ニューラルネットワークおよび空間内挿に基づく電波環境マップ構築に関する一考察

以下の講演で使用したスライドです。
佐藤光哉, 稲毛契, 藤井威生, "ニューラルネットワークおよび空間内挿に基づく電波環境マップ構築に関する一考察, " 信学技報, SR2018-106, pp.63-70, 2019年1月.

※Extended Work:
Koya Sato, Kei Inage, and Takeo Fujii, "On the Performance of Neural Network Residual Kriging in Radio Environment Mapping," IEEE Access, vol. 7, no. 1, pp.94557-94568, 2019.
https://ieeexplore.ieee.org/document/8763960

Transcript

1. χϡʔϥϧωοτϫʔΫ͓Αͼۭؒ಺ૠʹجͮ͘ ి೾؀ڥϚοϓߏஙʹؔ͢ΔҰߟ࡯ ࠤ౻ޫ࠸1, Ҵໟܖ 2, ౻ҪҖੜ 3 1 ౦ژཧՊେֶ ޻ֶ෦ిؾ޻ֶՊ 2 ౦ژ౎ཱ࢈ۀٕज़ߴ౳ઐ໳ֶߍ ిؾిࢠ޻ֶίʔε 3 ిؾ௨৴େֶ ઌ୺ϫΠϠϨεɾίϛϡχέʔγϣϯݚڀηϯλʔ E-mail: k sato@ieee.org 2019 ೥ 1 ݄ 24 ೔ K. Sato, K. Inage, T. Fujii 2019 ೥ 1 ݄ 24 ೔ 1 / 21
2. ి೾؀ڥϚοϓ (REM) ʹجͮ͘ి೾؀ڥਪఆ REM (Radio Environment Map): ”ฏۉड৴ిྗ஋ΛϚοϓԽͨ͠΋ͷ” ˠ؆қʹେہతͳి೾఻ൖಛੑΛਪఆ͢Δखஈͱͯ͠஫໨ LN ૹ৴ہ REM ͷར༻ྫ TV ଳҬʹ͓͚Δۭ͖ଳҬ༧ଌ ηϧϥʹ͓͚Δج஍ہؒͷׯব؅ཧ ༧ΊΫϥ΢υʹ֨ೲ͓ͯ͘͜͠ͱͰ ڑ཭ݮਰ+γϟυ΢Πϯά੒෼Λ؆қʹਪఆ (REM ͕ޡࠩΛؚΜͰ͍ͯ΋) प೾਺ར༻ޮ཰ͷ޲্͕Մೳ 1 1K. Sato, K. Inage and T. Fujii, ”Modeling the Kriging-Aided Spatial Spectrum Sharing over Log-Normal Channels, ” IEEE Wireless Commun. Lett., 2019 (in press). K. Sato, K. Inage, T. Fujii 2019 ೥ 1 ݄ 24 ೔ 2 / 21
3. Ϋϥ΢υηϯγϯάʹجͮ͘ REM ߏங εϚʔτϑΥϯ΍ं͕྆Ҡಈ؍ଌͨ͠ड৴ిྗΛΫϥ΢υʹू໿͢Δ͜ͱͰߏங ॴ๬ͷ৘ใ LN ૹ৴ہ ؍ଌ݁Ռ −100 −95 −90 −85 −80 −75 −70 Average Received Signal Power [dBm] ໰୊఺: ৘ใ͕ࣃൈ͚ʹͳΔͨΊɺपลͷσʔλ͔Βิؒਪఆ͢Δඞཁ ˠ؍ଌ஋ {P(x1 ), P(x2 ), · · · , P(xN )} ΑΓ೚ҙͷ஍఺Ͱͷड৴ిྗΛ͍͔ʹਫ਼౓ ྑ͘ਪఆ͢Δ͔ʁ K. Sato, K. Inage, T. Fujii 2019 ೥ 1 ݄ 24 ೔ 3 / 21
4. ۭؒ౷ܭతΞϓϩʔνʹجͮ͘ REM ߏங ૹ৴Ґஔ xTx ͷ৔߹ͷ x ʹ͓͚Δड৴ిྗ͸ɺఆ਺߲ PC , ڑ཭ݮਰ L, γϟυ΢ Πϯά W ΑΓɺ P(x) = PC − L(||x − xTx ||) (1) +W(x) (2) [dBm] (1) ఆ਺߲+ڑ཭ݮਰ ఆ਺ C ͱݮਰ܎਺ η ΑΓ y(d) = C − 10η log10 d ͷΑ͏ʹϞσϧԽ͠ɺճؼ෼ੳ͢Δ ͜ͱͰ OK (2) γϟυ΢Πϯά ௨ৗɺۙ๣ͷ஍఺ؒʹۭؒ૬ؔੑɻ ͦ͜ͰɺҎԼͷΑ͏ʹपลͰ؍ଌ͠ ͨγϟυ΢Πϯάʹର͠Ճॏฏۉ: ˆ W(x) = N ∑ i=1 ωi W(xi ) ΫϦΪϯά (ޙड़) ʹΑΓ܎਺ ωi Λ ࠷దԽ͢Δ͜ͱͰਫ਼౓ྑ͘ਪఆՄ K. Sato, K. Inage, T. Fujii 2019 ೥ 1 ݄ 24 ೔ 4 / 21
5. ۭؒ಺ૠʹجͮ͘ REM ߏஙͷྫ ૹ৴Ґஔ xTx ͷ৔߹ͷɺx ʹ͓͚Δड৴ిྗ: P(x) = (1) PC − L(||x − xTx ||) +W(x) (2) [dBm] ؍ଌ݁Ռ −100 −95 −90 −85 −80 −75 −70 Average Received Signal Power [dBm] (1) ճؼ෼ੳͷΈ −100 −95 −90 −85 −80 −75 −70 Average Received Signal Power [dBm] (2) ճؼ෼ੳ+಺ૠ −100 −95 −90 −85 −80 −75 −70 Average Received Signal Power [dBm] K. Sato, K. Inage, T. Fujii 2019 ೥ 1 ݄ 24 ೔ 5 / 21
6. ໰୊఺ɿڑ཭ݮਰಛੑͷҟํੑ ҰൠతͳԾఆ: PC − L(||x − xTx ||) = PC − 10η log10 d Ծఆ ํ֯ʹΑΒͣҰఆ ૹ৴ہ͸ϏʔϜΛܗ੒͠ͳ͍ 0 1000 2000 3000 4000 x [m] 0 1000 2000 3000 4000 [m] −110 −100 −90 −80 −70 −60 −50 −40 −30 −20 Average Received Signal Power [dBm] ࣮؀ڥ ํ֯ʹґଘ ૹ৴ہ͸ϏʔϜΛܗ੒ 0 1000 2000 3000 4000 x [m] 0 1000 2000 3000 4000 [m] −110 −100 −90 −80 −70 −60 −50 −40 −30 −20 Average Received Signal Power [dBm] Ծఆͱ࣮ࡍͷဃ཭ʹΑΔճؼޡࠩʹΑΓɺ಺ૠʹ͓͚Δ࠷దੑ΋่ΕΔڪΕ ҰํɺෳࡶͳϞσϧΛԾఆͯ͠΋ճؼੑೳʹ͸ݶք K. Sato, K. Inage, T. Fujii 2019 ೥ 1 ݄ 24 ೔ 6 / 21
7. ؔ࿈ݕ౼ͱຊݚڀͰͷϦαʔνΫΤενϣϯ χϡʔϥϧωοτϫʔΫ (NN) ʹΑΔڑ཭ݮਰಛੑͷਪఆʹ͍ͭͯ਺݅ͷใࠂ ྫ) M. Ayadi et al., July 2017 ೖྗ: ڑ཭, प೾਺, Ξϯςφߴ, ߏ ଄෺৘ใ ग़ྗ: ڑ཭ݮਰྔ [dB] UHF ଳʹͯطଘϞσϧͱൺֱͯ͠ ޡࠩΛ 2.5dB ఔ౓վળՄೳͱͷ݁Ռ ຊݚڀͰͷϦαʔνΫΤενϣϯ ճؼੑೳͷ޲্ʹΑΓɺ࠷ऴతͳ REM ͷߏஙੑೳ΋վળͰ͖ΔՄೳੑ ˠ NN ʹΑͬͯ REM ͷߏஙਫ਼౓ΛվળͰ͖Δ͔ʁ M. Ayadi et al., ”A UHF Path Loss Model Using Learning Machine for Heterogeneous Networks, ” IEEE Trans. Antennas Propag., July 2017. K. Sato, K. Inage, T. Fujii 2019 ೥ 1 ݄ 24 ೔ 7 / 21
8. χϡʔϥϧωοτϫʔΫͷ֓ཁ 1 χϡʔϩϯͷ৔߹ ⼊⼒ x 出⼒ y = h (wx+b) w h (གྷ) h (གྷ) ણਙ৲ঢ়ਯ(శ଍஄ঢ়ਯ) w ੎້બਯ b ৒ਯ 2 χϡʔϩϯΛܨ͛ͨ৔߹ ⼊⼒ x 出⼒ y = h (w1 x+b1 )+h (w2 x+b2 ) w1 h (གྷ) h (གྷ) w2 ඇઢܗग़ྗͷ࿨ΛऔΔ͜ͱͰؔ਺Λࣗࡏʹදݱ ܎਺ wi ͸؍ଌσʔληοτ͔Βઃܭ K. Sato, K. Inage, T. Fujii 2019 ೥ 1 ݄ 24 ೔ 8 / 21
9. NN ʹجͮ͘ճؼ෼ੳͰԿ͕Ͱ͖Δͷ͔ʁ ೖྗ x ʹର͢Δ؍ଌ஋ Z(x): Z(x) = f(x) ਪఆର৅ + ε ϊΠζ ड৴ిྗʹରԠͤ͞Δͱ: P(x) = PC − L(x) f(x) + W(x) ε ਂ૚ֶशʹΑΔ఻ൖ༧ଌͷྫ γϟυ΢Πϯά߲͸ NN ʹ͸ϊΠζͱͯ͠ݟ͑Δ NN Λ࢖༻ͨ͠ͱͯ͠΋ W(x) ͸ผ్ਪఆ͢ΔඞཁΞϦ J. Thrane et al., ”Drive test minimization using Deep Learning with Bayesian approximation, ” Proc. IEEE VTC2018-Fall, August 2018. K. Sato, K. Inage, T. Fujii 2019 ೥ 1 ݄ 24 ೔ 9 / 21
10. NN ʹΑΔճؼ෼ੳ+ৗΫϦΪϯάʹΑΔ REM ߏங λεΫ: N ஍఺Ͱ؍ଌͨ͠σʔληοτ (P(x1 ), P(x2 ), · · · , P(xN )) Λ࢖ͬͯ೚ ҙͷ஍఺ x0 Ͱͷ P(x0 ) Λਪఆ Ծఆ: ૹ৴ہ͸ 1 ୆ͰͦͷҐஔ͸ط஌ ݕ౼͢Δख๏ͷ֓ཁ 1 σʔληοτ͔Βڑ཭ݮਰಛੑΛܭࢉ͢Δ NN Λߏங (ޙड़) 2 ֤σʔλ͔Βγϟυ΢Πϯά੒෼ W(xi ) Λநग़ 3 W(xi ) ؒͷۭؒ૬ؔߏ଄ (૬ؔڑ཭΍ඪ४ภࠩ) Λܭࢉ 4 W(xi ) Λ༻͍ͯৗΫϦΪϯά (ޙड़) ʹΑΓ W(x0 ) Λ಺ૠ 5 NN Λ༻͍ͯ x0 ʹ͓͚Δڑ཭ݮਰಛੑΛਪఆ͠ɺ͜Εʹ W(x0 ) ΛՃࢉ ˞͜ͷΑ͏ͳख๏͸ Neural Network Regression Kriging (NNRK) ͱͯ͠஌ΒΕΔ M. Kanevsky et al., ʠ Artificial Neural Networks and Spatial Estimation of Chernobyl Fallout, ʡ Geoinformatics, 1996. K. Sato, K. Inage, T. Fujii 2019 ೥ 1 ݄ 24 ೔ 10 / 21
11. NN ʹΑΔڑ཭ݮਰಛੑਪఆ ⁹ ⁹ ⁹ 平均受信電⼒ >G%P@ d ș ⼊⼒層 র৑ಽ 出⼒層 xi Λڑ཭ di [m] ͱ֯౓ θi [deg] ʹม׵ di , θi , P(xi ) ΛͦΕͧΕ 0-1 ʹਖ਼نԽ ϛχόονֶशʹΑΔ܁Γฦֶ͠श ֶशنൣ: ฏۉೋ৐ޡࠩ (MSE: Mean Squared Error) ٯޡࠩ఻ൖ͓Αͼ Adam ʹΑΓ NN தͷ܎ ਺Λ࠷దԽ ˞ Python 3.6.5 ্ʹ Chainer 4.5.0 Λ༻͍࣮ͯ૷ͨ͠ ˞ؔ࿈ݕ౼ʹΑΔதؒ૚͸ 1-2 ૚ఔ౓Ͱे෼ͱͷ݁ՌΛࢀߟʹࠓճ͸ 1 ૚Ͱٞ࿦ K. Sato, K. Inage, T. Fujii 2019 ೥ 1 ݄ 24 ೔ 11 / 21
12. ৗΫϦΪϯά (OK: Ordinary Kriging) ؍ଌ஋ͷՃॏฏۉ͔Β஍఺ x0 ʹ͓͚Δ஋Λ಺ૠ ˆ W(x0 ) = N ∑ i=1 ωi W(xi ) (i = 1, 2, · · · , N) ৗΫϦΪϯά E[W(x)] = const.ɺ͔ۭͭؒ૬ؔߏ଄͕৔ॴʹґଘ͠ͳ͍ͱԾఆɻ ޡࠩͷ෼ࢄͷ࠷খԽΛ໨తʹ ωi Λ࠷దԽ min σ2 k = E [( W(x0 ) − ˆ W(x0 ) )2 ] = −γ(d0,0 ) − N ∑ i=1 N ∑ j=1 ωi ωj γ(di,j ) + 2 N ∑ i=1 ωi + γ(di,0 ) ηϛόϦΦάϥϜ s.t. N ∑ i=1 ωi = 1 (ෆภਪఆͷͨΊͷ੒໿) ˠ͜ΕΛϥάϥϯδϡͷະఆ৐਺๏ʹΑΓղ͘ K. Sato, K. Inage, T. Fujii 2019 ೥ 1 ݄ 24 ೔ 12 / 21
13. ճؼޡࠩͷ REM ͷਫ਼౓ʹର͢ΔӨڹͷߟ࡯ ͋Δํ֯ʹ͓͍ͯҎԼΛԾఆ: ਅͷڑ཭ݮਰಛੑ: P(d) = PC − 10η log10 d [dBm] ਪఆ݁Ռ: P(d) = ˆ PC − 10ˆ η log10 d [dBm] 101 102 103 -100 -80 -60 -40 ┿΅கႣῶࢦ≉ᛶ ᥎ᐃȆᯝ ೖಙᒁΉ ΅கႣ[m] கႣῶࢦฎ [dB] d ǻd İ(d ) İ(d+ǻd ) E[Z(x)] = const. Λຬͨ͢৚݅: ε(d) − ε(d + ∆d) = 0 ࠨลΛ੔ཧ͢Δͱɺ ε(d)−ε(d+∆d) = 10(η−ˆ η)log10 d + ∆d d ఆৗੑ΁Өڹ͢Δͷ͸ ˆ PC ͱ ˆ η ͷ͏ͪޙऀͷΈ ૹ৴ہʹ͍ۙ΄Ͳ಺ૠ݁Ռ΁ͷӨڹ͕ݦஶʹͳΔ ͜ͷ৚݅Λຬͨͤ͹ ε(d) ͸಺ૠ࣌ʹิঈ͞ΕΔͨΊɺε(d) ͦͷ΋ͷͷେ͖͞͸໰୊φγ K. Sato, K. Inage, T. Fujii 2019 ೥ 1 ݄ 24 ೔ 13 / 21
14. γϛϡϨʔγϣϯϞσϧ dTx R xi x0 xTx ଛਦଂ ௬੼৉ਡ ௴೾৉ਡ ৔ዠີ໌ઞ৷ ௴೾৉ਡ ৚షີຸ້ઞ৷ ϥϯμϜʹબ୒ͨ͠ N ஍఺Ͱ؍ଌ -100[dBm] Ҏ্ͷ৔߹࢖༻ ૹ৴Ξϯςφརಘ [dB]: G(θ) = min ( 12 ( θ θ3dB )2 , Gmin ) W(xi ) ͱ W(xj ) ͷ૬ؔ܎਺: ri,j = exp ( − ||xi − xj || dcor ln2 ) ˞ dcor : ૬ؔڑ཭ [m] ͋Δ 1 ஍఺ΛධՁ஍఺ͱ͠ɺ10000 ճࢼߦͨ͠ࡍͷ RMSE ಛੑΛܭࢉ͢Δ ૹ৴ऀ͔Βͷڑ཭Λύϥϝʔλͱ͢Δ K. Sato, K. Inage, T. Fujii 2019 ೥ 1 ݄ 24 ೔ 14 / 21
15. γϛϡϨʔγϣϯύϥϝʔλ ి೾఻ൖಛੑ γϟυ΢Πϯάͷ૬ؔڑ཭ dcor 300[m] γϟυ΢Πϯάͷඪ४ภࠩ σ 8.0[dB] ڑ཭ݮਰ܎਺ η 3.0 ϏʔϜ෯ θ3dB 60[deg] ࠷খΞϯςφརಘ Gmin -20[dB] ؍ଌ৚݅ ΤϦΞҰลͷ௕͞ L 5000[m] ิؒʹ࢖༻͢ΔΤϦΞͷ൒ܘ R 500[m] ؍ଌ஍఺਺ 1024 ड৴ᮢ஋ -100[dBm] ࢼߦճ਺ 10000 χϡʔϥϧωοτϫʔΫͷઃܭ ׆ੑԽؔ਺ ReLU Ϣχοτ਺ 100 ϛχόονॲཧʹ͓͚ΔόοναΠζ Nmb 256 ΤϙοΫ਺ Nepoch 500 K. Sato, K. Inage, T. Fujii 2019 ೥ 1 ݄ 24 ೔ 15 / 21
16. ૹ৴ہ͔Βͷڑ཭ʹର͢Δ RMSE ಛੑ ˞ OLS: Ordinary Least Squares ਺ඦ m ఔ౓·Ͱ͸ NN ʹΑΔޮՌ͋Γ ౳ํੑΛԾఆͯ͠΋ (ճؼ݁Ռ͸࢖͍෺ʹͳΒͳ͍͕) ࠷ऴతʹ͸े෼ͳਫ਼౓ K. Sato, K. Inage, T. Fujii 2019 ೥ 1 ݄ 24 ೔ 16 / 21
17. γϟυ΢Πϯάͷ૬ؔڑ཭ͷӨڹ ૬ؔڑ཭௕: ಺ૠ࣌ʹԕํͷ৘ใ΋׆༻Ͱ͖ΔͨΊਫ਼౓Λಘ΍͍͢ ૹ৴ہ͔Βͷڑ཭ 500m ૹ৴ہ͔Βͷڑ཭ 2000m ख๏ؒͷਫ਼౓ͷେখؔ܎ ૹ৴ऀ͔Βͷڑ཭ʹର͢ΔճؼޡࠩͷӨڹ ͸γϟυ΢Πϯά૬ؔʹґଘ͠ͳ͍ K. Sato, K. Inage, T. Fujii 2019 ೥ 1 ݄ 24 ೔ 17 / 21
18. ςϨϏ์ૹ೾ʹ͓͚Δ࣮σʔληοτΛ࢖༻ͨ͠਺஋ྫ 2013-14 ೥ʹ࡛ۄݝ۽୩ࢢʹͯं྆ 5 ୆Λ༻͍ͯҠಈ؍ଌ ֤ं྆ 2 ୆ͣͭ؍ଌػ (USRP) Λ౥ࡌ, ߴ଎ϑʔϦΤม׵ʹΑΔॠ࣌ిྗͷ؍ ଌΛ܁Γฦͨ͠ LN ૹ৴ہ ؍ଌप೾਺ 521.14[MHz] ϝογϡαΠζ 10[m] ϝογϡ਺ (˞) 22332 ؍ଌػث Ettus N210 αϯϓϦϯάप೾਺ 200[kHz] αϯϓϦϯά఺਺ 2048 ˞؍ଌ஋͸ϝογϡ͝ͱʹฏۉԽࡁΈ K. Sato, M. Kitamura, K. Inage and T. Fujii, ”Measurement-based Spectrum Database for Flexible Spectrum Management, ” IEICE Trans. Commun., October 2015. K. Sato, K. Inage, T. Fujii 2019 ೥ 1 ݄ 24 ೔ 18 / 21
19. ߏங݁Ռͷྫ (512 ϝογϡΑΓߏங) ઢܗճؼʹجͮ͘৔߹ −100 −95 −90 −85 −80 −75 −70 Average Received Signal Power [dBm] −100 −95 −90 −85 −80 −75 −70 Average Received Signal Power [dBm] NN ʹجͮ͘৔߹ −100 −95 −90 −85 −80 −75 −70 Average Received Signal Power [dBm] −100 −95 −90 −85 −80 −75 −70 Average Received Signal Power [dBm] K. Sato, K. Inage, T. Fujii 2019 ೥ 1 ݄ 24 ೔ 19 / 21
20. ࣮ଌ஋ʹ͓͚Δ RMSE ಛੑ ධՁखॱ 1 શσʔληοτ͔ΒϥϯμϜʹ N ஍఺બ୒͠ REM ߏங 2 ผ్બ୒ͨ͠ 10 ஍఺Ͱͷਫ਼౓ΛධՁ 3 ্هखॱΛ 100 ճ܁Γฦ͢͜ͱͰ N ʹର͢Δ RMSE ΛධՁ Table: ࣮ଌ஋ʹ͓͚Δ RMSE[dB] N = 256 N = 512 N = 1024 OLS 5.79 6.05 6.10 NN 5.41 5.20 5.04 OLS+ΫϦΪϯά 4.70 4.58 4.66 NN+ΫϦΪϯά 4.70 4.65 4.58 ճؼ෼ੳͷΈʹண໨͢Δͱ NN ʹΑͬͯ 1dB ఔ౓վળ ಺ૠ·ͰՃຯ͢Δͱͦͷࠩ͸΄΅ຒ·Δ ˠ͜ͷΑ͏ͳ (REM ͷద༻ઌͱͯ͠Ұൠʹ૝ఆ͞Ε͍ͯΔ) ؀ڥʹ͓͍ͯ͸ɺڑ཭ ݮਰಛੑਪఆͷઃܭ͸؆қͳख๏Ͱ OK K. Sato, K. Inage, T. Fujii 2019 ೥ 1 ݄ 24 ೔ 20 / 21
21. ·ͱΊ ໰͍: NN ʹΑΔڑ཭ݮਰಛੑਪఆͰ REM ͷਫ਼౓ΛվળͰ͖ͦ͏͔ʁ ݱ࣌఺Ͱͷ݁࿦ ʙkm:(ൺֱత୯७ͳධՁ؀ڥͰ΋) े෼ͳద༻ޮՌΞϦ ਺ kmʙ: ୯७ͳઢܗճؼͰ OK ࠓޙͷ՝୊ ͞ΒͳΔ࣮σʔληοτʹΑΔݕূ (e.g. ԰಺ WLAN) ૹ৴ऀͷҐஔ͕ݻఆͰ͸ͳ͍؀ڥ΁ͷԠ༻ (e.g. V2V) (গ͠ݸਓతͳ) એ఻ 3 ݄ͷҠಈ௨৴ϫʔΫγϣοϓ@YRP Ͱߨԋ༧ఆͰ͢: ࠤ౻ޫ࠸, ”[ґཔߨԋ] ి೾؀ڥϚοϓʹجͮ͘प೾਺ڞ༻ͷཧ࿦ͱ՝୊” K. Sato, K. Inage, T. Fujii 2019 ೥ 1 ݄ 24 ೔ 21 / 21