正交分頻多工系統載波間干擾之降低及頻率偏移之估測

國立交通大學

電機與控制工程學系

碩士論文

正交多頻分工系統載波間干擾之降低及

頻率偏移之估測

Intercarrier Interference Reduction and Frequency

Offset Estimation for OFDM systems

研究生：周琪展

指導教授：鄭木火博士

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f$,s3bíj¶Vj²¤½æ, øuJä ÑHgVÁ/ä0Púc_Í$^?í à, Çø†uâf£mU…™í/<Ôy4 ”, ào*¯U (training symbol) CU‚‡0 (cyclic prefix), C$l4”V,¿Í$íä0 R, ª7‹J^k
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…d?‡ú ùj¶T|ø|×–N (maximum likelihood) 5ä0P,l
Bb‡ú IEEE 802.11a ™Ä-ímU, ‚àwÔílû’e (preamble) 5Ô4, ªRû||×–N5,¿¶†V,lä 0R
¤Õ, Bb6Rû|¤ä0Rí Cr´amer-Rao -Ì
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Intercarrier Interference Reduction and Frequency

Offset Estimation for OFDM Systems

Student: Chichan-Chan Chou

Advisor: Dr. Mu-Huo Cheng

Institute of Electrical and Control Engineering

National Chiao-Tung University

Abstract

Orthogonal frequency-division multiplexing (OFDM) is very sensitive to frequency errors caused by frequency differences between transmitter and receiver local oscillators. There exists two approaches to deal with this problem. One is to mitigate the influence of frequency offset on the system performance at the expense of transmission bandwidth; the other is to employ some specific properties of the transmission signal, such as the training symbols, the cyclic prefix, or the statistical information to estimate and compensate for the frequency offset. The first approach consists of two methods, the self ICI cancellation and windowing. In this thesis, we formulate these two methods mathematically, explain their functions, and propose a design on windowing filter to improve the system performance. Simulations show that the improvement in SNIR (Signal-to-noise-plus-interference ratio) can be as high as 3 dB. For the second approach, we focus on the signal preamble of IEEE 802.11a standard and propose a maximum likelihood estimation algorithm to estimate the frequency offset. The Cr´amer-Rao bound of the frequency offset is also derived. Simulations are also performed to verify the effectiveness of the proposed algorithm.

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3.3 _Ò!‹ . . . 19

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Ç 3.8 j$¢¨DKaiser ¢¨íä$ . . . 22

Ç 3.9 øKaiser ¢¨j¶DA™-šÈß×¾Îj¶!¯5J(β) . . . 23

Ç 4.1 IEEE 802.11a lû’eí-ZÇ . . . 24

Ç 4.2 ¯¯IEEE 802.11a ™Äí ML -ZÇ . . . 25

Ç 4.3 Rayleigh ¦−_50§à@ . . . 29

Ç 4.4 slû¯Uí_bÑùvíÌjÏÏDCr´amer Rao -Ì . . . 30

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2.1

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Ñ7jZ–c, BbIPN/2−1_−N/2 wn = N
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(intercarrier interference, ICI), £Æm
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-ÞuwRû: Gl = N/2−1 X n=−N/2 rnwne−j2π l Nn (2.5) = N/2−1_X n=−N/2     N/2L−1_X m=−N/2L XmLHmLej2π n NmL   · ej2π_Nn_{+ v} n   · wne−j2π l Nn (2.6) = N/2L−1_X m=−N/2L XmLHmL N/2−1_X n=−N/2 wnej2π mL+−l N n+ N/2−1_X n=−N/2 wnvne−j2π l Nn (2.7) = N/2L−1_X m=−N/2L XmLHmL· W1(l − mL − ) + Vl (2.8)

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íl, Bb

cq]U {Xk} ¯¯ E[Xk] = 0 £ E[XiXj∗] = |X|2ij¥s_Ô4
6ÿuz, Êf£«äí

’euóÖ /ÌMÑÉ, Ì?¾Ñ |X|2
_{Τ5Õ, ̦−íÓï6\cqÑø_b,} E[|Hk|2] = |H|2
;WJ,ícq, BbZª)ƒJ-í!‹: E[|Sl|2] = E[|XlHlW1 · (−)|2] = |X|2|H|2|W1(−)|2 (2.15) E[|Il|2] = E    N/2L−1 X m=−N/2L m6=l/L XmLHmLW1(l − mL − ) · N/2L−1 X m=−N/2L m6=l/L X_mL∗ H_mL∗ W₁∗(l − mL − )    = N/2L−1 X m=−N/2L m6=l/L |X|2_|H|2_|W 1(l − mL − )|2 (2.16) E[|Vl|2] = E   N/2−1 X n=−N/2 wnvne−j2π l Nn· N/2−1 X m=−N/2 w_m∗v_m∗ej2πNlm   (2.17) = N/2−1 X n=−N/2 |wn|2· E[|vn|2] · ej2π l−l Nn (2.18) = 2σ_v2 N/2−1_X n=−N/2 w_n2 = 2σ2_v· W2(0) (2.19) w2

W2(f ) = N/2−1_X n=−N/2

w_n2e−j2πNnf (2.20)

wnÑõb, |wn|2 = w2n (2.21)

QO, ì2©_-š,íÌ?¾Ec = |X|2|H|2Ts, ĤEc/N0 = N |X|2|H|2/2σv2, w2 N0

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|(, Bb

I SNIRl H[QYƒl_]UGlíÌmUúÆm‹-šÈß×íªM, à-:

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2.1.2 ¢¨D-šÈß×íÉ[ âkÊvó ^kÊäTì , Ç2.2 ·H7¤ø¬˙
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BbªJõƒ, ʤ8”-, Glÿ/ßk XlHl, 7wF-š,ímUXkHk,k6=l· ƒÉ, ¤vÿ.æÊ-šÈß×
çf£«DQY«íËÓÂä0.°v, }ßÞøä0R, àÇ 2.3 Fý
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â (2.24) ªø, -šÈß×í×üDBbF²Ïí¢¨éò~íÉ[, Ç2.3(c) #7Bb ø_j²: JuBb?vƒø_is-±íÝ0í¢¨VHf$íj$¢, z.ìªJø-š Èí à±B|Q
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2.2

øí Rife D Vincent ¢¨

âkf$íj$¢, Êä$,}'×/«ÁíÝMíis, ¥úk;ÁQ-šÈß×íb °óç.‚
Ĥ,[2]2T|7øí Rife D Vincent ¢¨VÄ@¥_½æ, ¤¢¨à-: wn = 1 + Z X b=1 A(b) cos(2π(n + N 2)b N ), n = −N 2 , . . . , N 2 − 1 (2.25) w2Z[ý¤¢¨í¼b, 7Ê (2.25) 2í¡bA(b)Ñ A(b) = 2(−1)b b Y i=1 Z + 1 − i Z + i (2.26)

Bb*×üíä$ªJyªø¥7jøí Rife D Vincent ¢¨íÔ4, àÇ2.4Fý: âÇ 2.4, BbªJÀUíõ|, 碨í¼bò, wisÿ«Áí0, Í7, ¥1.H [ZªJÌÌ„íÓ‹
Bb·<ƒ,ZM‰×Î7¨Ais‰ü5Õ, -ÓíuMÚÓ×í3s (main-lobe)  , 7¥ÿòQ àƒLMí²¦

*Ç 2.5(a) ªJõƒ, ÖÍZ = 1˛U)is‹§‰ü, Oâk³_粦L, Ĥ¨Aw F-š,ímU6ø–\
Ê3s³Þ, ¤ví-šÈß×¥7}ªZ = 0vy×
y6éíu, ÿ

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− + + + + = ∗ = δ δ Ç 2.3: ‹pj$¢¨í£>}äÖ Í$ý<Ç(ä0R) δδδδ δ Ç 2.4: .°¼bíøíRife D Vincent ¢¨×üä$

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Ç 2.5: Uàø¼íRife D Vincent ¢¨ÊL = 1-, QY«{rn}íä$

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Ĥ àSÊZDL5ÈT¦Ÿ, .â;WUà6íÛbVd²ì
Ç 2.6 ý7Ê.°íZMDLM5-íSNIR
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Τ5Õ, BbªJ·<ƒ, Êó°LíÕ” -, = 0Ë¡,Z = 0í^?}ªZ = 1ß, â (2.24) ªJ7j¥øõ; âk¤ví óç ¡É,(2.24) í}ä£}‚íùá·˛ó, Ĥ¥v`íSNIRÿâÂjíW2(0)F²ì,

.ÍíuW2(0)Z=1> W2(0)Z=0, Ä7}¨A,Hí!‹

M)øTíu, çZ = 0£Z = 1víøí Rife D Vincent ¢¨}ú@ƒj$¢¨£ O±í Hanning ¢¨

δ

Ç 2.6: Uà.°¼bíRife D Vincent ¢¨Í$5^?ý<Ç

2.3

Kaiser¢¨

%¬,Hín5(, Bb˛%7j, u´Sà/ø_¢¨, w3sí Disí×üu|3 bí5¾
ku, …¹d²Ï7 Kaiser ¢¨Vdþt, ŸÄuóœk׶}í¢¨, à Hanning ¢¨,Hamming ¢¨,blackman ¢¨ 좨ƒb,Kaiser ¢¨ªJÓOw¡bV|c3sí  £is×üÈí¦Ÿ
J-u…íƒb: wn = ( I0[β(1−[(n−α)/α]2)1/2] I0(β) , 0 ≤ n ≤ M 0, otherwise (2.27)

w2α = M/2,I0(·)Ñøéíɼ Bessel ƒb
BbªJõƒ,kaiser ¢¨\M ¸β¥s_¡b

F−„, w2¢¨ÅM˛\²ì, ×üuN − 1, FJ”-?Z‰íÉβ
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Ñ7°) bβ, |òQíd¶@vuø (2.27) p (2.28)  2, âkBbuú }, FJ (2.28) ÉF²¦í¢¨É, 7 Kaiser ¢¨¢uβíƒb, FJ QOúβTR}¦”M, ZªJ)ƒ bβ
Í7, âklجµÆ, ̶%âA‰Rû|ø_Äü í$j; Ĥ, Ê…¹d2, Bb‚à MATLAB VBbêA¥á T, Q-Víøøý w }|Ví!‹

2.4

_Ò!‹

…øý‚à MATLAB Vl.°∆5-íJ(β), 1z¤v °)í bβDøí Rife D Vincent ¢¨£j$¢¨dªœ
2.4.1 L=1 ílBbÿ Kaiser ¢¨ÊL = 1íÕ”-, l¤ví bβ, Ç2.7 Ñw‡ú.°íEc/N0F } |Ví!‹
BbªJõƒ,J(β)í|×Mî|ÛÊβ = 0ív`, ¥[ý7Ê.¨‘ä í‘K-, j$¢¨u|ßí²Ï, ¤ví∆ = 0.5
0 1 2 3 4 5 6 7 8 9 10 −5 0 5 10 15 20 25 30 35 β

integral of SNIR₀ of L = 1 case with Kaiser window, ∆ = 0.5

2.4.2 L=2 …üøbýÊL = 2, £.°Ec/N0Dä0R¸ˇíÕ”-, ‚à…ıFÜí¢¨F)ƒ í SNIR
Ç2.8ÑL = 2£∆ = 0.55-‡ú.°íEc/N0F }|VíJ(β), ĤBbªJ)ƒÊ.°8 ”-íbβ
Ç2.9∼Ç2.13ÑL = 2, ∆ = 0.55-,Ec/N0 = 10 ∼ 50dB, ‚à.°í¢¨F_ÒíSN IR^ ?!‹
0 1 2 3 4 5 6 7 8 9 10 5 10 15 20 25 30 35 ∆ = 0.5 β J( β) dB 2.9 4.5 5.4 4.1 5.3 Ç 2.8: L = 2,∆ = 0.5£Ec/N0 = 10 ∼ 50dB 5-, ‚à Kaiser ¢¨l|íJ(β)

 2 ı ¢¨úæÊä0R5£>}äÖ Í$í à 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 3 4 5 6 7 8 9 10 E_c/N₀ = 10dB, L = 2 δ SNIR m 0 (dB) Z = 0 Z = 1 Kaiser(β=2.9)

Ç 2.9: L = 2, Ec/N0 = 10dB 5-, Uàɼ, ø¼ Rife D Vincent ¢¨¸ Kaiser ¢¨í^

? 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 5 10 15 20 E_c/N₀ = 20dB, L = 2 δ SNIR m 0 (dB) Z = 0 Z = 1 Kaiser(β=4.1)

Ç 2.10: L = 2, Ec/N0 = 20dB 5-, Uàɼ, ø¼ Rife D Vincent ¢¨¸ Kaiser ¢¨í^

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 5 10 15 20 25 30 E_c/N₀ = 30dB, L = 2 δ SNIR m 0 (dB) Z = 0 Z = 1 Kaiser(β=4.5)

Ç 2.11: L = 2,Ec/N0 = 30dB 5-, Uàɼ, ø¼ Rife D Vincent ¢¨¸ Kaiser ¢¨í^

? 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 5 10 15 20 25 30 35 40 E_c/N₀ = 40dB, L = 2 δ SNIR m 0 (dB) Z = 0 Z = 1 Kaiser(β=5.3)

Ç 2.12: L = 2,Ec/N0 = 40dB 5-, Uàɼ, ø¼ Rife D Vincent ¢¨¸ Kaiser ¢¨í^

 2 ı ¢¨úæÊä0R5£>}äÖ Í$í à 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 5 10 15 20 25 30 35 40 45 50 E_c/N₀ = 50dB, L = 2 δ SNIR m 0 (dB) Z = 0 Z = 1 Kaiser(β=5.4)

Ç 2.13: L = 2,Ec/N0 = 50dB 5-, Uàɼ, ø¼ Rife D Vincent ¢¨¸ Kaiser ¢¨í^

?

âk Kaiser ¢¨1.Å— Nyquist Ć, ¥[ýÿä0R = 0, EÍ}-šÈß× íæÊ
ĤÿSNIRÊ = 0Ë¡í^?,Rife D Vincent ¢¨}ª Kaiser ¢¨ß
Í7, [2.1 ªœ7.°¢¨5-íÌ^?[Û, BbªJõƒ, Ê׶}í8”5-, ´u Kaiser ¢¨œß
[ 2.1: ÌSNIR ªœÇ 10dB 20dB 30dB 40dB 50dB Kaiser 8.4921 17.9842 26.0120 31.3381 34.3520 Z = 1 7.5921 16.5446 23.8306 29.9927 35.8752 Z = 0 7.7366 14.6887 20.4841 26.3648 33.6539 zp: [³íÀPÑdB

A™-šÈß×¾Îj¶

Ê…ı³, Bbb܎âf£«mUº0íj¶VÁ/ä0RF¨Aí à, 16þtR û|ø_éNíSNIRä, |(yøwD¢¨íj¶Tø_ªœ
ε π − − π Ç 3.1: A™-šÈß×¾Îj¶-ZÇ

3.1

d.Ü£ TŸÜ

[3]ê7øPú}ä0Ríj¶, ±ÑA™-šÈß×¾Î
Ç 3.1 Ñw-Z
¥_j¶íx ÍÊkUàs_ó¹í-šf£°ø_mU, |(ÊQY«QYv, âkÊ¥s_-š,»-í…V ÿuó°ímU, Ĥøwó‹ÎJùÿuBbbímU, ¥šd.cªJYƒ£üímU, ´ªJ

 3 ı A™-šÈß×¾Îj¶ ¾Î¥s_ÌÉíÆm

Ç 3.2 2, õ(uBbFbímU, ™(†u-šÈß×
BbªJÀUíõƒ, âkBbd7 ó¹í¦−ó¥_cq, FJʝ|«ó¹s_-šímUuó°í, ø,-s_Mó‹(, ˘k mUí¶}uq4ß−, ˘k-šÈß×í¶}îuú;4ß−, ¥ÿu¤j¶±åíâV
- øRû|êcíbçVð„¥_j¶í TŸÜ
= + + = + + + + Ç 3.2: QYmUGlDGl+1

3.2

ä0RDmUúÆm‹-šÈß×5ªM

Ê…2, Bbø}Rûà2.2.1íbç, 1°š6ì2|ø_SNIRVTÑ¿¾Í$^? í™Ä
ílBbIó¹íf£mUÑó°, QOcqó¹í¦−6uóí, ªJ)ƒ, Xl = Xl+1 (3.1) Hl = Hl+1, l = − N 2, − N 2 + 2, . . . , N 2 − 2 (3.2)

QO, ;W (2.8) , øLH1, BbQYƒíl£l + 1_mU, ªJ[ýA-Þíä, Gl = N/2−1 X k=−N/2 XkHk· W1(l − k − ) + Vl (3.3) Gl+1 = N/2−1_X k=−N/2 XkHk· W1(l + 1 − k − ) + Vl+1 (3.4) w2Vl¸W1(f )î°,øıFì2
QO, BbøGl£Gl+1ó‹ÎJù, ÿuBbö£bímU, ¦

±ÑAl
°ší,Al6ª\[ýÑú_áí¸, }ÑmU¶}, -šÈß׶}, £Æm¶M, à-,

Al = 1 2(Gl+ Gl+1) (3.5) = 1 2 N/2−1_X k=−N/2 XkHk· (W1(l − k − ) + W1(l + 1 − k − )) + 1 2(Vl+ Vl+1) (3.6) = 1 2{XlHl· [W1(−) + W1(1 − )] + Xl+1Hl+1· [W1(−1 − ) + W1(−)]} + 1 2 N/2−1_X k=−N/2 k6=l,l+1 XkHk· (W1(l − k − ) + W1(l + 1 − k − )) + 1 2(Vl+ Vl+1) (3.7) = 1 2{XlHl· [W1(1 − ) + 2W1(−) + W1(−1 − )]} + 1 2        N/4−1 X k=−N/4 k6= l₂ XkHk· [W1(l − 2k + 1 − ) + 2W1(l − 2k − ) + W1(l − 2k − 1 − )]        + 1 2(Vl+ Vl+1) (3.8) = S_lA+ I_lA+ V_lA (3.9) ÛÊBbb}·HmU (Sl), -šÈß× (Il), Æm (Vl) ¥ú_MÊ$l,í4”
íl,

 3 ı A™-šÈß×¾Îj¶ ¥Z sž²|‰Âí5‡í’euóÖ /ÌMÑÉ, Ì?¾Ñ |X|2
_{Τ5Õ, ̦} −íÓï6\cqÑø_b, E[|Hk|2] = |H|2
;WJ,ícq, BbZª)ƒ5-í!‹: E[|SA l |2] = 1 4 · |X| 2_|H|2_{· |W} 1(1 − ) + 2W1(−) + W1(−1 − )|2 (3.10) E[|IA l |2] = 1 4 · N/4−1_X k=−N/4 k6= l₂ |X|2_|H|2_{· |W} 1(l − 2k + 1 − ) + 2W1(l − 2k − ) + W1(l − 2k − 1 − )|2 = 1 4 · |X| 2_|H|2_{· W (l, k, ) (3.11)} E[|V_lA|2] = 1 4 · E[(V A l + Vl+1A )(VlA∗+ Vl+1A∗)] (3.12) = 1 4(E[V A

l VlA∗] + E[Vl+1A Vl+1A∗] + E[Vl+1A VlA∗] + E[VlAVl+1A∗]) (3.13)

= 1 4(2σ 2 vW2(0) + 2σ2vW2(0) + 2σv2W2(1) + 2σv2W2(−1)) (3.14) = 1 4(2σ 2 v · (2W2(0) + 2Re{W2(1)}) (3.15)

QO, ì2©_-š,íÌ?¾Ec = |X|2|H|2Ts, ĤEc/N0 = N |X|2|H|2/2σv2, w2

N0ÑË‹ëÆmʦä¦−íÀiŠ0ä$ò,TsÑø_£>}äÖ Í$í¯UU‚
|(, B bI SNIRA l H[QYƒl_]UAlíÌmUúÆm‹ß×íªM, à-: SN IR_lA = E[|S A l |2] E[|VA l |2] + E[|IlA|2] , l = −N 2 , −N 2 + 2, . . . , −N 2 − 2 (3.16) = |X| 2_|H|2_|W 1(1 − ) + 2W1(−) + W1(−1 − )|2 2σ2 v · (2W2(0) + 2Re{W2(1)}) +PN/4−1k=−N/4 k6= l₂ |X|2_|H|2_{· W (l, k, )} (3.17) = Ec N0 · |W1(1 − ) + 2W1(−) + W1(−1 − )| 2 2N · (W2(0) + Re{W2(1)}) + E_Nc₀ ·PN/4−1k=−N/4 k6= l₂ W (l, k, ) (3.18) B¤, Bb˛ì27SNIRA l ¥_¿¾Í$^?í™Ä, -Þø, ÿuBb;W (3.18) í _Ò!‹5n

3.3

_Ò!‹

…ø‚à (2.24) D (3.18) í_Ò!‹VªœA™-šÈß׾Σ Kaiser ¢¨í^ ?
ÊBbÇá_Ò5‡, sõ.â5?, ø, uf£ä í×ü
âkñ‡íA™-šÈß× ¾Îj¶, BbIXl = Xl+1, Ĥwf£ä Éf$£>}äÖ Í$íøš, FJÊ¢¨íj ¶2, Bb.âqìL = 2
ù, us6ífŠ0.âó
JøA™-šÈß×¾ÎífŠ 0ìÑE, µóL = 2í Kaiser ¢¨, wA™-šÈß×¾ÎZÉE/2
à¤øV,Hsj¶ n?\tíªœ
Ç 3.3 ƒÇ 3.7 }_Ò7L = 2, ∆ = 0.5, Ec/N0 = 10 ∼ 50dB 5-íSN IRúä0R 퉓
*¥<_ÒÇ2, ªœÔíuÇ 3.3, BbªJõƒÆmœ×í=1-, A™-šÈß ×j¶í^?pé˪ Kaiser ¢¨j¶ß,rÖ, ¥uâkëÆmÊä$,íFä0·ó° í?¾, Í7 Kaiser ¢ä$í3s ªj$¢í´b×, ĤÊó°íëÆm?¾5-,Kaiser ¢3sF
ƒí–ªœÖ, Ĥ^?ÿóúÁQ7, Ç 3.8 ªJÀUízp¤õ
óœkf$í£ >}äÖ Í$, A™-šÈß×¾ÎD¢¨¤sj¶íü·ªJÁ/Í$ä0RF¨Aí-šÈß×, Í7, ʤ°vº6· ¥f£mUíä 
Ĥ, àSÊ^?Df£ä 5ÈT¦Ÿ, .â;WUà6íÛbVd²ì
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 6.5 7 7.5 8 8.5 9 9.5 10 δ SNIR m 0 (dB) 10dB Kaiser window self ICI cancellation

 3 ı A™-šÈß×¾Îj¶ 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 10 11 12 13 14 15 16 17 18 19 20 20dB δ SNIR 0 (dB) Kaiser window self ICI cancellation

Ç 3.4: A™-šÈß×¾ÎDKaiser ¢¨j¶ÊEc/N0 = 20dB 5-í^? 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 10 12 14 16 18 20 22 24 26 28 30 δ SNIR m 0 (dB) 30dB Kaiser window self ICI cancellation

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 10 15 20 25 30 35 40 40dB δ SNIR 0 (dB) Kaiser window self ICI cancellation

Ç 3.6: A™-šÈß×¾ÎDKaiser ¢¨j¶ÊEc/N0 = 40dB 5-í^? 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 10 15 20 25 30 35 40 45 50 δ SNIR m 0 (dB) 50dB Kaiser window self ICI cancellation

 3 ı A™-šÈß×¾Îj¶ −6 −4 −2 0 2 4 6 −90 −80 −70 −60 −50 −40 −30 −20 −10 0 δ |W1 (δ )| (dB)

Kaiser window Rectangular window

Ç 3.8: j$¢¨DKaiser ¢¨íä$ [ 3.1: ÌSNIR ªœÇ 10dB 20dB 30dB 40dB 50dB Kaiser¢¨ 8.4921 17.9842 26.0120 31.3381 34.3520 A™-šÈ¾Î 9.0394 17.2054 23.8477 29.7731 35.8319 zp: [³íÀPÑdB [ 3.1ªœ7A™-šÈß×j¶D Kaiser ¢¨j¶íÌ^?[Û, BbªJõƒ, Ê ä0Rœüv, A™-šÈß×j¶í^?ª Kaiser ¢¨j¶bß, ¥uâk Kaiser ¢¨1. ¯¯ Nyquist Ćíí]; ¥5, çä0Rœ×v, âk Kaiser ¢¨íis«ÁËœ0, Ĥw ^?ªA™-šÈß×¾Îj¶bß

ÇÕ, Ç3.9uBbþtOø Kaiser ¢¨j¶A™-šÈß×¾Îj¶Ê∆ = 0.55-!¯ í_Ò!‹, ªJõƒ, Ê.°íEc/N0-, îuβ = 0(j$ window) Ñ|ß, ĤBb7jƒ¤

0 1 2 3 4 5 6 7 8 9 10 0 5 10 15 20 25 30 35 β

integral of SNIR₀ of self cancellation with Kaiser window, ∆ = 0.5

 4 ı

IEEE 802.11a

_{-Z-íä0R,¿}

Ê…ı³, Bb* [7]í|×–N¶|ê, Rû|ö£_¯ IEEE 802.11a
_slû’e (short preamble) Uàí|×–N¶£w Cr´amer Rao -Ì, |(yN¬.°í¦−Vd_Ò

4.1

IEEE 802.11a

lû’eí-Z

µ

=

+

µ

=

×

_×

₊

_×

₌

_µ

Ç 4.1: IEEE 802.11a lû’eí-ZÇ

Ç4.1Ñ IEEE 802.11a lû’eí-Z, …â10_êró°ís¯U (SS) £2_êr ó°íůU (LS) F A, wÅ}Ñ 16 £ 64 _‚š (sample), Τ5Õ,GI uůUíè ¨È½ (Guard Interval), …uůUí|(32°’eíµ`
Ê¥‚È, QY«.âêAmU ¿, ä0R,¿, vÈ°¥, D¦−,¿
…ı¹uÜʤ-Z-íä0R,¿

4.2

|×–N¶

[7]FT|í|×–N¶, u‚às¨½µímU5ÈíóÉ4Vv|ä0R£vÈR
Í 7,IEEE 802.11a ílû’eº.És_, Ĥ, BbwÑ* IEEE 802.11a í-Z, ªJ¾¦| yÖÉä0£vÈRí’m

Ç4.2uBb‚à IEEE 802.11a ™Äí
_slû¯UVRû|×–N¶í-ZÇ, w2Ls[ ý½µs¯UíÅ,NsH[½µs¯Uí_b,LuBbFh¿í¸ˇ, 7θuvÈRíP0
B bì2¦šÕ¯

θ

Ç 4.2: ¯¯IEEE 802.11a ™Äí ML -ZÇ Ip _{≡ {θ + pL} s, . . . , θ + (p + 1)Ls− 1}, p = 0, 1, . . . , N s − 1 (4.1)

w2©_ÊIp_{³íMîu½µí’e
QO, BbøQYƒímUì2ÑøL×1í²¾r = [r(1) · · · r(L)]}T

BbªJ·<ƒ, Êr2, rÊU‚‡0Dwµ`í¦šõr(k),k ∈ SN s−1_p=0 Ip _{uóÉ4í, 6ÿ} uz, ∀k ∈ I0, E[r(k + nLs)r∗(k + mLs)] =    σ2 s + σn2, m = n σ2 se−j2π  N(m−n)Ls, (m − n) = 1 . . . N s − 1 0, otherwise w2Ñä0R

θ¸íúb-ª?4 (log-likelihood) ƒbΛ(θ, ), uúf (r|θ, )¦úb(í!‹, 7f (r|θ, )u BbFh¿ƒírÊ#ìθ¸5-íœ0òƒb
âkFó‹ÁC£bó íb, î.} à BbøΛ(θ, )|ד5(F)ƒí!‹, ĤÊQ-VíbçRû2, Bb}ø¤ébêrI ¥
‚àrFxíóÉ4,Λ(θ, )ªJ\[ýÑJ-íä, Λ(θ, ) = log f (r|θ, ) = log      Y k∈I0 f (r(k), r(k + Ls), . . . , r(k + (N s − 1)Ls)) · Y k /∈SN s−1_p=0 Ip f (r(k))     

 4 ı IEEE 802.11a -Z-íä0R,¿ = log ( Y k∈I0 f (r(k), r(k + Ls), . . . , r(k + (N s − 1)Ls)) f (r(k))f (r(k + Ls)) · · · f (r(k + (N s − 1)Ls))) Y k f (r(k)) ) (4.2) (4.3) Ê (4.3) 2,Q_kf (r(k))Dθ£ÌÉ, FJBbªJø…I
QO, BbªJõƒ,(4.3) 2í }‚uNs_ø&íµbòg}0íœ0òƒbó , w!‹à-, f (r(k)) = exp(− |r(k)|2 σ2 s+σn2) π(σ2 s+ σn2) (4.4) N s−1_Y l=0 f (r(k + lLS)) =  1 π(σ2 s+ σ2n) N s · exp − PN s−1 l=0 |r(k + lLs)2| σ2 s + σn2 ! (4.5) (4.6) Q-VuªœµÆí}ä¶}, âk}äÑNs&íµbòg}0, wu°íœ0òƒbÑ,

f (z) = 1 π det(R)exp(−z H_R−1_{z) (4.7)} w2 z=      r(k) r(k + Ls) .. . r(k + (N s − 1)Ls)      (4.8) R = E[zzH_{] (4.9)} = E[      r(k) r(k + Ls) ... r(k + (N s − 1)Ls)     ·  r∗_{(k) r}∗_{(k + Ls) · · · r}∗_{(k + (N s − 1)Ls)} _] =      σ2 s + σn2 σs2e−j2π  NLs σ2 se−2j2π  NLs · · · σ2 se−j(N s−1)2π  NLs σ2 sej2π  NLs σ2 s+ σn2 ... . .. σ2 sej(N s−1)2π  NLs σ2 s+ σn2      (4.10) = σ2_nI + σ2_sxxH, w2 x =      1 ej2πNLs ... ej(N s−1)2π_NLs      (4.11)

âkR/ßOÔyí!Z, ĤBbªJ‚à¥ä³ìÜ (matrix inversion lemma) Vl |R−1_£det(R), R−1 = 1 σ2 n I − 1 σ2 n Ix( 1 σ2 s I + xH 1 σ2 n Ix)−1xH 1 σ2 n I (4.12) = 1 σ2 n I − σ 2 s σ2 n(σn2 + Nsσ2s) xxH (4.13) det(R) = (σ2_n)Ns−1_(σ2 n+ Nsσ2s) (4.14) Ĥ, f (r(k), r(k + Ls), . . . , r(k + (N s − 1)Ls)) f (r(k))f (r(k + Ls)) · · · f (r(k + (N s − 1)Ls))) (4.15) = exp−zH₍ 1 σ2 nI − σ2 s σ2 n(σ2n+Nsσ2s)xx H_)z_/πN s_(σ2 n)Ns−1(σn2 + Nsσs2) exp−PN s−1l=0 |r(k+lLs)2| σ2 s+σ2n  /πN s_(σ2 n+ σ2s)N s (4.16) = (σ 2 n+ σs2)Ns (σ2 n)Ns−1(σ2n+ Nsσ2s) · exp − 1 σ2 n zHz+ σ 2 s σ2 n(σ2n+ Nsσs2) zHxxHz+ PN s−1 l=0 |r(k + lLs)2| σ2 s + σn2 ! = (σ 2 n+ σs2)Ns (σ2 n)Ns−1(σ2n+ Nsσ2s) · exp  − 1 σ2 n zHz+ σ 2 s σ2 n(σn2 + Nsσs2) (zHz+ Q) + z H_z σ2 s + σ2n  = c1· exp(c2· Q − c3· zHz) (4.17) w2 N s−1_X l=0 |r(k + lLs)|2 _{= z}H_{z (4.18)} zHxxHz = N s−1_X l=0 |r(k + lLs)|2+ NXs−2 α=0 NXs−1 β=α+1 2Re{r(k + αLs)r∗(k + βLs)ej(β−α)2π  NLs} = zHz+ Q (4.19) c1 = (σ2 n+ σs2)Ns (σ2 n)Ns−1(σ2n+ Nsσs2) (4.20) c2 = σ2 s σ2 n(σn2+ Nsσ2s) (4.21) c3 = −σ2 s(σn2 + σs2) − σ2n(σn2+ Nsσ2s) + (σ2n+ Nsσs2)(σn2+ σs2) σ2 n(σn2 + Nsσs2)(σn2 + σs2) (4.22) = (N s − 1)σ 4 s σ2 n(σn2+ Nsσ2s)(σn2 + σs2) (4.23)

 4 ı IEEE 802.11a -Z-íä0R,¿ B¤, úbª?4ƒbª\“A-: Λ(θ, ) = log f (r|θ, ) (4.24) = log ( Y k∈I0 c1· exp(c2· Q − c3 · zHz) ) (4.25) = θ+LXs+1 k=θ {log c1+ c2· Q − c3· zHz} (4.26) âkc1Ñø×kÉíb, ÊBb|דíTÜ2ª\I, ‹,c2,c3ó°íĪø–\¾¥, Ĥ, Žâ|ד“(í (4.23) , BbªJ)ƒbθM LDbM L, à-, b θM L, bM L = arg max θ,  θ+LXs−1 k=θ (c2· Q − c3· zHz) (4.27) = arg max θ,  θ+LXs−1 k=θ (Q − ρ(Ns− 1)zHz) (4.28) = arg max θ,  { θ+LXs−1 k=θ NXs−2 α=0 NXs−1 β=α+1 2Re{r(k + αLs)r∗(k + βLs)ej(β−α)2π  NLs} −ρ(Ns− 1) θ+LXs−1 k=θ zHz} (4.29) w2 ρ = σ 2 s σ2 s + σn2 (4.30) ƒ¤, ø¯¯ IEEE 802.11a ™Äí|×–Nƒb˛Rû!!, -ÞøZuBbN¬ (4.26) Fdí_Ò, 1DÜ,í Cr´amer Rao -ÌTø_ªœ
ÇÕ, BbªJ·<ƒJøNs = 2p (4.26), Zª)ƒD [7]êró°í!‹, ¥6ÈQ„p7BbRûí£ü4

4.3

_Ò!‹

…øý.°lû’eÅÊË‹ëÆm¦−£ Rayleigh fading ¦−5-, ,¿|íä0 P5ÌjÏÏ (mean-squared error) DÜ,í Cr´amer Rao -Ìdªœ

4.3.1 Ö½˜¦−_

âkÊÛõíÌ(¦m=12}æÊrÖ¾óÓV®°mUf£í˜, FJÊ׶}í8” -, Î7mòª (light of sight) ˜(5Õ, ´rÖ¨AmU~¦í˜
Ĥ, ø_ªX.°í Ì(¦mÍ$óªœ/?ø_4 (consistent) !‹í¦−_u.âí
Ñ7¤øñí,IEEE 802.11 TÈÑSà7-Hí¦−_Vã¿ IEEE 802.11a(5GHz) íÖ½˜WÑ, Ç4.3Ѥ ¦−_í0§à@, w2©ø_vÈõ,, ·u×üÑ Rayleigh }Ó, iÑÌG}ÓíµbM, /wÌ?¾ÓOvÈíÓ‹ONb˙í«Á
-Þuwbç_: hk = N  0,1 2σ 2 k  + jN  0,1 2σ 2 k  (4.31) σk2 = σ02e−kTS/TRM S (4.32) σ₀2 = 1 − e−TS/TRM S _(4.33) w2N 0,1 2σ 2 k
uÌÑÉ, ‰æÑ1 2σ 2 kíògÓœ‰b, 7σ02 = 1 − e−TS/TRM SuÑ7Å—Ì Š0Ñø (Pkmax k=0 = 1) íd¸

âk IEEE 802.11a Ê!äí¦š§0Ñ 20MHz, ;W [7]íqñ, BbF_Ò Rayleigh fading ¦−_í¡bTRM S = 100ns(óçk 2 _¦š), D|×íôb¸ˇKmax(delay spread)

Ñ0.75µs(óçk15_¦š)
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

0.8 Rayleigh fading channel impulse response

k

Magnitude

 4 ı IEEE 802.11a -Z-íä0R,¿ 4.3.2 _Ò!‹

Ç 4.4, Ç4.5, £Ç4.6}Ñslû¯Uí_bÑù, ü,
v, %¬Ë‹ëÆm¦−£ Rayleigh fading ¦−íÌjÏÏDÜ,í-Ì5ªœ

*-Þú_ÇBbªJõƒ, çBbFUàíslû¯Uí_bÖ, wÌjÏÏD Cr´amer Rao -Ì6ÿü, ¥uâkBbªàí’mÖíí]
0 1 2 3 4 5 10−3 10−2 10−1 Ns = 2 SNR MSE & CRB CRB

Rayleigh fading channel AWGN channel

0 1 2 3 4 5 10−4 10−3 10−2 Ns = 5 SNR MSE & CRB CRB

Rayleigh fading channel AWGN channel Ç 4.5: slû¯Uí_bÑüvíÌjÏÏDCr´amer Rao -Ì 0 1 2 3 4 5 10−5 10−4 10−3 Ns = 10 SNR MSE & CRB CRB

Rayleigh fading channel AWGN channel

 5 ı

!

ñ‡j²ä0Rú£>}äÖ Í$F¨AíÝ°¥ à3bùj¶
ÊJä ÑHg VÁ/ä0Púc_Í$^?íj¶,, BbSà Kaiser ¢¨VqlFÛí˙šÂ, %_Òð„ ¤qlíüÊ^?,?FT¯
…d6ÜA™-šÈß×¾Îíj¶, 1D¢¨j¶Vdª œ, êÛâk‡øj¶FÛfŠ0¬×, A™-šÈß×j¶í^?ÉÊmUÆmª (SNR) ü v}œ74?, .Í׶}í8”-I\¢¨j¶ø¿
Êâf£mU…™í/<Ôy4”,lä 0R,, …d‡úÊ IEEE 802.11a ™Ä-5lûmU-5Ô4, Rû||×–N5,lj¶ 1°|£wÜ,í Cr´amer-Rao -Ì. %_Ò!‹BbêÛÖͤj¶l¬˙µÆOwÄü4 'ò

Ë“

A.1

Cr´

amer Rao

-ÌíRû

f (r|θ, ) = Y k∈I0 C1exp(C2Q − C3zHz) (A.1) ln f (r|θ, ) = θ+L_Xs−1 k=θ (ln C1+ C2Q − C3zHz) (A.2) ∂2 ∂2 ln f (r|θ, ) = C2 θ+LXs−1 k=θ ∂2_Q ∂2 (A.3) w2 Q = NXs−2 α=0 NXs−1 β=α+1 2Re{r(k + αLs)r∗(k + βLs)ej(β−α)j2π (β−α)Ls N } (A.4) ∂2_Q ∂2 = −2( 2πLs N ) 2 NXs−2 α=0 NXs−1 β=α+1 2Re{r(k + αLs)r∗(k + βLs)(β − α)2ej2π (β−α)Ls N }

FJ,Cr´amer Rao Bound Ñ

V ar [b(r) − ] (A.5) ≥  −E[∂ 2_{ln f (r|θ, )} ∂2 ] −1 (A.6) = ( 2 · C2· ( 2πLs N ) 2 θ+LXs−1 k=θ NXs−2 α=0 NXs−1 β=α+1 (β − α)2Re{E[r(k + αLs)r∗(k + βLs)]ej2π (β−α)Ls N  )−1 = ( 2 · C2· ( 2πLs N ) 2 θ+LXs−1 k=θ NXs−2 α=0 NXs−1 β=α+1 (β − α)2Re{σ_s2e−j2π(β−α)LsN ej2π (β−α)Ls N  )−1 (A.7) = ( 2 · σ 2 s σ2 n(σ2n+ Nsσs2) · (2πLs N ) 2_{· σ}2 s θ+L_Xs−1 k=θ N_Xs−2 α=0 N_Xs−1 β=α+1 (β − α)2 )−1 (A.8)

 A ı Ë“ = ( 2 · σ 2 s σ2 n(σ2n+ Nsσs2) · (2πLs N ) 2_{· σ}2 s · Ls· NXs−1 t=1 (Ns− t)t2 )−1 (A.9) = N 2_σ2 n(σ2n+ Nsσs2) 8π2_L3 sσ4s PNs−1 t=1 (Ns− t)t2 (A.10)

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