 (E-S)(s-s) SPACE RES. SAT. (E-S)(s-s) EARTH EXPL. (E-S)(s-s) SPACE OP. MOB. FX. 2110 2025 FIXED Mobile 2000 MARITIME OF SPECTRUM OCCUPIED. TRUM SEGMENTS SHOWN IS NOT PROPORTIONAL TO THE ACTUAL AMOUNT PLEASE NOTE: THE SPACING ALLOTTED THE SERVICES IN THE SPEC- 202.0 MOBILE FIXED 22.55 FIXED MOBILE S) 2155 AMATEUR AMATEUR SATELLITE 21.0 MOBILE FIXED MOBILE MARITIME MOBILE FIXED FIXED MOBILE FIXED (E-S) SATELLITE FIXED MOBILE INTER-SATELLITE FIXED FIXED MOBILE 2180 2160 BROADCASTING 21.45 MARITIME MOBILE (TELEPHONY) 2065 2107 FIXED MOBILE 23.55 MOBILE SATELLITE (S-E) 2200 R a d i o - 216.0 AERONAUTICAL MOBILE (R) FIXED 21.924 21.85 FIXED MOBILE LAND MOBILE MOBILE MARITIME ASTRONOMY RESEARCH SATELLITE EXPLORATION 217.0 RADIO ASTRONOMY SPACE RES. EARTH EXPL. 23.6 FIXED (LOS) MOBILE (LOS) (s-E)(s-s) RESEARCH SPACE OPERATION SPACE (s-E)(s-s) EXPLORATION SAT. (s-E)(s-s) EARTH F i x e d LAND MOBILE M o b i l e F I X E D l o c a t i o n F I X E D Radiolocation M O B I L E Amateur 220.0 222.0 MARITIME MOBILE 22.0 MOBILE (DISTRESS AND CALLING) MARITIME MOBILE (TELEPHONY) 2173.5 2170 160 RADIO (Passive) SPACE (Passive) EARTH (Passive) SAT. (Passive) 24.0 SPACE RES..(S-E) FIXED Amateur MOBILE** 2300 2290 AMATEUR Radiolocation 225.0 FIXED FIXED Mobile* 23.0 22.855 MARITIME MOBILE (TELEPHONY) 2194 2190.5 FIXED MOBILE MARITIME FIXED Radio- 231.0 AMATEUR AMATEUR SATELLITE Radiolocation Amateur RADIOLOCATION Mobile Fixed MOB MOBILE** FX FIXED R- LOC. B-SAT 2305 2310 2320 FIXED MOBILE AERONAUTICAL MOBILE (OR) 23.2 23.35 LAND MOBILE FIXED FIXED MOBILE MOBILE FIXED SPACE RES. SATELLITE (S-E) location EARTH EXPL. 235.0 Satellite Earth Expl. LOCATION RADIO- Amateur Radio- 24.05 Mobile location Radio- Fixed BCST-SATELLITE FIXED MOBILE** 24.89 FIXED MOBILE MOBILE MARITIME ISM – 245.0 ± 1GHz FIXED MOBILE SATELLITE(S-E) SATELLITE (S-E) FIXED (Passive) Radio- SAT. (Passive) location 241.0 238.0 (Active) FIXED location 24.45 24.25 Radiolocation Mobile Fixed MOB FX R- LOC. B-SAT 2345 235.0 AMATEUR SATELLITE STANDARD FREQ. AND TIME SIGNAL (25,000 kHz) AMATEUR 25.005 24.99 AERONAUTICAL 190 RADIO- LOCATION Amateur Satellite Amateur 248.0 ISM – 24.125 ± 0.125 GHz RADIONAVIGATION INTER-SATELLITE ISM – 2450.0 ± 50 MHz MOBILE RADIOLOCATION Fixed 2360 STANDARD FREQ. LAND MOBILE Space Research 25.01 RADIONAVIGATION 200 AMATEUR SATELLITE AMATEUR 250.0 Earth Expl. INTER-SATELLITE RADIOLOCATION SATELLITE (E-S) 24.65 MOBILE FIXED 2390 2385 LAND MOBILE MARITIME MOBILE 25.07 25.21 STANDARD FREQ. AND TIME SIGNAL (2500kHz) 2501 2495 RADIONAVIGATION SPACE RES. (Passive) SATELLITE (Passive) NAVIGATION EARTH EXPLORATION NAVIGATION 252.0 Satellite (Active) INTER-SATELLITE SATELLITE (E-S) RADIOLOCATION FIXED 24.75 AMATEUR AMATEUR 2400 FIXED RADIO ASTRONOMY MOBILE** 25.55 25.67 25.33 STANDARD FREQ. AND TIME SIGNAL STANDARD FREQ. Space Research 2502 AERONAUTICAL Aeronautical MOBILE SATELLITE MOBILE RADIO- SATELLITE RADIO- Exploration Earth RADIONAVIGATION Standard Frequency and SATELLITE FIXED (E-S) MOBILE 25.05 Radiolocation Amateur 2417 2450 MOBILE SATELLITE MARITIME MOBILE BROADCASTING 26.175 26.1 2505 Mobile SATELLITE ASTRONOMY 265.0 FIXED (S-S) Satellite Time Signal Satellite (E-S) FIXED SATELLITE (E-S) FIXED MOBILE Radiolocation 2483.5 FIXED MOBILE FIXED LAND MOBILE FIXED MOBILE** 26.95 26.48 MOBILE LAND MOBILE MOBILE MARITIME FIXED MOBILE (E-S) FIXED RADIO- std freq Satellite (S-S) & time e-e-sat (s-s) e-e-sat Earth Exploration FIXED FIXED INTER-SAT. INTER-SAT. MOBILE MOBILE 25.5 25.25 BCST - SAT. RADIODETERMINATION SAT. (S-E) E-Expl Sat Radio Ast MOBILE** Space res. FX-SAT (S - E) MOBILE SATELLITE (S-E) FX FIXED 2500 2655 ISM – 27.12 ± .163 MHz FIXED MOBILE** MOBILE** 26.96 27.23 FIXED 275.0 Earth Exploration Satellite (S-S) FIXED SATELLITE INTER- MOBILE MOBILE 27.0 RADIO ASTRON. SPACE RESEARCH EARTH EXPL SAT MOB** B- SAT. FX-SAT 2690 2700 FIXED FIXED LAND MOBILE MOBILE 27.41 27.54 300 GHz FIXED MOBILE 30 GHz FIXED MOBILE SAT (E-S) FIXED 27.5 AERONAUTICAL METEOROLOGICAL Radiolocation 300 MHz 30 MHz AMATEUR AMATEUR SATELLITE 28.0 29.7 3 MHz 2850 300 kHz Maritime 275 FIXED SATELLITE (E-S) MOBILE SATELLITE (E-S) 29.5 3 GHz RADIONAVIGATION AIDS 2900 LAND MOBILE FIXED 29.89 29.8 AERONAUTICAL MOBILE (R) RADIONAVIGATION AERONAUTICAL MARITIME Aeronautical Mobile Aeronautical Radionavigation (Radio Beacons) 285 300.0 FIXED SATELLITE (E-S) MOBILE SATELLITE (E-S) 30.0 29.9 RADIONAVIGATION MARITIME Radiolocation 3000 300 FIXED FIXED MOBILE 30.0 29.91 3000 RADIONAVIGATION (RADIO BEACONS) Radionavigation (Radio Beacons) 300 Jan. 2007 5 / 60
Example 2: DSL Network (More Later) CO TX RX Customer (Central Office) crosstalk RT TX RX Customer (Remote Terminal) Copper-based last-mile broadband access network Project: FAST Copper (Princeton, Stanford, Fraser Research, AT&T) Physically distributed: phone lines terminate at different equipments Performance coupling: mutual interferences J. Huang (Princeton University) Distributed Resource Allocation Jan. 2007 6 / 60
Example 3: Mobile Ad Hoc Network (MANET) Infrastructureless mobile wireless network Project: Control-based MANET (large DARPA Team, incl. Princeton) Physically distributed: nodes join and leave, move around Performance coupling: multihop relay, mutual interferences J. Huang (Princeton University) Distributed Resource Allocation Jan. 2007 7 / 60
We Need Good Resource Allocation Algorithms Need to design good resource allocation algorithms ◮ Distributed ◮ Low complexity ◮ Local computation ◮ Limited or no message passing Turn competition into cooperation J. Huang (Princeton University) Distributed Resource Allocation Jan. 2007 8 / 60
How to Achieve The Desired Solutions? Mathematical Approaches ◮ Optimization theory ◮ Game theory ◮ Distributed computation and control ◮ Microeconomics Engineering Implications ◮ Realistic network deployments and tests ◮ Engineering problem structure J. Huang (Princeton University) Distributed Resource Allocation Jan. 2007 9 / 60
Outline Introduction 1 Case I: Cognitive Radio Network 2 Case II: DSL Network 3 Summary 4 J. Huang (Princeton University) Distributed Resource Allocation Jan. 2007 10 / 60
Outline Introduction 1 Case I: Cognitive Radio Network 2 Case II: DSL Network 3 Summary 4 J. Huang (Princeton University) Distributed Resource Allocation Jan. 2007 11 / 60
What is Cognitive Radio? Fixed Radio: transmit parameters (i.e., frequency, modulation) determined by hardware Adaptive Radio: parameters determined by software, easy to adapt to anticipated events Cognitive Radio : sense their environment and learn how to adapt J. Huang (Princeton University) Distributed Resource Allocation Jan. 2007 12 / 60
Why Cognitive Radio? Improve spectrum utilization ◮ Licensed bands: IEEE 802.22 (Television band) ◮ Unlicensed bands: IEEE 802.19 Improve reliability ◮ Emergency networks ◮ Military networks Support interoperability Reduce costs of wireless communications J. Huang (Princeton University) Distributed Resource Allocation Jan. 2007 13 / 60
Spectrum Sharing for Licensed Band Primary owner: the exclusive licensee of the spectrum Secondary users: the cognitive radio devices Primary owner gets extra revenue by allowing secondary users to transmit in an unharmful way J. Huang (Princeton University) Distributed Resource Allocation Jan. 2007 14 / 60
Spectrum Sharing for Licensed Band Primary owner: the exclusive licensee of the spectrum Secondary users: the cognitive radio devices Primary owner gets extra revenue by allowing secondary users to transmit in an unharmful way Interference temperature constraint : ◮ Maximum allowed interference measured at a measurement point ◮ Equivalent to a total received power constraint J. Huang (Princeton University) Distributed Resource Allocation Jan. 2007 14 / 60
Network Model T 1 T 2 User Receivers Measurement Point T 3 More general model (with no new math challenges) will be discussed later J. Huang (Princeton University) Distributed Resource Allocation Jan. 2007 15 / 60
Mathematical Model P 1 T 1 h 1 P 2 h 2 T 2 User Receivers Measurement Point h 3 P 3 T 3 Multi-user interference channel User n ’s ◮ Transmission power: p n ◮ Channel gain: h n ◮ Signal-to-interference plus noise ratio (SINR): p n h n SINR n ( p ) = �� � n 0 + 1 m � = n p m h m B Interference temperature constraint: � n p n h n ≤ P J. Huang (Princeton University) Distributed Resource Allocation Jan. 2007 16 / 60
Utility Function U (SINR ) n n SINR n Characterize QoS as function of SINR Increasing and strictly concave: elastic data application Private user information ⇒ challenges to distributed solution J. Huang (Princeton University) Distributed Resource Allocation Jan. 2007 17 / 60
Network Objective I: Efficiency Efficiency : maximize the total network utility: Efficiency Problem � maximize U n ( SINR n ( p )) n � subject to p n h n ≤ P n variables p n ≥ 0 , ∀ n Example: U n ( SINR n ) = θ n log(1 + SINR n ) ◮ Maximizing total weighted rate J. Huang (Princeton University) Distributed Resource Allocation Jan. 2007 18 / 60
Network Objective II: Fairness Fairness : fair share of resource, independent of location Fairness Problem maximize SINR 1 ( p ) subject to U ′ n ( SINR n ( p )) = U ′ m ( SINR m ( p )) , ∀ m � = n � p n h n ≤ P n variables p n ≥ 0 , ∀ n Example: U n ( SINR n ) = θ n log( SINR n ) ◮ Weighted max-min fair J. Huang (Princeton University) Distributed Resource Allocation Jan. 2007 19 / 60
Technical Challenges Non-convexity: ◮ SINR and utility may not be concave in power Physically distributed: ◮ Local information: utility functions, channel gains ◮ Selfish objectives Performance coupling: ◮ Mutual interference ◮ Shared received power at measurement point J. Huang (Princeton University) Distributed Resource Allocation Jan. 2007 20 / 60
Technical Challenges Non-convexity: ◮ SINR and utility may not be concave in power Physically distributed: ◮ Local information: utility functions, channel gains ◮ Selfish objectives Performance coupling: ◮ Mutual interference ◮ Shared received power at measurement point Our solution : auction-based resource allocation algorithm ◮ Distributed in nature ◮ Capture interactions between users J. Huang (Princeton University) Distributed Resource Allocation Jan. 2007 20 / 60
Background on Auction J. Huang (Princeton University) Distributed Resource Allocation Jan. 2007 21 / 60
Background on Auction Example: painting auction ◮ Highest bidder gets the good and pays the bid J. Huang (Princeton University) Distributed Resource Allocation Jan. 2007 21 / 60
Background on Auction Example: painting auction ◮ Highest bidder gets the good and pays the bid Elements of auction: ◮ Good: resource ◮ Auctioneer (manager): representing seller of the good ◮ Bidders (users): buyers of the good J. Huang (Princeton University) Distributed Resource Allocation Jan. 2007 21 / 60
Background on Auction Example: painting auction ◮ Highest bidder gets the good and pays the bid Elements of auction: ◮ Good: resource ◮ Auctioneer (manager): representing seller of the good ◮ Bidders (users): buyers of the good Rules of auction: ◮ Bids: what the bidders submit to the auctioneer ◮ Allocation: how auctioneer allocates the good to the bidders ◮ Payments: how the bidders pay the auctioneer J. Huang (Princeton University) Distributed Resource Allocation Jan. 2007 21 / 60
Background on Auction Example: painting auction ◮ Highest bidder gets the good and pays the bid Elements of auction: ◮ Good: resource ◮ Auctioneer (manager): representing seller of the good ◮ Bidders (users): buyers of the good Rules of auction: ◮ Bids: what the bidders submit to the auctioneer ◮ Allocation: how auctioneer allocates the good to the bidders ◮ Payments: how the bidders pay the auctioneer Types of auction ◮ Indivisible auction ◮ Divisible auction: suitable for communication resource allocation J. Huang (Princeton University) Distributed Resource Allocation Jan. 2007 21 / 60
Auction-based Comm. Resource Allocation Network Coupling Bid Efficiency Rep. Paper Wireline simple complex Yes Lazar-Semret’98 Wireline simple simple Yes Maheswaran-Basar’98 Wireline simple simple No Johari-Tsitsiklis’04 J. Huang (Princeton University) Distributed Resource Allocation Jan. 2007 22 / 60
Auction-based Comm. Resource Allocation Network Coupling Bid Efficiency Rep. Paper Wireline simple complex Yes Lazar-Semret’98 Wireline simple simple Yes Maheswaran-Basar’98 Wireline simple simple No Johari-Tsitsiklis’04 Wireless simple simple No Sun-Modinao-Zheng’03 Wireless simple complex No Dramitinos et al.’04 J. Huang (Princeton University) Distributed Resource Allocation Jan. 2007 22 / 60
Auction-based Comm. Resource Allocation Network Coupling Bid Efficiency Rep. Paper Wireline simple complex Yes Lazar-Semret’98 Wireline simple simple Yes Maheswaran-Basar’98 Wireline simple simple No Johari-Tsitsiklis’04 Wireless simple simple No Sun-Modinao-Zheng’03 Wireless simple complex No Dramitinos et al.’04 Wireless complex simple Yes Huang-Berry-Honig’04 J. Huang (Princeton University) Distributed Resource Allocation Jan. 2007 22 / 60
Auction-based Comm. Resource Allocation Network Coupling Bid Efficiency Rep. Paper Wireline simple complex Yes Lazar-Semret’98 Wireline simple simple Yes Maheswaran-Basar’98 Wireline simple simple No Johari-Tsitsiklis’04 Wireless simple simple No Sun-Modinao-Zheng’03 Wireless simple complex No Dramitinos et al.’04 Wireless complex simple Yes Huang-Berry-Honig’04 We design two auctions: efficient and fair allocation Proposed framework is general J. Huang (Princeton University) Distributed Resource Allocation Jan. 2007 22 / 60
Divisible Auction for Spectrum Sharing Initialization : manager announces A fixed reserve bid β > 0: to make the auction result unique A price π : to determine the payment J. Huang (Princeton University) Distributed Resource Allocation Jan. 2007 23 / 60
Divisible Auction for Spectrum Sharing Initialization : manager announces A fixed reserve bid β > 0: to make the auction result unique A price π : to determine the payment Rules : Bids: user n submits b n ≥ 0 to the manager J. Huang (Princeton University) Distributed Resource Allocation Jan. 2007 23 / 60
Divisible Auction for Spectrum Sharing Initialization : manager announces A fixed reserve bid β > 0: to make the auction result unique A price π : to determine the payment Rules : Bids: user n submits b n ≥ 0 to the manager Allocation: the manager allows user n to generate interference at the measurement point with b n p n h n = n b n + β P � ◮ Weighted proportional allocation rule ◮ Positive reserve bid makes sure that the values of bids count, not just the ratio J. Huang (Princeton University) Distributed Resource Allocation Jan. 2007 23 / 60
Two Different Payments SINR auction : user n pays C n ( π ) = π × SINR n ◮ User-centric payment ◮ Proportional to user’s achieved QoS (SINR) ◮ Leads to fair allocation Power auction : user n pays C n ( π ) = π × p n h n ◮ Network-centric payment ◮ Proportional to the allocated resource (power) ◮ Leads to efficient allocation J. Huang (Princeton University) Distributed Resource Allocation Jan. 2007 24 / 60
Best Response and Nash Equilibrium Users participate in a non-cooperative game ◮ User’s payoff (benefit) = utility - payment ◮ Both utility and payment depend on b n and b − n � ( b m , ∀ m � = n ) J. Huang (Princeton University) Distributed Resource Allocation Jan. 2007 25 / 60
Best Response and Nash Equilibrium Users participate in a non-cooperative game ◮ User’s payoff (benefit) = utility - payment ◮ Both utility and payment depend on b n and b − n � ( b m , ∀ m � = n ) A user n wants to choose bid to maximize its own payoff ◮ Best response : B n ( b − n ) B n ( b − n ) = arg max b n [ U n ( SINR n ( b n ; b − n )) − C n ( π, b n ; b − n )] J. Huang (Princeton University) Distributed Resource Allocation Jan. 2007 25 / 60
Best Response and Nash Equilibrium Users participate in a non-cooperative game ◮ User’s payoff (benefit) = utility - payment ◮ Both utility and payment depend on b n and b − n � ( b m , ∀ m � = n ) A user n wants to choose bid to maximize its own payoff ◮ Best response : B n ( b − n ) B n ( b − n ) = arg max b n [ U n ( SINR n ( b n ; b − n )) − C n ( π, b n ; b − n )] Solution of the game: everyone is happy with the result ◮ Nash Equilibrium (N.E.) : b ∗ = { b ∗ n , ∀ n } ◮ Fixed point solution of all users’ best responses b ∗ b ∗ � � n = B , ∀ n − n ◮ Stable outcome of the game J. Huang (Princeton University) Distributed Resource Allocation Jan. 2007 25 / 60
Network Objectives Efficiency Problem Fairness Problem (Optimization Problems) Efficient Allocation Solutions Fair Allocation Solutions N.E. N.E. Divisible Auction SINR Auction Power Auction (Non−cooperative Game) J. Huang (Princeton University) Distributed Resource Allocation Jan. 2007 26 / 60
What Do We Want to Know? When does an N.E. exist? Is it unique? What are the properties of the N.E.? (Fairness? Efficiency?) How to achieve the N.E. in a distributed fashion? J. Huang (Princeton University) Distributed Resource Allocation Jan. 2007 27 / 60
What Do We Want to Know? When does an N.E. exist? Is it unique? What are the properties of the N.E.? (Fairness? Efficiency?) How to achieve the N.E. in a distributed fashion? J. Huang (Princeton University) Distributed Resource Allocation Jan. 2007 28 / 60
Sufficiently Large Price Leads to Unique N.E. Theorem (Sufficiently Large Price Leads to Unique N.E.) In SINR Auction, there is a threshold price π th , s.t. π > π th ⇒ unique N.E. π < π th ⇒ no N.E. J. Huang (Princeton University) Distributed Resource Allocation Jan. 2007 29 / 60
Sufficiently Large Price Leads to Unique N.E. Theorem (Sufficiently Large Price Leads to Unique N.E.) In SINR Auction, there is a threshold price π th , s.t. π > π th ⇒ unique N.E. π < π th ⇒ no N.E. Proof : matrix analysis. J. Huang (Princeton University) Distributed Resource Allocation Jan. 2007 29 / 60
Proof Outline User n ’s payoff is strictly quasi-concave in b n ⇒ unique best response 1 J. Huang (Princeton University) Distributed Resource Allocation Jan. 2007 30 / 60
Proof Outline User n ’s payoff is strictly quasi-concave in b n ⇒ unique best response 1 Linear best responses in matrix form 2 B ( b ) = K ( π ) b + k 0 ( π ) β J. Huang (Princeton University) Distributed Resource Allocation Jan. 2007 30 / 60
Proof Outline User n ’s payoff is strictly quasi-concave in b n ⇒ unique best response 1 Linear best responses in matrix form 2 B ( b ) = K ( π ) b + k 0 ( π ) β Unique fixed point if spectral radius ρ ( K ( π )) < 1 3 � ∞ � b ∗ = B ( b ∗ ) ⇒ b ∗ = � K i k 0 ( π ) β (N.E.) i =0 J. Huang (Princeton University) Distributed Resource Allocation Jan. 2007 30 / 60
Proof Outline User n ’s payoff is strictly quasi-concave in b n ⇒ unique best response 1 Linear best responses in matrix form 2 B ( b ) = K ( π ) b + k 0 ( π ) β Unique fixed point if spectral radius ρ ( K ( π )) < 1 3 � ∞ � b ∗ = B ( b ∗ ) ⇒ b ∗ = � K i k 0 ( π ) β (N.E.) i =0 Determine spectral radius through max-min operation 4 N 1 � ρ ( K ( π )) = x ≥ 0 , x � = 0 min max k mn ( π ) x n x m m , x m � =0 m =1 J. Huang (Princeton University) Distributed Resource Allocation Jan. 2007 30 / 60
Proof Outline User n ’s payoff is strictly quasi-concave in b n ⇒ unique best response 1 Linear best responses in matrix form 2 B ( b ) = K ( π ) b + k 0 ( π ) β Unique fixed point if spectral radius ρ ( K ( π )) < 1 3 � ∞ � b ∗ = B ( b ∗ ) ⇒ b ∗ = � K i k 0 ( π ) β (N.E.) i =0 Determine spectral radius through max-min operation 4 N 1 � ρ ( K ( π )) = x ≥ 0 , x � = 0 min max k mn ( π ) x n x m m , x m � =0 m =1 Show ρ ( K ( π )) is continuous and nonincreasing in price π . 5 J. Huang (Princeton University) Distributed Resource Allocation Jan. 2007 30 / 60
Proof Outline User n ’s payoff is strictly quasi-concave in b n ⇒ unique best response 1 Linear best responses in matrix form 2 B ( b ) = K ( π ) b + k 0 ( π ) β Unique fixed point if spectral radius ρ ( K ( π )) < 1 3 � ∞ � b ∗ = B ( b ∗ ) ⇒ b ∗ = � K i k 0 ( π ) β (N.E.) i =0 Determine spectral radius through max-min operation 4 N 1 � ρ ( K ( π )) = x ≥ 0 , x � = 0 min max k mn ( π ) x n x m m , x m � =0 m =1 Show ρ ( K ( π )) is continuous and nonincreasing in price π . 5 � � Find a price π > max m U ′ Ph mm , s.t. ρ ( K ( π )) < 1. 6 m n 0 h 0 m J. Huang (Princeton University) Distributed Resource Allocation Jan. 2007 30 / 60
Proof Outline User n ’s payoff is strictly quasi-concave in b n ⇒ unique best response 1 Linear best responses in matrix form 2 B ( b ) = K ( π ) b + k 0 ( π ) β Unique fixed point if spectral radius ρ ( K ( π )) < 1 3 � ∞ � b ∗ = B ( b ∗ ) ⇒ b ∗ = � K i k 0 ( π ) β (N.E.) i =0 Determine spectral radius through max-min operation 4 N 1 � ρ ( K ( π )) = x ≥ 0 , x � = 0 min max k mn ( π ) x n x m m , x m � =0 m =1 Show ρ ( K ( π )) is continuous and nonincreasing in price π . 5 � � Find a price π > max m U ′ Ph mm , s.t. ρ ( K ( π )) < 1. 6 m n 0 h 0 m Find a price π > 0, s.t. ρ ( K ( π )) > 1. 7 J. Huang (Princeton University) Distributed Resource Allocation Jan. 2007 30 / 60
Proof Outline User n ’s payoff is strictly quasi-concave in b n ⇒ unique best response 1 Linear best responses in matrix form 2 B ( b ) = K ( π ) b + k 0 ( π ) β Unique fixed point if spectral radius ρ ( K ( π )) < 1 3 � ∞ � b ∗ = B ( b ∗ ) ⇒ b ∗ = � K i k 0 ( π ) β (N.E.) i =0 Determine spectral radius through max-min operation 4 N 1 � ρ ( K ( π )) = x ≥ 0 , x � = 0 min max k mn ( π ) x n x m m , x m � =0 m =1 Show ρ ( K ( π )) is continuous and nonincreasing in price π . 5 � � Find a price π > max m U ′ Ph mm , s.t. ρ ( K ( π )) < 1. 6 m n 0 h 0 m Find a price π > 0, s.t. ρ ( K ( π )) > 1. 7 There exists π th ∈ [ π, π ], s.t. ρ ( K ( π )) < 1 iff π > π th . 8 J. Huang (Princeton University) Distributed Resource Allocation Jan. 2007 30 / 60
Network Objectives Efficiency Problem Fairness Problem (Optimization Problems) Efficient Allocation Solutions Fair Allocation Unique Solutions N.E. N.E. (Positive Reserve Bid) (Large Price) Divisible Auction SINR Auction Power Auction (Non−cooperative Game) J. Huang (Princeton University) Distributed Resource Allocation Jan. 2007 31 / 60
What Do We Want to Know? When does a unique N.E. exist? What are the properties of the N.E.? (Fairness? Efficiency?) How to achieve the N.E. in a distributed fashion? J. Huang (Princeton University) Distributed Resource Allocation Jan. 2007 32 / 60
SINR Auction: N.E. Achieves Fair Allocation Theorem (SINR auction: Fair Allocation) Under properly chosen price, the unique N.E. leads to a power allocation that is arbitrary close to the fair allocation. J. Huang (Princeton University) Distributed Resource Allocation Jan. 2007 33 / 60
SINR Auction: N.E. Achieves Fair Allocation Theorem (SINR auction: Fair Allocation) Under properly chosen price, the unique N.E. leads to a power allocation that is arbitrary close to the fair allocation. Implication : Positive reserve bid β leads to resource waste This waste can be made very small by properly chosen price Argument can be made precise by defining an ǫ -system Proof : Satisfy fairness conditions (equalizing marginal utility) 1 Minimum SINR n can not be further improved 2 J. Huang (Princeton University) Distributed Resource Allocation Jan. 2007 33 / 60
Power Auction: N.E. Achieves Efficient Allocation Large bandwidth ⇒ the efficiency problem becomes convex ◮ Example: logarithmic utility U n ( SINR n ) = log( SINR n ) B > P / n 0 J. Huang (Princeton University) Distributed Resource Allocation Jan. 2007 34 / 60
Power Auction: N.E. Achieves Efficient Allocation Large bandwidth ⇒ the efficiency problem becomes convex ◮ Example: logarithmic utility U n ( SINR n ) = log( SINR n ) B > P / n 0 Theorem (Power Auction: Efficient Allocation) Under properly chosen price, the unique N.E. leads to a power allocation that is arbitrary close to the efficient allocation. Proof : Power allocation at the N.E. satisfies KKT conditions. 1 KKT conditions are necessary and sufficient for efficient allocation. 2 J. Huang (Princeton University) Distributed Resource Allocation Jan. 2007 34 / 60
Network Objectives Efficiency Problem Fairness Problem (Optimization Problems) Efficient Allocation Solutions Fair Allocation Arbitrarily Close (Under Proper Price) Unique Solutions N.E. N.E. (Positive Reserve Bid) (Large Price) Divisible Auction SINR Auction Power Auction (Non−cooperative Game) J. Huang (Princeton University) Distributed Resource Allocation Jan. 2007 35 / 60
What Do We Want to Know? When does a unique N.E. exist? What are the properties of the N.E.? (Fairness? Efficiency?) How to achieve the N.E. in a distributed fashion? J. Huang (Princeton University) Distributed Resource Allocation Jan. 2007 36 / 60
Best Response Updates For user n at time iteration t , update bid as � � b ( t ) b ( t − 1) = B n − n J. Huang (Princeton University) Distributed Resource Allocation Jan. 2007 37 / 60
Best Response Updates For user n at time iteration t , update bid as � � b ( t ) b ( t − 1) = B n − n SINR auction b ( t ) k mn b ( t − 1) � = + k 0 n β n m m � = n J. Huang (Princeton University) Distributed Resource Allocation Jan. 2007 37 / 60
Best Response Updates For user n at time iteration t , update bid as � � b ( t ) b ( t − 1) = B n − n SINR auction b ( t ) k mn b ( t − 1) � = + k 0 n β n m m � = n Theorem (BR Updates Locally Computable) Best response update of user n can be written as b ( t ) = g ( t − 1) b ( t − 1) n n n where coefficient g ( t − 1) only depends on n ◮ Common information: P, n 0 and π . ◮ Local information: U n , h n and SINR ( t − 1) . n J. Huang (Princeton University) Distributed Resource Allocation Jan. 2007 37 / 60
Convergence of Best Response Updates SINR Auction Theorem (Global Convergence of BR Updates) Under a fixed price, best response updates globally and geometrically converge to the unique N.E. ◮ Only limited explicit message passing: ⋆ bid (user to manager) and resource allocation (manager to user) ◮ No need to know anything about other users J. Huang (Princeton University) Distributed Resource Allocation Jan. 2007 38 / 60
Convergence of Best Response Updates SINR Auction Theorem (Global Convergence of BR Updates) Under a fixed price, best response updates globally and geometrically converge to the unique N.E. ◮ Only limited explicit message passing: ⋆ bid (user to manager) and resource allocation (manager to user) ◮ No need to know anything about other users Power auction ◮ Similar arguments also apply for the power auction ◮ Only works for specific utility functions ⋆ Examples: log(1 + SINR n ) and log( SINR n ) J. Huang (Princeton University) Distributed Resource Allocation Jan. 2007 38 / 60
Network Objectives Efficiency Problem Fairness Problem (Optimization Problems) Efficient Allocation Solutions Fair Allocation Arbitrarily Close Distributed BR Updates (Under Proper Price) Unique Solutions N.E. N.E. (Positive Reserve Bid) (Large Price) Divisible Auction SINR Auction Power Auction (Non−cooperative Game) J. Huang (Princeton University) Distributed Resource Allocation Jan. 2007 39 / 60
��� ��� ��� ��� ��� ��� Extension to General Network Model All results related to SINR auction go through J. Huang (Princeton University) Distributed Resource Allocation Jan. 2007 40 / 60
Extension to General Network Model All results related to SINR auction go through 24 T T 3 R 1 1 23 user 1 user 2 22 user 3 Achieved SINR (dB) 21 ��� ��� R M R 20 3 2 ��� ��� 19 ��� ��� 18 17 T 2 16 0 5 10 15 20 Iterations Convergence of SINR Network Topology SINR Auction Same logarithmic utility function ⇒ same SINR allocation J. Huang (Princeton University) Distributed Resource Allocation Jan. 2007 40 / 60
Summary Topic : spectrum sharing in licensed bands Key idea : simple divisible auction Performance ◮ SINR auction: fair allocation ◮ Power auction: efficient allocation ◮ Large system: two auctions are both efficient Algorithm : best response updates: distributed, provable convergence Practice : a first step towards building a flexible cognitive-radio based spectrum sharing network Main contribution : a new modeling framework and solution methodology for distributed resource allocation in a coupled system J. Huang (Princeton University) Distributed Resource Allocation Jan. 2007 41 / 60
Outline Introduction 1 Case I: Cognitive Radio Network 2 Case II: DSL Network 3 Summary 4 J. Huang (Princeton University) Distributed Resource Allocation Jan. 2007 42 / 60
Digitial Subscriber Line (DSL) Networks Wireline communications networks based telephone copper lines Cost-effective broadband access network More than 160 million users world-wide CO TX RX Customer (Central Office) crosstalk RT TX RX Customer (Remote Terminal) J. Huang (Princeton University) Distributed Resource Allocation Jan. 2007 43 / 60
Digitial Subscriber Line (DSL) Networks Wireline communications networks based telephone copper lines Cost-effective broadband access network More than 160 million users world-wide Speed is the bottleneck CO TX RX Customer (Central Office) crosstalk RT TX RX Customer (Remote Terminal) J. Huang (Princeton University) Distributed Resource Allocation Jan. 2007 43 / 60
How DSL Works? Copper line can support signal transmissions over a large bandwidth Voice transmission: up to 3 . 4 KHz DSL transmissions: up to 30 MHz ◮ Multi-carrier transmissions: Discrete Multitone Modulation Voice DSL 0 3.4 Frequency (KHz) J. Huang (Princeton University) Distributed Resource Allocation Jan. 2007 44 / 60
Network and Channel Model CO TX RX Customer (Central Office) crosstalk RT TX RX Customer (Remote Terminal) Mathematical model : multi-user multi-carrier interference channel Each telephone line is a user (transmitter-receiver pair) Generate mutual crosstalks over multiple frequency tones J. Huang (Princeton University) Distributed Resource Allocation Jan. 2007 45 / 60
Network and Channel Model CO TX RX Customer (Central Office) crosstalk RT TX RX Customer (Remote Terminal) Physical model : mixed CO/RT case Channel attenuates with distance Central Office (CO) connect customers who are reasonably close Remote Terminal (RT) connect customers who are farther away J. Huang (Princeton University) Distributed Resource Allocation Jan. 2007 45 / 60
Network and Channel Model CO TX RX Customer (Central Office) crosstalk RT TX RX Customer (Remote Terminal) Frequency-Dependent Channel Direct channel gain decreases with frequency Crosstalk channel gain increases with frequency J. Huang (Princeton University) Distributed Resource Allocation Jan. 2007 45 / 60
Network and Channel Model CO TX RX Customer (Central Office) crosstalk RT TX RX Customer (Remote Terminal) Frequency-Dependent Channel Direct channel gain decreases with frequency Crosstalk channel gain increases with frequency Lead to near-far problem ◮ RT generates strong crosstalk to CO line, especially in high tones ◮ CO generates little crosstalk to RT in all tones J. Huang (Princeton University) Distributed Resource Allocation Jan. 2007 45 / 60
Network Objective: Maximize Rate Region Rate Region : set of all achievable rate vectors R 1 Rate Region R 2 J. Huang (Princeton University) Distributed Resource Allocation Jan. 2007 46 / 60
Network Objective: Maximize Rate Region Rate Region : set of all achievable rate vectors R 1 Rate Region R 2 Problem A: (Find One Point On the Rate Region Boundary) � maximize w n R n { p n ∈P n } n n � 1 + SINR k � User n ’s achievable rate R n = � k log . n ◮ No multi-user joint decoding n ≤ P max �� k p k , p k � User n chooses a power vector p n ∈ P n = n ≥ 0 . n J. Huang (Princeton University) Distributed Resource Allocation Jan. 2007 46 / 60
Network Objective: Maximize Rate Region Rate Region : set of all achievable rate vectors R 1 Rate Region R 2 Problem A: (Find One Point On the Rate Region Boundary) � maximize w n R n { p n ∈P n } n n � 1 + SINR k � User n ’s achievable rate R n = � k log . n ◮ No multi-user joint decoding n ≤ P max �� k p k , p k � User n chooses a power vector p n ∈ P n = n ≥ 0 . n Changing different weights trace the entire rate region boundary J. Huang (Princeton University) Distributed Resource Allocation Jan. 2007 46 / 60
Network Objective: Maximize Rate Region Rate Region : set of all achievable rate vectors R 1 Rate Region R 2 Problem A: (Find One Point On the Rate Region Boundary) � maximize w n R n { p n ∈P n } n n � 1 + SINR k � User n ’s achievable rate R n = � k log . n ◮ No multi-user joint decoding n ≤ P max �� k p k , p k � User n chooses a power vector p n ∈ P n = n ≥ 0 . n Changing different weights trace the entire rate region boundary A suboptimal algorithm leads to a reduced rate region J. Huang (Princeton University) Distributed Resource Allocation Jan. 2007 46 / 60
Properties of Problem A Technical difficulties ◮ Non-convexity: total weighted rate not concave in power. ◮ Physically distributed: local channel information ◮ Performance coupling: across users (interferences) and tones (power constraint) J. Huang (Princeton University) Distributed Resource Allocation Jan. 2007 47 / 60
Properties of Problem A Technical difficulties ◮ Non-convexity: total weighted rate not concave in power. ◮ Physically distributed: local channel information ◮ Performance coupling: across users (interferences) and tones (power constraint) Difference from the wireless case ◮ Static channels ◮ Multi-carrier transmissions ◮ Typical network topology ◮ Unique channel frequency responses with good empirical models ◮ Cannot decode explicit message passing J. Huang (Princeton University) Distributed Resource Allocation Jan. 2007 47 / 60
Properties of Problem A Technical difficulties ◮ Non-convexity: total weighted rate not concave in power. ◮ Physically distributed: local channel information ◮ Performance coupling: across users (interferences) and tones (power constraint) Difference from the wireless case ◮ Static channels ◮ Multi-carrier transmissions ◮ Typical network topology ◮ Unique channel frequency responses with good empirical models ◮ Cannot decode explicit message passing Our Solution : ASB algorithm J. Huang (Princeton University) Distributed Resource Allocation Jan. 2007 47 / 60
Dynamic Spectrum Management (DSM) State-of-art DSM algorithms: ◮ IW: Iterative Water-filling [Yu, Ginis, Cioffi’02] R 1 IW R 2 Algorithm Operation Complexity Performance IW Autonomous O ( KN ) Suboptimal J. Huang (Princeton University) Distributed Resource Allocation Jan. 2007 48 / 60
Dynamic Spectrum Management (DSM) State-of-art DSM algorithms: ◮ IW: Iterative Water-filling [Yu, Ginis, Cioffi’02] ◮ OSB: Optimal Spectrum Balancing [Cendrillon et al.’04] ◮ ISB: Iterative Spectrum Balancing [Liu, Yu’05] [Cendrillon, Moonen’05] R 1 OSB/ISB IW R 2 Algorithm Operation Complexity Performance IW Autonomous O ( KN ) Suboptimal � Ke N � OSB Centralized O Optimal � KN 2 � ISB Centralized O Near Optimal J. Huang (Princeton University) Distributed Resource Allocation Jan. 2007 48 / 60
Dynamic Spectrum Management (DSM) State-of-art DSM algorithms: ◮ IW: Iterative Water-filling [Yu, Ginis, Cioffi’02] ◮ OSB: Optimal Spectrum Balancing [Cendrillon et al.’04] ◮ ISB: Iterative Spectrum Balancing [Liu, Yu’05] [Cendrillon, Moonen’05] ◮ ASB: Autonomous Spectrum Balancing [Huang et al.’06] R 1 OSB/ISB /ASB IW R 2 Algorithm Operation Complexity Performance IW Autonomous O ( KN ) Suboptimal � Ke N � OSB Centralized O Optimal � KN 2 � ISB Centralized O Near Optimal ASB Autonomous O ( KN ) Near Optimal J. Huang (Princeton University) Distributed Resource Allocation Jan. 2007 48 / 60
Key Idea: Reference Line Reference line : static pricing for static channel ◮ A virtual line representative of the typical victim in the network ◮ Good choice: the longest CO line ◮ Parameters (power, noise, crosstalk) are publicly known Each user will choose its transmit power to protect the reference line J. Huang (Princeton University) Distributed Resource Allocation Jan. 2007 49 / 60
Reference Line CO CP RT CP RT CP RT CP J. Huang (Princeton University) Distributed Resource Allocation Jan. 2007 50 / 60
Reference Line CO CP Reference Line CO CP Actual Line RT CP RT CP RT CP J. Huang (Princeton University) Distributed Resource Allocation Jan. 2007 50 / 60
Reference Line’s Rate User n’s obtains the reference line parameters locally p k,ref Reference Power: Operator Reference Line Reference Noise: σ k,ref Database Length & Location α k,ref Reference Crosstalk: n J. Huang (Princeton University) Distributed Resource Allocation Jan. 2007 51 / 60
Reference Line’s Rate User n’s obtains the reference line parameters locally p k,ref Reference Power: Operator Reference Line Reference Noise: σ k,ref Database Length & Location α k,ref Reference Crosstalk: n The reference line rate � � p k , ref R ref � = log 1 + n α k , ref n + σ k , ref p k n k ◮ Interference only depends on user n ’s transmit power p k n ◮ Locally computable without explicit message passing J. Huang (Princeton University) Distributed Resource Allocation Jan. 2007 51 / 60
Payoff and Best Response User n ’s payoff � R ref � � � � S n p n ; p − n n ( p n ) + w n R n p n ; p − n J. Huang (Princeton University) Distributed Resource Allocation Jan. 2007 52 / 60
Payoff and Best Response User n ’s payoff � R ref � � � � S n p n ; p − n n ( p n ) + w n R n p n ; p − n Best response � � � arg max � � p − n p n ∈P n S n p n ; p − n B ◮ Requires solving a nonconvex optimization problem ◮ Duality gap is zero (under large number of tones) ◮ Satisfied in real DSL networks (ADSL: 256 tones, VDSL: 4096 tones) ◮ Can be solved using dual decomposition J. Huang (Princeton University) Distributed Resource Allocation Jan. 2007 52 / 60
Frequency Selective Water-filling Under high SNR approximation of the reference line + w n � B k h k n , m / h k n , n p k m − σ k � � p − n = − n /σ k , ref · 1 { p k , ref > 0 } n λ n + α k , ref n m � = n ◮ Reference line is not active in high frequency tones Special case: traditional water-filling (ignore α k , ref /σ k , ref ) n J. Huang (Princeton University) Distributed Resource Allocation Jan. 2007 53 / 60
Frequency Selective Water-filling Under high SNR approximation of the reference line + w n � B k h k n , m / h k n , n p k m − σ k � � p − n = − n /σ k , ref · 1 { p k , ref > 0 } n λ n + α k , ref n m � = n ◮ Reference line is not active in high frequency tones Special case: traditional water-filling (ignore α k , ref /σ k , ref ) n Power Interference & Noise Frequency Traditional Water−Filling J. Huang (Princeton University) Distributed Resource Allocation Jan. 2007 53 / 60
Frequency Selective Water-filling Under high SNR approximation of the reference line + w n � B k h k n , m / h k n , n p k m − σ k � � p − n = − n /σ k , ref · 1 { p k , ref > 0 } n λ n + α k , ref n m � = n ◮ Reference line is not active in high frequency tones Special case: traditional water-filling (ignore α k , ref /σ k , ref ) n Power Interference & Noise Frequency Active Reference Line Frequency−Selective Water−Filling J. Huang (Princeton University) Distributed Resource Allocation Jan. 2007 53 / 60
Convergence of ASB Algorithm ASB Algorithm: users update their individual power allocation according to best responses either sequentially or in parallel Theorem ASB algorithm globally and geometrically converges to the unique N.E. if the crosstalk channel is small, i.e., h k 1 n , m max < N − 1 . h k n , m , k n , n Independent of the reference line parameters. Recover the convergence of iterative water-filling as a special case. Proof : contraction mapping J. Huang (Princeton University) Distributed Resource Allocation Jan. 2007 54 / 60
Proof Outline Key Lemma : min-max of an increasing function and an decreasing 1 function is achieved at the intersection. Construct two such functions based on the ASB algorithm. 2 Show the maximum difference between the PSD during adjacent 3 iterations is decreasing. �� � � + � − � � p k , t +1 − p t , t � p k , t +1 − p k , t max max , n n n n n k k �� � � + � − � � � p k , t − p k , t − 1 p k , t − p k , t − 1 ≤ max max , n n n n n k k ◮ Sequential updates: bound the maximum eigenvalue of the mapping matrix. ◮ Parallel updates: more realistic with cleaner proof. J. Huang (Princeton University) Distributed Resource Allocation Jan. 2007 55 / 60
ASB Performance 4 ADSL lines. Mixed CO/RT deployment. Practical channel and background noise models. 5Km User 1 CO CP 2Km 4Km User 2 RT CP 3.5Km 3Km RT CP User 3 4Km 3Km User 4 RT CP J. Huang (Princeton University) Distributed Resource Allocation Jan. 2007 56 / 60
ASB Performance 4 ADSL lines. Mixed CO/RT deployment. Practical channel and background noise models. Both users 2 and 3 acheive fixed rates 2Mbps. Examine the rate region in terms of users 1 and 4’s rates. 5Km User 1 CO CP 2Km 4Km User 2 RT CP 3.5Km 3Km RT CP User 3 4Km 3Km User 4 RT CP J. Huang (Princeton University) Distributed Resource Allocation Jan. 2007 56 / 60
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