估測正交頻率多重傳輸系統時間偏移的最佳脈衝整型濾波器
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(2) ,¿£>ä0Ö½fÍ$vÈRí|70 §c˙šÂ û˝Þ: Û6›. Nû`¤: wƒÊ²=. Å >¦×çÚœD−„ ˙çÍ. ¿b Ê£>ä0Ö½f (Orthogonal frequency-division multiplexing) Í$2, vÈR (timing offset) £ä0R (frequency offset) í,¿u'½bí{æ Êd.2'Öj¶V,¿¥ s_¡b, <j¶u‚ào*å (training sequences) CäN¯U (pilot symbols), <j¶ †u‚àU‚ÓG4 (cyclostationary) VT,¿ Ê‚ào*åCäN¯Uíj¶³uJQY ƒ’eíóÉ4 (correlation) C|×–Nƒb (likelihood function) V,¿vÈ£ä0R … dFníj¶u‚à|×–NƒbV,¿vÈ£ä0R md.íj¶1³5?ƒÄ¦ švÈÏÏF¨AíÝcbvÈR Ĥ…dí3bõ.uøÝcbvÈR‹p5¾ Bb êÛUà.°í0§c˙šÂ (pulse shaping filter) wvÈ£ä0Rí,¿ÏÏ6.° B b1Rû|¤ù,¿¡b5 CR iä (Cram´er-Rao bounds), 7/qlø0§c˙šÂJU) ,¿vÈRÏÏ5 CR iäÑ|ü, 5(yJ_Ò!‹ð}wi4. ÉœÈ: £>ä0Ö½f |×–N¶ 0§c˙šÂ. i.
(3) Optimal Pulse Shaping Filter for Timing Offset Estimation in OFDM System Student: Pey-Huan Lu. Advisor: Dr. Mu-Huo Cheng. Institute of Electrical and Control Engineering National Chiao-Tung University Abstract It is important to estimate the frequency offset and timing offset in an orthogonal frequency-division multiplexing (OFDM) system. Many approaches have been developed in literature. Some approaches use training sequences or pilot symbols, others use the property of cyclostationarity for estimation. Those approaches via training sequences or pilot symbols employ the correlation or the maximum likelihood function for parameter estimation. This thesis focuses on the maximum likelihood approach. In literature, the approaches via the maximum likelihood function, as far as we know, only estimate integer timing offset but neglect the inevitable noninteger timing offset.This thesis considers this noninteger timing error. It is observed that the pulse shaping filter will influence the estimation performance. Thus we derive the Cram´er-Rao bound and use this bound as the measure to design optimal pulse shaping filter such that the Cram´er-Rao bound for the estimation error of timing offset is minimized. Simulations are then performed to verify the usefulness of this design.. Keywords: OFDM, Maximum Likelihood, pulse shaping filter.. ii.
(4) Ðá ¤d?ß‚êA, bÔöyË>áBíNû`¤wƒÊ`¤, Ê¥ssísû˝Þ®2, Ìu&AQÓíy^ö£CµçGíÃã -, ÌUBÊÞº£ç…,×ïGÖ Ä¤Ê…d GF5Ò, úk:£f−¤“í4_,|y£íá< ʨt‚ÈwPŠÀé`¤¸ŠÄI`¤Æ˛N£1TXrÖ£í<c ʤ>á5bí: °v>áH“çÅyÞ ‰ï \¨ ¼ TÔí‹“H−, J£õðíFAº: P+ Ù Áó ÅQ ?& ó¼ ]G §QÊ{“,í~}n£Þº,í¡;®x, ÑÓ À|íû˝ÞºÓ¼.ýH˘ |(b>áBíðA, âkFbíG|¸.iË2¥, éB?Ì(è5Rí*9û˝, ß‚êA ç“, 1/?‰Þú-øší˚ØD‘D. iii.
(5) ñ“. 2d¿b. i. Ld¿b. ii. Ðá. iii. Çñ“. vi. [ñ“. viii. 1 é. 1. 1.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 1. 1.2 û˝qñ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 1. 1.3 d-Z . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 2. 2 vÈDä0Rí,¿. 3. 2.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 3. 2.2 Í$_ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 3. 2.3 |×–Nƒb . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 4. 2.4 vÈDä0Rí CR iä . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 8. 3 |7“í0§c˙šÂ. 10. 3.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 3.2 |7“j¶ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 3.3 |7“0§c˙šÂ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12. iv.
(6) 3.4 |7“0§c˙šÂDwF˙šÂíªœ . . . . . . . . . . . . . . . . . . . . 17 4 _Ò!‹. 21. 4.1 _Ò¡bqì . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 4.2 |7“0§c˙šÂ_Ò!‹ . . . . . . . . . . . . . . . . . . . . . . . . . . 22 4.3 Nb0§c˙šÂ_Ò!‹ . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 4.4 ¯ìý0§c˙šÂ_Ò!‹ . . . . . . . . . . . . . . . . . . . . . . . . . . 29 4.5 n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 5 !. 34. ¡5d.. 35. v.
(7) Çñ“. Ç 2.1 £>ä0Ö½fÍ$ý<Ç . . . . . . . . . . . . . . . . . . . .. 3. ½º’eíh¿ý<Ç . . . . . . . . . . . . . . . . . .. 4. Ç 2.2 ¨Ö Ns. Ç 3.1 Ê.°SNR 5-í|7“0§c˙šÂ . . . . . . . . . . . . . . . 14 Ç 3.2 |7“0§c˙šÂÊ.°SNR £vÈRívÈ,¿ÏÏ . . . . . . . 15 Ç 3.3 SNR=0dB 5|7“0§c˙šÂÊ.° SNR £vÈRívÈ,¿ÏÏ . 15 Ç 3.4 SNR=10dB 5|7“0§c˙šÂÊ.° SNR £vÈRívÈ,¿ÏÏ . 16 Ç 3.5 SNR=20dB 5|7“0§c˙šÂÊ.° SNR £vÈRívÈ,¿ÏÏ . 16 Ç 3.6 Nb£¯ìý0§c˙šÂ . . . . . . . . . . . . . . . . . . . . 17 Ç 3.7 Nb0§c˙šÂvÈ,¿ÏÏ . . . . . . . . . . . . . . . . . . 18 Ç 3.8 ¯ìý0§c˙šÂvÈ,¿ÏÏ. . . . . . . . . . . . . . . . . . 18 Ç 3.9 ®_0§c˙šÂvÈDvÈ,¿ÏÏÉ[Ç . . . . . . . . . . . . . 19 Ç 4.1 IEEE 802.11a lû¯U-Z . . . . . . . . . . . . . . . . . . . . 21 Ç 4.2 |7“0§c˙šÂÊ θ = 0.1 víä0£vÈ,¿ÏÏ. . . . . . . . . 23 Ç 4.3 |7“0§c˙šÂÊ θ = 0.2 víä0£vÈ,¿ÏÏ. . . . . . . . . 23 Ç 4.4 |7“0§c˙šÂÊ θ = 0.3 víä0£vÈ,¿ÏÏ. . . . . . . . . 24 Ç 4.5 |7“0§c˙šÂÊ θ = 0.4 víä0£vÈ,¿ÏÏ. . . . . . . . . 24 Ç 4.6 SNR=10 dB 5|7“0§c˙šÂÊ θ = 0.1 víä0£vÈ,¿ÏÏ . . 25 Ç 4.7 SNR=10 dB |7“0§c˙šÂÊ θ = 0.2 víä0£vÈ,¿ÏÏ . . . 25 Ç 4.8 SNR=10 dB 5|7“0§c˙šÂÊ θ = 0.3 víä0£vÈ,¿ÏÏ . . 26 Ç 4.9 SNR=10 dB |7“0§c˙šÂÊ θ = 0.4 víä0£vÈ,¿ÏÏ . . . 26 Ç 4.10 Nb0§c˙šÂÊ θ = 0.1 víä0£vÈ,¿ÏÏ . . . . . . . . . 27. vi.
(8) Ç 4.11 Nb0§c˙šÂÊ θ = 0.2 víä0£vÈ,¿ÏÏ . . . . . . . . . 27 Ç 4.12 Nb0§c˙šÂÊ θ = 0.3 víä0£vÈ,¿ÏÏ . . . . . . . . . 28 Ç 4.13 Nb0§c˙šÂÊ θ = 0.4 víä0£vÈ,¿ÏÏ . . . . . . . . . 28 Ç 4.14 ¯ìý0§c˙šÂÊ θ = 0.1 víä0£vÈ,¿ÏÏ . . . . . . . . 29 Ç 4.15 ¯ìý0§c˙šÂÊ θ = 0.2 víä0£vÈ,¿ÏÏ . . . . . . . . 29 Ç 4.16 ¯ìý0§c˙šÂÊ θ = 0.3 víä0£vÈ,¿ÏÏ . . . . . . . . 30 Ç 4.17 ¯ìý0§c˙šÂÊ θ = 0.4 víä0£vÈ,¿ÏÏ . . . . . . . . 30 Ç 4.18 0§c˙šÂÊ θ = 0.1 vívÈ,¿ÏÏ . . . . . . . . . . . . . 31 Ç 4.19 0§c˙šÂÊ θ = 0.2 vívÈ,¿ÏÏ . . . . . . . . . . . . . 32 Ç 4.20 0§c˙šÂÊ θ = 0.3 vívÈ,¿ÏÏ . . . . . . . . . . . . . 32 Ç 4.21 0§c˙šÂÊ θ = 0.4 vívÈ,¿ÏÏ . . . . . . . . . . . . . 33. vii.
(9) [ñ“. [ 3.1 ®SNR ví c1 , c2 M. . . . . . . . . . . . . . . . . . . . . . . 13 [ 3.2 ®0§c˙šÂÊ.°SNR ví J M . . . . . . . . . . . . . . . . 20. viii.
(10) 1ı é 1.1 Ê£>ä0Ö½f (orthogonal frequency-division multiplexing) Í$52, QY«í °¥ (synchronization) uø_'½bí¥ ¤°¥¨Ö7-šä0R (carrier frequency offset) £¯UvÈR (symbol timing offset) í,¿, ÄÑbÄüí^k¥s_Rj|| Ÿ…í’e, .âbÄü,¿|¥s_^@ rÖd.[2]-[10] ˛%T|,¿íj¶, <j¶u ‚ào*å(training sequences) CäN¯U (pilot symbols)[2]-[7], <j¶‚àU‚ÓG 4(cyclostationary)[8][9][10] VT,¿ Ê‚ào*åCäN¯Uíj¶³u‚àQYƒ’e íóÉ4[2][3] C|×–Nƒb[4][5][6][7]V,¿vÈ£ä0R 7BbœEíuJ|×–N ¶(maximum likelihood) °)vÈ£ä0R, 6ÿuÊFhôƒ’eíœ0òƒb (probability density function) Ñ|×v, wvÈ£ä0R¹Ñ,¿M md.2[4][5][6][7]‚à|× –Nƒb,¿v1³5?ƒÄ¦švÈÏÏF¨AíÝcbvÈR Ĥ…døÝcbvÈ R‹p5¾, ‚à|×–Nƒb,¿vÈ£ä0R BbêÛUà.°í0§c˙šÂ(pulse shaping filter) wvÈ£ä0Rí,¿ÏÏ6}.° Bb6Rû|¤s¡bí CR iä (Cram´erRao bound), 1J CR iäÑĆqlU,¿vÈRÏÏ5 CR iäÑ|üí0§c˙šÂ 5(yJ IEEE 802.11a[1] 2íslû¯UÑW, øFql|í0§c˙šÂªW_Ò, ð}w i4. 1.2 û˝qñ Ñ°vÈR,¿íÄ, …døÝcbÈR‹p5¾, ‚à|סNƒb,¿£>ä0Ö ½fÍ$2ä0£vÈR ,¿!‹éý, Uà.°í0§c˙šÂ} àƒä0£vÈR. 1.
(11) 1 ı é í,¿!‹ ĤBbJCR iäÑĆ, ql|ø0§c˙šÂ, ¤0§c˙šÂøU,¿v ÈRÏÏÑ|ü. 1.3 d-Z …d-Zà-: ùı ÜÍ$_1/Ê‹p0§c˙šÂ(, J|×–N¶,¿|v È£ä0R, 1/Rûw CR iä úı ÜJ|7“j¶ql0§c˙šÂí¬˙, /D wFàí0§c˙šÂTªœ ûı, ø¤|7“J£wFàí0§c˙šÂ, Uàƒ| ×–N¶vÈ£ä0R,¿ªW_Ò üıÑ…dí!. 2.
(12) 2ı vÈDä0Rí,¿ 2.1 Ê¥øı, BbøRû|×–Nƒb, J,¿£>ä0Ö½fÍ$2ívÈDä0R â k[4] í_21³5?ƒÝcb¶MívÈR, ĤBbø¤_‹p0§c˙šÂ, J) ƒÝcbvÈRí,¿M, 1/Rû|vÈDä0í CR iäM. 2.2 Í$_. Ç 2.1: £>ä0Ö½fÍ$ý<Ç. Ç2.1 u£>ä0Ö½fÍ$íý<Ç cqQYƒímUÑ (2.1) , w2 s(k) uf £|ímU, ÑëògÓœ}0, N Ñø_£>ä0ä0Ö½f¯UíŸ-š (subcarriers) b ñ, [ýf£«DQY«PÓÂíä0ÏÏ, J-šÈ ÑÀP Ñ7)ƒÝcb¶MívÈR ÏÏ, Bbùpø_0§c˙šÂ h(t) , 1/cqä Ñ—D , Ä¤Ê |t| ≥ Tx /2 v, h(t) = 0 , θ [ývÈíR, Ñøõb, Jf£mUíU‚ Tx ÑøÀP, θI = int(θ + 0.5), int(x) [ý. 3.
(13) 2 ı vÈDä0Rí,¿ ¦ x ícbM, n(k) †uµbË‹ëÆm (additive white Gaussian noise) r(k) = s(k − θI )h(θ − θI )ej2πk/N + n(k). (2.1). Ç (2.2) ÑBbhô7 L _’eíý<Ç, w2dè™2 1 ƒ L Ñ(2.1) 2í k M, H[Bb. Ç 2.2: ¨Ö Ns. ½º’eíh¿ý<Ç. Fh¿í¸ˇ, ¸ˇ×kc_slû¯U, 7¥ L _mU³¨Öí Ns. ½º’e, J I p V[ý,. p = 0, 1, · · · , Ns − 1 ,, 7©øˇ½º’e³¨Ö7 Ls _‚š (sample), 7ÄÑQY«1.ø− vÈRÑÖý, Ĥì2¦šÕ¯: I p ≡ {θI + pLs , θI + pLs + 1, · · · , θI + pLs + (Ls − 1)},. p = 0, 1, · · · , Ns − 1. (2.2). 2.3 |×–Nƒb à°l‡F·H, ©_ I p , p = 0, 1, · · · , Ns − 1 í’euó°í, ĤBbJøFh¿ƒí L _mUì2Ñø_ L × 1 í²¾ r = [r(1) . . . r(L)]T , ,™ T [ýøä³0 (transpose), ÿªJ·<ƒrÊ I p , p = 0, 1, · · · , Ns − 1,í r(k) 5ÈuóÉ4í (correlated), 6ÿu z, úk m, n ∈ [0, Ns − 1] , ∀k ∈ I 0 : 2 2 m = n; σs h (θ − θI ) + σn2 , 0 ∗ E[r(k + nLs )r (k + mLs )] = σs2 h2 (θ − θI )e−j(m−n) , m = 6 n; 0, otherwise,. (2.3). w2 0 = 2πLs /N , E[·] [ý¦‚M, σs2 = E[s2 (k)] , ÑmU?¾, σn2 = E[n2 (k)] , ÑÆm S s −1 p ?¾ 7úk r(k), k ∈ / N p=0 I uóÌóÉ4í (uncorrelated) 4.
(14) 2 ı vÈDä0Rí,¿ Q-VBbRû θ ¸ íúb-ª?4 (log-likelihood) ƒb, Λ(θ, ) ¥_úb-ª?4ƒ buú L _Fh¿ƒí’e r Ê#ìvÈR θ £ä0R víœ0òƒb (probability density function), f (r|θ, ) , ¦úb(í!‹ ‚à (2.3) 2Fhôƒí r óÈíóÉ44 ”, úb-ª?4ƒbª[ýÑ: Λ(θ, ) = ln f (r|θ, ) Y f (r(k), r(k + Ls ), . . . , r(k + (Ns − 1)Ls )) = ln( k∈I 0. Y. f (r(k))). SNs −1 p I k∈ / p=0 L. = ln(. Y. k∈I 0. f (r(k), r(k + Ls ), . . . , r(k + (Ns − 1)Ls )) Y f (r(k))) f (r(k))f (r(k + Ls )) · · · f (r(k + (Ns − 1)Ls )) k∈1. A = ln( C) B = ln A + ln C − ln B. (2.4). Q Bbøúb-ª?4ƒb}Ñú_¶MVRû, w2 A = k∈I 0 f (r(k), r(k+Ls), . . . , r(k+(Ns − Q Q 1)Ls ) , B = k∈I 0 f (r(k))f (r(k + Ls )) · · · f (r(k + (Ns − 1)Ls )) , C = Lk∈1 f (r(k)) úÀ. ø_ r(k) Vz, …íœ0òƒb f (r(k)) uø_ø&íµbòg}0 (Gaussian distribution) ƒb, ª[ýÑ: f (r(k)) =. 1 |r(k)|2 exp(− ) π(σs2 h2 (θ − θI ) + σn2 ) σs2 h2 (θ − θI ) + σn2. (2.5). 7 A ¶MÑ Ns &íµbòg}0, J (2.6) ý[ý, θI +L Ys −1. f (r(k), r(k + Ls ), . . . , r(k + (Ns − 1)Ls )). = ln. θI +L Ys −1. f (z(k)). = ln. θI +L Ys −1. ln A = ln. k=θI. k=θI. k=θI. π Ns. 1 exp(−zH (k)R−1 z(k)) det(R). = −Ns Ls ln π − Ls ln det(R) −. θI +L Xs −1 k=θI. 5. zH (k)R−1 z(k). (2.6).
(15) 2 ı vÈDä0Rí,¿ w2 . z(k) = . . r(k) r(k + Ls ) .. .. . r(k + (Ns − 1)Ls ). (2.7). 7,™ H [ýøä³0u (transpose conjugate (hermitian)), R u z(k) íóÉ4ä³, ‚à (2.3) íÉ[ , ªJ)ƒóÉ4ä³ (2.8) R = E[z(k)zH (k)] σs2 h2 (θ − θI ) + σn2 0 σs2 h2 (θ − θI )ej = .. .. 0. 0. . . . σs2 h2 (θ − θI )e−j(Ns −1) 0 . . . σs2 h2 (θ − θI )e−j(Ns −2) .. .. . .. σs2 h2 (θ − θI )e−j σs2 h2 (θ − θI ) + σn2 .. .. σs2 h2 (θ − θI )ej(Ns −1). 0. σs2 h2 (θ − θI )ej(Ns −2). 0. .... σs2 h2 (θ − θI ) + σn2. = σn2 I + σs2 h2 (θ − θI )qqH. . (2.8). 0. 0. w2í q = [1, ej , . . . , ej(Ns −1) ]T , BbªJòQ°) (2.9), J£‚à¥ä³ìÜ (matrix inversion lemma)[11]°) R−1 , [ýà(2.10), w2í I uÀPä³, 7¥_ÀPä³í&D R ó det(R) = (σn2 )Ns −1 (Ns σs2 h2 (θ − θI ) + σn2 ) R−1 =. 1 σs2 h2 (θ − θI ) I − qqH σn2 σn2 (Ns σs2 h2 (θ − θI ) + σn2 ). (2.9) (2.10). P s −1 2 ø (2.9) D (2.10) Hp (2.6) , ª) (2.11) , w2í zH (k)z(k) = N m=0 |r(k + mLs )| , P s −1 ∗ 7 zH (k)qqH z(k) †à° (2.12) F[ý, w2í γm (k) Ñ N p=m r(k + (p − m)Ls )r (k + pLs ) , ,™ ∗ u¦u µbí<2. ln A = −Ns Ls ln π − Ls ln[(σn2 )Ns −1 (Ns σs2 h2 (θ − θI ) + σn2 )] θI +L Xs −1 zH (k)z(k) θI +L Xs −1 σs2 h2 (θ − θI ) − + zH (k)qqH z(k) 2 2 (N σ 2 h2 (θ − θ ) + σ 2 ) σ σ s s I n n n k=θ k=θ I. H. H. z (k)qq z(k) =. (2.11). I. N s −1 X. 2. |r(k + mLs )| + 2. m=0 H. = z (k)z(k) + 2. N s −1 N s −1 X X. 0. <{r(k + (p − m)Ls )r ∗ (k + pLs )ejm }. m=1 p=m. N s −1 X. 0. <{γm (k)ejm }. m=1. 6. (2.12).
(16) 2 ı vÈDä0Rí,¿ |(ø (2.12) Hp (2.11) ¹ª)ƒ A ¶Mí!‹ ln A = −Ns Ls ln π − Ls ln[(σn2 )Ns −1 (Ns σs2 h2 (θ − θI ) + σn2 )] θI +L s −1 Xs −1 NX 2σs2 h2 (θ − θI ) 0 + 2 <{γm (k)ejm } 2 2 2 σn (Ns σs h (θ − θI ) + σn ) k=θ m=1 I. θ +Ls −1 σ 2 + (Ns − 1)σs2 h2 (θ − θI ) I X H − n2 z (k)z(k) σn (Ns σs2 h2 (θ − θI ) + σn2 ) k=θI. (2.13). B ¶MÑ Ns × Ls _ø&µbòg}0íœ0òƒbó , !‹àln B = ln. θI +L s −1 Ys −1 NY. f (k + mLs ). = ln. θI +L s −1 Ys −1 NY. 1 |r(k + mLs )|2 ) exp(− π(σs2 h2 (θ − θI ) + σn2 ) σs2 h2 (θ − θI ) + σn2. k=θI. k=θI. = −. m=0. m=0. θI +L s −1 Xs −1 NX k=θI. (ln π + ln(σs2 h2 (θ − θI ) + σn2 )). m=0. 1 − 2 2 σs h (θ − θI ) + σn2. =. θI +L s −1 Xs −1 NX. |r(k + mLs )|2. m=0 k=θI 2 2 −Ns Ls ln π − Ns Ls ln(σs h (θ − θI ) + σn2 ) θI +L s −1 Xs −1 NX 1 − 2 2 zH (k)z(k) σs h (θ − θI ) + σn2 k=θ m=0 I. (2.14). 7 C ¶M†u L _ø&µbòg}0íœòƒbó , [ýÑ: ln C = ln. L Y. f (r(k)). k=1 L Y. = ln(. k=1. 1 |r(k)|2 exp(− )) π(σs2 h2 (θ − θI ) + σn2 ) σs2 h2 (θ − θI ) + σn2. = −L ln π − L ln(σs2 h2 (θ − θI ) + σn2 ) −. L X 1 |r(k)|2 (2.15) 2 2 2 σs h (θ − θI ) + σn k=1. |(ø (2.13),(2.14) £ (2.15) Hp (2.4) , w2D θ ¸ ÌÉíb¶M, 1.} à|ד Λ(θ, ) í!‹, ĤBbªJø… I, %¬cÜ£«5(¹ª)ƒF° θ ¸ íúb-ª?4 ƒb,. 7.
(17) 2 ı vÈDä0Rí,¿. Λ(θ, ) = ln f (r|θ, ) = ln A + ln C − ln B L X (σ 2 h2 (θ − θI ) + σn2 )Ns Ls −L 1 = ln s 2 2 − |r(k)|2 (Ns σs h (θ − θI ) + σn2 )Ls σs2 h2 (θ − θI ) + σn2 k=1 2σs2 h2 (θ − θI ) + 2 σn (Ns σs2 h2 (θ − θI ) + σn2 ). θI +L s −1 Xs −1 NX k=θI. 0. <{γm (k)ejm }. m=1. (Ns − 1)σs4 h4 (θ − θI ) − 2 σn (Ns σs2 h2 (θ − θI ) + σn2 )(σs2 h2 (θ − θI ) + σn2 ). θI +L Xs −1. zH (k)z(k). (2.16). k=θI. )ƒ θ ¸ íúb-ª?4ƒb(, BbJ|×–N¶,¿vÈDä0íR θˆM L D ˆM L , ÿu ʤúb-ª?4ƒbÑ|×Mví θ £ , [ýà-, L X (σ 2 h2 (θ − θI ) + σn2 )Ns Ls −L 1 θˆM L , ˆM L = arg max ln s 2 2 |r(k)|2 − θ, (Ns σs h (θ − θI ) + σn2 )Ls σs2 h2 (θ − θI ) + σn2 k=1. 2σs2 h2 (θ − θI ) + 2 σn (Ns σs2 h2 (θ − θI ) + σn2 ) −. θI +L s −1 Xs −1 NX k=θI. 0. <{γm (k)ejm }. m=1. (Ns − 1)σs4 h4 (θ − θI ) σn2 (Ns σs2 h2 (θ − θI ) + σn2 )(σs2 h2 (θ − θI ) + σn2 ). θI +L Xs −1. zH (k)z(k). (2.17). k=θI. 2.4 vÈDä0Rí CR iä âkvÈDä0ÏÏí,¿!‹JuQª CR iä, †¤,¿^ï, ĤBbÊ…R ûvÈ£ä0Rí CR iä, 1/Ê_Ò¶MøBbí,¿!‹D CR iäTªœ 7vÈ£ä 0Rí CR iä°)j¶à (2.19)(2.18):. Var(ˆ ) ≥ {−E[. ln ∂ 2 f (r|θ, ) −1 ]} ∂2. (2.18). ˆ ≥ {−E[ Var(θ). ln ∂ 2 f (r|θ, ) −1 ]} ∂θ 2. (2.19). 8.
(18) 2 ı vÈDä0Rí,¿ w2ä0Rí CR iäRûà (2.20) F[ý:. −E[. ∂ 2 lnf (r|θ, ) 2σs2 h2 (θ − θI ) 2πLs 2 ] = ( ) 2 2 2 2 2 ∂ σn (N sσs h (θ − θI ) + σn ) N θ+L s −1 N s −1 N s −1 X X X 0 · m2 <{E[r(k + (p − m)Ls )r ∗ (k + pLs )]ejm } k=θ. m=1 p=m. N s −1 X 8π 2 L3s σs4 h4 (θ − θI ) = m2 (Ns − m) N 2 σn2 (σn2 + Ns σs2 h2 (θ − θI )) m=1. =. 2π 2 L3s Ns2 (Ns2 − 1)σs4 h4 (θ − θI ) 3N 2 σn2 (σn2 + Ns σs2 h2 (θ − θI )). (2.20). Ĥä0Rí CR iäÑ Var(ˆ ) = E[(ˆ − )2 ] ≥. 3N 2 σn2 (σn2 + Ns σs2 h2 (θ − θI )) 2π 2 L3s Ns2 (Ns2 − 1)σs4 h4 (θ − θI ). (2.21). 7vÈRÏÏí¶M, ÄÑwl¬˙ݵÆ, Bb‚à MATLAB ³¯U«íj¶, V° )ùŸ}í!‹, ĤvÈRÏÏí CR iäÑ (2.22) , w2 η = ˆ ≥ Var(θ). 1 (1 4. σs2 2 2 h (θ σn. − θI ). + ηNs )2 (1 + η)2. I) 2 ηSNR[ dh(θ−θ ] [η 2 Ns2 (L + Ls (1 − Ns )) + 2ηLNs + L + Ns Ls (Ns − 1)] dθ. 9. (2.22).
(19) 3ı |7“í0§c˙šÂ 3.1 Ê,ø³, Bb°)7vÈDä0Rí CR iä, 7â (2.22) ªhô|, ¥_vÈR í™ÄÏ}Ä0§c˙šÂí×üJ£é0í.°7Z‰, ¥_vÈRí™ÄÏu h £. dh dθ. íƒb, h ¢u θ íƒb, ĤJBbı?D°|ÊvÈÏÏÑ 0 ƒ 0.5 5È™ÄÏÑ|üí0 §c˙šÂ, à° (3.1) Fý, Bbı°)?DU J Ñ|üí0§c˙šÂ h(θ) , w2 η=. σs2 2 2 h (θ) σn. J = =. Z Z. 1 (1 4. 0.5. + ηNs )2 (1 + η)2. ]2 [η 2 Ns2 (L + Ls (1 − Ns )) + 2ηLNs + L + Ns Ls (Ns − 1)] ηSNR[ dh(θ) dθ. 0. dθ. 0.5. f (θ, h(θ), h0 (θ))dθ. (3.1). 0. Ñ7°|¤!‹, Bb‚à‰}¶ (Calculus of Variations)[12] 2, ‡úªj|¤é|7“½æí ¶MVj|BbFbí|7“0§c˙šÂ. 3.2 |7“j¶ … ‰}¶[12] 2ªj|‡ú|7“0§c˙šÂFÛbí|½b¶M ʤ|7“j ¶íñíuÊ°||7“½æíj, 7¥<½æuÊ#ìø_¨Öj˙ , (, C6[ÞíÕ¯5 2, v|x/|×C|ü“Ô4íø_ w½æ ªJ (3.2) V[ý Z b J(y) = f (x, y(x), y 0(x))dx. (3.2). a. ı°|U J(y) Ñ|üMí y , 7w2 y uÊ x ∈ [a, b] ³í˃b (smooth functions), a D b †uiäõ, ya £ yb udìíiäM. 10.
(20) 3 ı |7“í0§c˙šÂ Ê[12] ç2, Bb)øF°í|7“j y0 .âÅ—«…}j˙ (Euler differential equation), 6ÿu (3.3) w2 fy [ý¨ÖÖ_‰bíƒb f ú y ¦R}, 6ÿu. fy0 (x) −. d 0 f 0 (x) = 0, dx y. for all x ∈ (a, b). ∂ f ∂y. . (3.3). 7w2 fy (x, y0 (x), y00 (x)) = fy0 (x) fy0 (x, y0 (x), y00 (x)) = fy00 (x). (3.4). ¤Õ, Bb6ø−, úkø_.Ö x íƒb f , 6ÿuÊ fx = 0 í8”5-, ªJUàø_ H ƒ b, à (3.5) Fý: H(x) = y00 (x)fy00 (x) − f (x, y0 (x), y00 (x)). (3.5). Q-Vø H ƒbú x }%¬cÜ(, ªø«…}j˙ Hpl, ÿªJ)ƒ H ƒbí} Ñ 0 , [ýà-: H 0 (x) = y000 (x)fy00 (x) + y00 (x) = −y00 (x)(fy0 (x) −. d 0 fy0 − fy0 (x)y00 (x) − fy00 (x)y000 (x) dx. d 0 f 0 (x)) dx y. = 0. (3.6). Ĥ, H(x) Ñø_b, à (3.7) Fý H(x) = y00 (x)fy00 (x) − f (x, y0 (x), y00 (x)) = c. (3.7). 7¤vªJõ|,(3.7) uø_ y J£ y 0 íj˙ , JuBbªJj|¥_ú y 0 íj˙ , ÿª J)ƒø_ y 0 = g(y, c) íj˙ , ½æÿ‰)'ÀÓ7, Q-VÉbJ}׉b (separation of variables) ¶ÿªJø½æj|V7. 11.
(21) 3 ı |7“í0§c˙šÂ. 3.3 |7“0§c˙šÂ ÛʇúBbí½æ (3.1), ½µà (3.8), Bbø‚à‡øí!‹Vj|¤½æí|7“j, )ƒF‚í|7“0§c˙šÂ. J = =. Z. 1 (1 4. 0.5. ηSNR[ dh(θ) ]2 [η 2 Ns2 (L + Ls (1 − Ns )) + 2ηLNs + L + Ns Ls (Ns − 1)] dθ. 0. Z. + ηNs )2 (1 + η)2. dθ. 0.5. f (θ, h(θ), h0 (θ))dθ. (3.8). 0. ú΃‡ø,x ú@ƒ…í θ , 7 y ú@ƒ…í h , † h Å—«…}j˙ (3.9), /âk f ɨÖ7 h £. dh dθ. s_‰b, .¨Ö θ , 6ÿuú θ íR} fθ = 0 , ʤ8”-BbÿªJ. Uàƒ H ƒbÑøbíÔ4, à° (3.10) F[ý fh (θ) −. d fh0 (θ) = 0, dθ. for all h ∈ (a, b). (3.9). H(θ) = h0 (θ)fh0 (θ) − f (θ, h(θ), h0 (θ)) = c. (3.10). FJ«à7 h Å—«…}j˙ (3.9), J£ H ƒb (3.10) íÔ4, Bbø f (θ, h(θ), h0 (θ)) Hp (3.10) , y%¬l, ªJ)ƒ. 1 (1 + ηNs )2 (1 + η)2 ∂ 4 H(θ) = { 0 } ∂h (θ) ηSNR[ dh(θ) ]2 [η 2 Ns2 (L + Ls (1 − Ns )) + 2ηLNs + L + Ns Ls (Ns − 1)] dθ 1 (1 + ηNs )2 (1 + η)2 4 ·h0 (θ) − ηSNR[ dh(θ) ]2 [η 2 Ns2 (L + Ls (1 − Ns )) + 2ηLNs + L + Ns Ls (Ns − 1)] dθ (−2) 14 (1 + ηNs )2 (1 + η)2 = h0 (θ) ηSNR[ dh(θ) ]3 [η 2 Ns2 (L + Ls (1 − Ns )) + 2ηLNs + L + Ns Ls (Ns − 1)] dθ 1 (1 4. −. + ηNs )2 (1 + η)2. ηSNR[ dh(θ) ]2 [η 2 Ns2 (L + Ls (1 − Ns )) + 2ηLNs + L + Ns Ls (Ns − 1)] dθ 3 (1 + ηNs )2 (1 + η)2 = − 4 ηSNR[ dh(θ) ]2 [η 2 Ns2 (L + Ls (1 − Ns )) + 2ηLNs + L + Ns Ls (Ns − 1)] dθ. = c. (3.11). 12.
(22) 3 ı |7“í0§c˙šÂ ÄÑ (3.11) 2í c Ñø_b, FJªø c D − 34 ¯9AÑÇø_b, Bbø…IÑ c2 , †y%¬cÜ, )ƒ-Þí ä,. dh(θ) (1 + ηNs )(1 + η) 1 =− p dθ c1 ηSNR[η 2 Ns2 (L + Ls (1 − Ns )) + 2ηLNs + L + Ns Ls (Ns − 1)]. (3.12). BbªJõ|,(3.12) u0§c˙šÂ h úvÈ θ í}, 6ÿu0§c˙šÂé0íj˙ ĤBbÉbøiä‘KHpj|b¶M, ÿªJ)ƒF°í|7“0§c˙šÂ. kuø (3.12) ‚à}׉b¶VT«, 6ÿuø¨Ö h í¶MD dh [Êj˙ í˝i, ø¨ Ö θ D dθ í¶M[ʬi, yúsi¦ }, à ä (3.13) F[ý, Z p =−. Z. ηSNR[η 2 Ns2 (L + Ls (1 − Ns )) + 2ηLNs + L + Ns Ls (Ns − 1)] dh (1 + ηNs )(1 + η). 1 dθ + c2 c1. (3.13). (3.13) 2Ö c1 D c2 s_bá, ÿªJâiä‘KV°), ¤iä‘KÿuÊ θ = 0 v, h = 1 , Ê θ = 0.5 v, h = 0 , 7 (3.13) 2, θ ¶Mí }'ñq)ƒ, Ou h ¶Mí }†Ýy Å, ĤBbâ MATLAB í6Œ°) h ¶Mí }, yâiä‘K°) c1 D c2 , H (3.12) , J MATLAB ¹ª°)|7“í0§c˙šÂ h [3.1 ÑJ MATLAB l|Ê SNR Ñ 0 dB,5 dB, · · · ,20 dB ví c1 £ c2 M 7Ç (3.1) Ñ|7“í0§c˙šÂ, â,7-} Ñ SNR=0 B 20dB. SNR c1 c2. [ 3.1: ®SNR ví c1 , c2 M 0 dB 5 dB 10 dB 15 dB. 20 dB. 0.0824 0.0483 0.0318 0.0231 0.0180 23.2441 27.5251 32.9070 38.8300 44.9562. 13.
(23) 3 ı |7“í0§c˙šÂ. the optimal pulse shaping filter. 1. 0.9. 0.8. SNR=0 dB. 0.7. opt. h (θ). 0.6. 0.5. SNR=20 dB. 0.4. 0.3. 0.2. 0.1. 0. 0. 0.1. 0.2. θ. 0.3. 0.4. 0.5. Ç 3.1: Ê.°SNR 5-í|7“0§c˙šÂ. ÛÊBb°)7|7“í0§c˙šÂ, Z?D)ƒ…Ê.°ívÈR£ SNR 5-í| ×–NvÈR,¿ÏÏí™ÄÏ, -Ç (3.2) ¹Ñ SNR |7“0§c˙šÂúvÈR,¿Ï Ï™ÄÏ, dWÑvÈ θ , óWÑvÈ,¿ÏÏ, 7â,B-}Ñ SNR = 0 dB,5dB,...,20dBv í8”, ªJõƒâkBbF°íÊ θ = 0 ƒ θ = 0.5 ví|7“0§c˙šÂ, FJʤ–È 2í,¿ÏÏÓOvÈÏÏíZ‰î\MÊó°í×ü. 7âkÊ.° SNR 5-}.°í|7“0§c˙šÂ, ĤªJ‡úBbÍ$í SNR .°, 7²Ï.° SNR í|7“0§c˙šÂ,(3.3),(3.4),(3.5) }Ñ SNR = 0 dB,10dB,20dB ví|7“c˙šÂ TÊ® SNR vívÈ,¿ÏÏ[ýÇ, w2ªõ|, JuÍ$2í SNR DøÇá²àíMóÏÊ ±10 dB 5qv, wÏÏ6·?DQ¡|7“í®(. 14.
(24) 3 ı |7“í0§c˙šÂ. h. opt. −2. 10. SNR=0 dB −3. MSE. 10. −4. 10. SNR=20 dB. −5. 10. 0. 0.2. 0.1. θ. 0.3. 0.4. 0.5. Ç 3.2: |7“0§c˙šÂÊ.°SNR £vÈRívÈ,¿ÏÏ. h. opt. −2. 10. of SNR=0 dB, operate on different SNR. SNR=0 dB. −3. 10. SNR=20 dB −4. MSE. 10. −5. 10. −6. 10. −7. 10. 0. 0.1. 0.2. θ. 0.3. 0.4. 0.5. Ç 3.3: SNR=0dB 5|7“0§c˙šÂÊ.° SNR £vÈRívÈ,¿ÏÏ. 15.
(25) 3 ı |7“í0§c˙šÂ. h. opt. −1. 10. of SNR=10 dB, operate on different SNR. −2. 10. −3. 10. MSE. SNR=0 dB. SNR=20 dB. −4. 10. −5. 10. −6. 10. 0. 0.2. 0.1. θ. 0.3. 0.4. 0.5. Ç 3.4: SNR=10dB 5|7“0§c˙šÂÊ.° SNR £vÈRívÈ,¿ÏÏ. h. opt. 0. 10. of SNR=20 dB, operate on different SNR. −1. 10. −2. MSE. 10. −3. 10. SNR=0 dB. −4. 10. SNR=20 dB. −5. 10. 0. 0.1. 0.2. θ. 0.3. 0.4. 0.5. Ç 3.5: SNR=20dB 5|7“0§c˙šÂÊ.° SNR £vÈRívÈ,¿ÏÏ. 16.
(26) 3 ı |7“í0§c˙šÂ. 3.4 |7“0§c˙šÂDwF˙šÂíªœ Ê,øBb)ƒ7|7“0§c˙šÂ hopt , 7Bbø¥_|7“0§c˙šÂD¯ì ý (raised cosine) 0§c˙šÂJ£Nb (exponential) 0§c˙šÂ, ‡ú…bUàÊ OFDM Í$vvÈRÏÏ,¿í™ÄÏTªœ âkBbí|7“0§c˙šÂíiä‘KÑ h(0) = 1 , J£ h(0.5) = 0 , ĤBb²Ï 7œQ¡¤iä‘Kí α = 0.5 , T = Tx /2 í¯ìý0§c˙šÂ hrc , J£ µ = 0.1 íNb 0§c˙šÂ hexp , w2 hexp (θ) = exp(−. hrc (θ) =. |θ| ) µ. (3.14). sinc( Tθ ) cos( παθ ) T αθ 2 1 − 4( T ). (3.15). 7Ç (3.6) uNb0§c˙šÂ hexp £¯ìý0§c˙šÂ hrc íý<Ç, w2©è™H[ vÈ θ , Jf£mUíU‚ Tx ÑÀP. hexp. 1. 0.9. 0.9. 0.8. 0.8. 0.7. 0.7. 0.6. 0.6. 0.5. 0.5. 0.4. 0.4. 0.3. 0.3. 0.2. 0.2. 0.1. 0.1. 0. 0. 0.1. 0.2. θ. hrc. 1. 0.3. 0.4. 0. 0.5. 0. 0.1. Ç 3.6: Nb£¯ìý0§c˙šÂ. 17. 0.2. θ. 0.3. 0.4. 0.5.
(27) 3 ı |7“í0§c˙šÂ çBb}ø hexp J£ hrc UàÊ 2 ıF·HíÍ$v, J|×–N¶ (2.17) úvÈR T,¿, ÿ}}.°íÏÏ, BbøwÏÏí CR iä (2.22) JÇ$[ý, dWÑvÈ θ , óWÑ CR iä, â,B-}Ñ SN R = 0 dB,5dB,...,20dB ví8”, 0. 10. −1. 10. −2. MSE. 10. −3. SNR=0 dB. 10. −4. 10. SNR=20 dB. −5. 10. 0.1. 0. 0.2. θ. 0.3. 0.4. 0.5. 0.4. 0.5. Ç 3.7: Nb0§c˙šÂvÈ,¿ÏÏ. 0. 10. −1. MSE. 10. −2. 10. −3. 10. SNR=0 dB. −4. 10. SNR=20 dB −5. 10. 0. 0.1. 0.3. 0.2. θ. Ç 3.8: ¯ìý0§c˙šÂvÈ,¿ÏÏ. 18.
(28) 3 ı |7“í0§c˙šÂ -Ç (3.9) u hopt hexp J£ hrc vÈR,¿ÏÏ™ÄÏÊ 10 dB v, vÈúvÈ,¿ÏÏ íÉ[Ç:. −1. 10. h exp hrc h opt. −2. MSE. 10. −3. 10. −4. 10. −5. 10. 0. 0.1. 0.2. 0.3. 0.4. 0.5. θ. Ç 3.9: ®_0§c˙šÂvÈDvÈ,¿ÏÏÉ[Ç. Bb}ú¤ú0§c˙šÂÊ SNR Ñ 0 dB,10 dB, £ 20 dB v¦ J 5M, 6ÿu (3.8) , ½ºà-: J=. Z. 1 (1 4. 0.5 0. + ηNs )2 (1 + η)2. ηSNR[ dh(θ) ]2 [η 2 Ns2 (L + Ls (1 − Ns )) + 2ηLNs + L + Ns Ls (Ns − 1)] dθ. dθ. †¤ú0§c˙šÂJ£ SNR Ñ 10 dB |70§c˙šÂí J M‚à MATLAB l! ‹à[3.2 Fý:. 19.
(29) 3 ı |7“í0§c˙šÂ. [ 3.2: ®0§c˙šÂÊ.°SNR ví J M 0 dB 5 dB 10 dB 15 dB hopt hopt10dB hexp hrc. 8.49 × 10−4 1.61 × 10−3 3.25 × 10−2 9.62 × 10−3. 2.92 × 10−4 3.41 × 10−4 3.83 × 10−3 5.74 × 10−3. 1.26 × 10−4 1.26 × 10−4 5.96 × 10−4 3.55 × 10−3. 6.66 × 10−5 7.58 × 10−5 1.51 × 10−4 2.86 × 10−3. 20 dB 4.05 × 10−5 6.17 × 10−5 6.11 × 10−5 2.72 × 10−3. [3.2 u}ú hopt , hrc , hexp , J£ SNR Ñ 10 dB í hopt í CR iäú θ }F)í !‹ BbªJpéõ|, Ê SNR Ñ 0 dB v, Jopt < Jopt10dB < Jrc < Jexp ; Ê SNR Ñ 10 dB v, Jopt < Jopt10dB < Jexp < Jrc ; Ê SNR Ñ 20 dB v, Jopt < Jexp < Jopt10dB < Jrc , 6ÿu Ê θ = 0 ƒ 0.5 5È, Bbí|7“0§c˙šÂí J MÑ|ü, Ĥúk‚à|×–N¶,¿ vÈRv, Uà|7“0§c˙šÂí^‹}u|ßí JuUà SNR Ñ10 dBí|7“0§ c˙šÂ, Ê ±10dB 5qvw,¿vÈRí^‹6u'ßí. 20.
(30) 4ı _Ò!‹ Ê¥øıBbø|7“0§c˙šÂJ£NbD¯ìý0§c˙šÂUàƒ (2.17) , 6 ÿuJ|×–N¶,¿vÈR£ä0Rí!‹ªW_Ò, 1DF°|í CR iädªœ. 4.1 _Ò¡bqì Ê_Òí¶M, âk IEEE 802.11a dìíslû¯U¯¯Bbí-Z, 6ÿu¨Ö7½ºí ’e, FJBbø¥¶M“VªW_Ò Ç (4.1) u IEEE 802.11a lû¯Uí-ZÇ:. + ' + 2 (- 3 () 4) + 2 + 3 (. 1. 0. /. .. -. ,. 1 4) + ' 1 40 1 2 + 3 +. *. (). &1. (. 1. ) + ' 0 1 2/ 3 &# ". &. ! " #. ) + ' 0 1 2/ 3 &. (. !%& ' $. Ç 4.1: IEEE 802.11a lû¯U-Z. Ç (4.1) 2, ‡ 16 µs í¶MÑlû¯Uí¶M, w2¨Ö7so*¯U (training symbols) £Å o*¯U, w2 t1 ƒ t10 H[ó°íso*¯U, T1 £ T2 [ýó°íÅo*¯U, à°l‡FU àí-Z, Bbʤ¦à¥ 10 _slû¯UV,¿vÈ£ä0ÏÏ, Ĥ Ns = 10 , 7Ÿ-šíb ¾ N = 64 , ¦šä0Ñ 20 MHz, w2ø_slû¯UvÈÑ 0.8 µs , Ĥ©ø_slû¯U³. 21.
(31) 4 ı _Ò!‹ ¨Ö7 Ls = 16 _‚š 7Bbú©ø8”ªW7 1000 Ÿ_Ò, ¦,¿ÏÏjíÌM, } ú SNR=0 dB,5 dB, · · · ,20 dBªW_Ò Ê¤Bb6‡úÖ½˜¦−vívÈ£ä0R,¿!‹VT_Ò, FUàíÖ½˜¦− _uéN[4] 2FUàí_, wôb¸ˇ (delay spread) Kmax Ñ 0.75 µs , óçk 15 _¦š, 7wÌ?¾ÓOvÈÓ‹×ÛNb˙í«Á, Ê©_vÈõ·u×üÑ Rayleigh }Ó, iÌ G}ÓíµbM, wbç_à-: 1 1 hk = N (0, σk2 ) + jN (0, σk2 ) 2 2 2 2 −kTs /TRM S σk = σ 0 e σ02 = 1 − e−Ts /TRM S. (4.1) (4.2) (4.3). w2 N (0, 21 σk2 ) H[ÌMÑ 0, ™ÄÏÑ 12 σk2 íògÓœ‰b,(4.3) †uÑ7é¤Ö½˜¦ −ÌŠ0Ñ 1 7qíd¸, w2 TRM S = 100 ns, óçk 2 _¦š ÊÇ (4.2) ƒ (4.21) 2, Ç (a) ÑvÈR,¿, Ç (b) Ñä0R,¿, dWÑ SNR(dB), óWÑ,¿ÏÏí™ÄÏ; 7Ç2í(¶M, CRBH[ CR iäM, AWGN H[ÊË‹ëÆm ¦−_Ò!‹, RAY H[ÊÖ½˜¦−_Ò!‹, âkBbœÊ<íuvÈR,¿í¶M, Ä ¤Q-VFªWí_Ò, ·Éúä0RÑ 0.15 ví8”T_Ò, 6ÿuQ-Ví_Òä0R í¶M·Ñ 0.15, ø.yºH. 4.2 |7“0§c˙šÂ_Ò!‹ Ê¥ø‚àÇ (3.1) Fýí|7“c˙šÂ, Ê.°í SNR 5-}óú@íc˙š Â, Uàƒ (2.17) í|×–N¶ªWvÈRJ£ä0R,¿, Ç (4.2) ƒ (4.5) Ñ_Òí! ‹, }uúvÈR θ Ñ 0.1, 0.2, · · · , 0.4 FTí_Ò!‹ Êúı2Bb)ø, ¤|7“c˙šÂúvÈRí,¿, w,¿ÏÏ1.}ÓOvÈR 7Z‰, ĤÊÇ (4.2) ƒ (4.5) í (a) Ç2, w CR iä·uøší, ÊË‹ëÆm¦−í_Ò !‹, œ˛·Ýûª¤ CR iä, ,¿!‹·'Äü, ÊÖ½˜¦−í¶M, ÖÍR×7 CR i äM, Ê SNR œ×v,¿ÏÏ6·Q¡ 10−3 ; 7ä0Rí,¿, ÊË‹ëÆm¦−£Ö½˜ ¦−í,¿_Ò!‹·'Q¡CR iä, ,¿^‹6·u'ßí Ç (4.6) BÇ (4.9) Ñ SNR=10 dB í|7“c˙šÂúvÈ£ä0,¿!‹, wvÈR. 22.
(32) 4 ı _Ò!‹ ,¿ÏÏÊ 10 dB v, w,¿ÏÏ.Ó θ Z‰7Z‰; Bbªõ|Êä0R,¿í¶M, ÊË‹ ëÆm¦−£Ö½˜¦−í,¿·ÝQ¡ CR iä, [ý,¿!‹”7; 7ÊvÈR,¿¶ M, Ë‹ëÆm¦−í,¿!‹6ÝQ¡ CR iäM, OuÊÖ½˜¦−ví,¿ÿœÑR× CR iä, O6·ÊªQ§í¸ˇ5q (a). −2. 10. (b). −3. 10. CRB AWGN RAY. CRB AWGN RAY. −3. −4. MSE (time). MSE (frequency). 10. −4. 10. −5. 10. −6. −5. 10. 10. 0. 5. 10 SNR (dB). 15. 10. 20. 0. 5. 10 SNR (dB). 15. 20. Ç 4.2: |7“0§c˙šÂÊ θ = 0.1 víä0£vÈ,¿ÏÏ. (a). −2. 10. (b). −2. 10. CRB AWGN RAY. CRB AWGN RAY. −3. −3. MSE (time). MSE (frequency). 10. −4. 10. −5. 10. 10. −4. 10. −5. 0. 5. 10 SNR (dB). 15. 10. 20. 0. 5. 10 SNR (dB). 15. Ç 4.3: |7“0§c˙šÂÊ θ = 0.2 víä0£vÈ,¿ÏÏ. 23. 20.
(33) 4 ı _Ò!‹. (a). −2. 10. (b). −2. 10. CRB AWGN RAY. CRB AWGN RAY. −3. −3. MSE (time). MSE (frequency). 10. −4. 10. −5. 10. 10. −4. 10. −5. 0. 5. 10 SNR (dB). 15. 10. 20. 0. 5. 10 SNR (dB). 15. 20. Ç 4.4: |7“0§c˙šÂÊ θ = 0.3 víä0£vÈ,¿ÏÏ. (a). −2. 10. (b). −2. 10. CRB AWGN RAY. CRB AWGN RAY. −3. MSE (time). MSE (frequency). 10. −4. 10. −4. −5. 10. −3. 10. 0. 5. 10 SNR (dB). 15. 10. 20. 0. 5. 10 SNR (dB). 15. Ç 4.5: |7“0§c˙šÂÊ θ = 0.4 víä0£vÈ,¿ÏÏ. 24. 20.
(34) 4 ı _Ò!‹. (a). −2. 10. (b). −3. 10. CRB AWGN RAY. CRB AWGN RAY. MSE (frequency). MSE (time). −4. −3. 10. −5. 10. −6. −4. 10. 10. 0. 5. 10 SNR (dB). 15. 10. 20. 0. 5. 10 SNR (dB). 15. 20. Ç 4.6: SNR=10 dB 5|7“0§c˙šÂÊ θ = 0.1 víä0£vÈ,¿ÏÏ. (a). −2. 10. (b). −2. 10. CRB AWGN RAY. CRB AWGN RAY −3. MSE (frequency). MSE (time). 10. −3. 10. −4. 10. −5. 10. −6. −4. 10. 0. 5. 10 SNR (dB). 15. 10. 20. 0. 5. 10 SNR (dB). 15. 20. Ç 4.7: SNR=10 dB |7“0§c˙šÂÊ θ = 0.2 víä0£vÈ,¿ÏÏ. 25.
(35) 4 ı _Ò!‹. (a). −2. 10. (b). −2. 10. CRB AWGN RAY. CRB AWGN RAY. MSE (frequency). MSE (time). −3. −3. 10. −4. 10. 10. −4. 10. −5. 0. 5. 10 SNR (dB). 15. 10. 20. 0. 5. 10 SNR (dB). 15. 20. Ç 4.8: SNR=10 dB 5|7“0§c˙šÂÊ θ = 0.3 víä0£vÈ,¿ÏÏ. (a). −2. 10. (b). −1. 10. CRB AWGN RAY. CRB AWGN RAY −2. 10 −3. MSE (time). MSE (frequency). 10. −4. 10. −3. 10. −4. 10. −5. −5. 10. 0. 5. 10 SNR (dB). 15. 10. 20. 0. 5. 10 SNR (dB). 15. 20. Ç 4.9: SNR=10 dB |7“0§c˙šÂÊ θ = 0.4 víä0£vÈ,¿ÏÏ. 26.
(36) 4 ı _Ò!‹. 4.3 Nb0§c˙šÂ_Ò!‹ Ç (4.10) BÇ (4.13) ÑNb0§c˙šÂàÊ,¿vÈ£ä0ÏÏRí_Ò!‹, } ÑvÈR θ Ñ 0.1,0.2,0.3,0.4, ä0RÑ 0.15 ví_Ò!‹, ªõ|vÈR,¿ÏÏÊË‹ ëÆm¦−,¿_Ò'û¡ CR iä, Ö½˜¦−†œR×, 7ä0R,¿ÏÏÊË‹ëÆm ¦−£Ö½˜¦−ví,¿·'Q¡ CR iäM (a). −2. 10. (b). −3. 10. CRB AWGN RAY. −3. CRB AWGN RAY. −4. 10. MSE (time). MSE (frequency). 10. −4. −5. 10. 10. −5. 10. −6. 0. 5. 10 SNR (dB). 15. 10. 20. 0. 5. 10 SNR (dB). 15. 20. Ç 4.10: Nb0§c˙šÂÊ θ = 0.1 víä0£vÈ,¿ÏÏ. (a). −2. 10. (b). −2. 10. CRB AWGN RAY. −3. CRB AWGN RAY. −3. 10. MSE (time). MSE (frequency). 10. −4. −4. 10. 10. −5. 10. −5. 0. 5. 10 SNR (dB). 15. 10. 20. 0. 5. 10 SNR (dB). Ç 4.11: Nb0§c˙šÂÊ θ = 0.2 víä0£vÈ,¿ÏÏ. 27. 15. 20.
(37) 4 ı _Ò!‹. (a). −2. 10. (b). −1. 10. CRB AWGN RAY. CRB AWGN RAY. −2. 10 −3. MSE (time). MSE (frequency). 10. −3. 10. −4. 10. −4. 10. −5. 10. −5. 0. 5. 10 SNR (dB). 15. 10. 20. 0. 5. 10 SNR (dB). 15. 20. Ç 4.12: Nb0§c˙šÂÊ θ = 0.3 víä0£vÈ,¿ÏÏ. (a). −1. 10. (b). 0. 10. CRB AWGN RAY. CRB AWGN RAY. −1. 10 −2. MSE (time). MSE (frequency). 10. −2. 10. −3. 10. −3. 10. −4. 10. −4. 0. 5. 10 SNR (dB). 15. 10. 20. 0. 5. 10 SNR (dB). Ç 4.13: Nb0§c˙šÂÊ θ = 0.4 víä0£vÈ,¿ÏÏ. 28. 15. 20.
(38) 4 ı _Ò!‹. 4.4 ¯ìý0§c˙šÂ_Ò!‹ Ç (4.14) BÇ (4.17) ѯìý0§c˙šÂàÊ,¿vÈ£ä0ÏÏRí_Ò!‹, }Ñ vÈR θ Ñ 0.1,0.2,0.3,0.4, ä0RÑ 0.15 ví_Ò!‹, ªõ|vÈR,¿ÏÏÊË‹ë Æm¦−,¿_Ò'û¡ CR iä, Ö½˜¦−†œR×, 7ä0R,¿ÏÏÊË‹ëÆm¦ −£Ö½˜¦−ví,¿·'Q¡ CR iäM (a). −2. 10. (b). −3. 10. CRB AWGN RAY. CRB AWGN RAY. −4. MSE (frequency). MSE (time). 10. −3. 10. −5. 10. −4. 10. −6. 0. 5. 10 SNR (dB). 15. 10. 20. 0. 5. 10 SNR (dB). 15. 20. Ç 4.14: ¯ìý0§c˙šÂÊ θ = 0.1 víä0£vÈ,¿ÏÏ. (a). −2. 10. (b). −3. 10. CRB AWGN RAY. CRB AWGN RAY. −4. MSE (frequency). MSE (time). 10. −3. 10. −5. 10. −4. 10. −6. 0. 5. 10 SNR (dB). 15. 10. 20. 0. 5. 10 SNR (dB). Ç 4.15: ¯ìý0§c˙šÂÊ θ = 0.2 víä0£vÈ,¿ÏÏ. 29. 15. 20.
(39) 4 ı _Ò!‹. (a). −2. 10. (b). −2. 10. CRB AWGN RAY. CRB AWGN RAY. −3. 10 −3. MSE (time). MSE (frequency). 10. −4. 10. −4. 10. −5. 10. −5. 10. −6. 0. 5. 10 SNR (dB). 15. 10. 20. 0. 5. 10 SNR (dB). 15. 20. Ç 4.16: ¯ìý0§c˙šÂÊ θ = 0.3 víä0£vÈ,¿ÏÏ. (a). −2. 10. (b). −1. 10. CRB AWGN RAY. CRB AWGN RAY. −2. 10 −3. MSE (time). MSE (frequency). 10. −3. 10. −4. 10. −4. 10. −5. 10. −5. 0. 5. 10 SNR (dB). 15. 10. 20. 0. 5. 10 SNR (dB). Ç 4.17: ¯ìý0§c˙šÂÊ θ = 0.4 víä0£vÈ,¿ÏÏ. 30. 15. 20.
(40) 4 ı _Ò!‹ Ç (4.18) BÇ (4.21) †uú0§c˙šÂÊ θ Ñ 0.1,0.2,0.3,0.4 v, ÊëògÆA ¦−í,¿ÏÏý<Ç, w2™(¶MÑ CR iä ªJõ|Ê θ œüv, Nb0§˙šÂí,¿ ÏÏœ hopt ü, OÊ θ œ×v, Nb0§˙šÂí,¿ÏÏÿ}ª hopt Ví× Ê¯ìýí¶M† uÊ θ œüv, ,¿ÏÏœ×, Ê θ œ×v, ,¿ÏÏÿª hopt ü Ouúc_ θ TÌv, âk _Ò!‹éý,¿'Q¡ CR iä, FJà°,øıFzí, hopt í,¿ÏÏ}u|üí. −2. 10. h exp h rc h opt. −3. MSE (time). 10. −4. 10. −5. 10. 0. 5. 10. 15. SNR (dB). Ç 4.18: 0§c˙šÂÊ θ = 0.1 vívÈ,¿ÏÏ. 31. 20.
(41) 4 ı _Ò!‹. −2. 10. h exp h rc h opt. −3. MSE (time). 10. −4. 10. −5. 10. 0. 5. 10. 15. 20. SNR (dB). Ç 4.19: 0§c˙šÂÊ θ = 0.2 vívÈ,¿ÏÏ. −2. 10. h exp h rc h opt. −3. MSE (time). 10. −4. 10. −5. 10. 0. 5. 10. 15. SNR (dB). Ç 4.20: 0§c˙šÂÊ θ = 0.3 vívÈ,¿ÏÏ. 32. 20.
(42) 4 ı _Ò!‹. −2. 10. h exp h rc h opt. −3. MSE (time). 10. −4. 10. −5. 10. 0. 5. 10. 15. 20. SNR (dB). Ç 4.21: 0§c˙šÂÊ θ = 0.4 vívÈ,¿ÏÏ. 4.5 n Ê_Ò!‹2, |7“, Nb, £¯ìý0§c˙šÂÊvÈR,¿Ï϶M, Ë‹ëÆm ¦−,¿!‹·'Q¡ CR iä; 7Ö½˜¦−,¿¶M·}œR×, OuBbªJhôƒ, |7 “0§c˙šÂí,¿ÏÏÊ¥¶Muœüí 7Êä0R,¿¶M, †·u?Äü,¿, Ou }ÓO θ íÓ‹, 0§c˙šÂíMÁü, ä0R,¿Äü} O±Q 7âk_Ò!‹D CR iäó¯, Ĥà°úıFH, Ê θ = 0 B 0.5 5ÈÌ}0v, Bb FRû|í0§c˙šÂʤ|×–N¶,¿vÈRv, Ñ|7“í0§c˙šÂ. 33.
(43) 5ı !. ¥¹dí½õÊk‡ú,¿vÈRíÄ, ‚à IEEE 802.11a slû¯UíÔ4Rû ||×–Nƒb, °|vÈ£ä0ÏÏí,¿M, 1Rû| CR iä, ‚à|ü“ CR iäV°)| 7“í0§c˙šÂ, úk.°í SNR M}®_óúí|7c˙šÂ, Ĥúk.° SNR ²Ïó¯¯í0§c˙šÂ, Z?DUvÈRí,¿®ƒyÄí,¿!‹, 7°v6?\Mä 0R,¿íÄ; wÿõ†ul¾óúíTò, Ĥà‹;bTòvÈR,¿íÄ, U à|7“c˙šÂ†ÛG|l,íµÆ 7â_Ò!‹éý, FRû|í|7“c˙šÂ, ¿!‹üõ\M7ÊvÈR,¿,íÄ4. 34.
(44) ¡5d.. [1] IEEE Std 802.11a: “Wireless LAN medium access control(MSC) and physical layer(PHY) specifications: high-speed physical layer in the 5 GHz band,” Dec. 1999. [2] T. M. Schmidl and D. C. Cox, “Robust frequency and timing synchronization for OFDM,” IEEE Trans. Commun., Vol. 45, no. 12, pp. 1613-1621, Dec. 1997. [3] H. Minn, M. Zeng, and V. K. Bhargava, “On timing offset estimation for OFDM systems,” IEEE Commun. Lett., Vol. 4, no. 7, pp. 242-244, Jul. 2000. [4] J.J. van de Beek, M. Sandell, and P.O. Borjesson, “ML estimation of time and frequency offset in OFDM systems,” IEEE Trans. on Signal Processing, Vol. 45, No. 7, pp. 1800-1805, Jul. 1997. [5] M. Li and W. Zhang, “A novel method of carrier offset estimation for OFDM systems, ”IEEE Trans. Consumer Electron., Vol. 49, pp. 975-971, Nov. 2003. [6] E. Chiavaccini and G. M. Vitetta, “Maximum-likelihood frequency recovery for OFDM signals transmitted over multipath fading channels, ”IEEE Trans. Commun., Vol. 52, pp. 244-251, Feb. 2004. [7] P. H. Moose, “A technique for orthogonal frequency division multiplexing frequency offset correction,” IEEE Trans. Commum., Vol. 42, pp. 2908-2914, Oct. 1994. [8] F. Gini and G.B. Giannakis, “Frequency offset and symbol timing recovery in flatfading channels: a cyclostationary approach,” IEEE Trans. Commun., Vol. 46, pp. 400-411, Mar. 1998.. 35.
(45) ¡5d. [9] H. Bolcskei, “Blind estimation of symbol timing and carrier frequency offset in wireless OFDM systems,” IEEE Trans. Commun., Vol. 49, pp. 988-999, Jun. 2001. [10] B. Park, H. Cheon, and E. Ko, “A blind OFDM synchronization algorithm based on cyclic correlation,” IEEE Signal Processing Letters, Vol. 11, pp. 83-85, Feb. 2004. [11] G. H. Golub and C. F. V. Loan, Matrix Computation, 2nd ed. The Johns Hopkins University Press, 1989. [12] U. B. Manderscheid, Introduction to the Calculus of Variations, Chapman and Hall, 1991.. 36.
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