Ê [3]¹dıç2, T6Uà7ø_óçh˛í–1D;¶, V0§í°),¿, UFÛbíl
¾××íòü, 1/O.˜í¦−,¿ÏÏ^?J£Pj˜Ï0^?. BbJ-V}&FFT
|íj¶. íl, Bbl5?øˇó¹©/í;|, k, ..., l , 1/¥<;|Oœ×íÓïà@
(magnitude response). FFT|íj¶, w| ½bí–1uz, cqçHJ(ρk)íM'Äüív`, Î7óP.üìÄä λk = {ej2πnJ }J−1n=0´„øí8”-, H(ρk)íMwõªJ'Äüí\l|V :
H(ρk) = λk|HJ(ρk)|1/J· ej]HJJ(ρk) (49)
7¥<þ„øíóP.üìÄä, úk©_;|Vz·Jª?. Bb6˛ø−, úJ = 2ív`, óP.üìÄä¹Ñ{1, −1}. 7J = 4ívv`, .üìÄäÑ{1, −1, i, −i}. µó , Bbÿ²Ïw 2í/ø_.üìÄä (Wàús8”Vz, Bb·²Ï1), Í(Zª JdÀ/0§íLH«.
püøõVz, ílBbÊ;|k,²Ï7”1”¥_óPÄä, ¹H(ρk) = 1·|HJ(ρk)|1/J·ej]HJJ(ρk), 7 λk = 1.µóBbªJUà-íLHä, w2[HJ(ρk)]1/J = |HJ(ρk)|1/J · ej]HJJ(ρk) :
λk+1 = arg min
λ |H(ρk) − λ[HJ(ρk+1)]1/J| , H(ρk+1) = λk+1[HJ(ρk+1)]1/J λk+2 = arg min
λ |H(ρk+1) − λ[HJ(ρk+2)]1/J| , H(ρk+2) = λk+2[HJ(ρk+2)]1/J ...
λl = arg min
λ |H(ρl−1) − λ[HJ(ρl)]1/J| , H(ρl) = λl[HJ(ρl)]1/J
âkBbÊ;|k,F²íóP.üìÄäu”1”, 7J,íLH¢uóúkH(ρk)FT íLH, Ĥ
Bb}Ê¥<FLH|VíMç2, O;|køšíóPÔ4. BbÊJ, íLHäç2, U à7|ü (min,minimum) ퟆ, wŸÄuÄÑúk²¾hLSó¹ ís_ä[bVz, …bí bMøì}'Q¡. ¥uâk×àZ s²ä³«(F¨AíÔ4.
QOBbZªJYÕnFLH|Ví,¿MH(ρk), ..., H(ρl), ø…b§Aøò²¾(, ÇÕ yøFí.üìÄä#‹, , ĤªJ)ƒ-Þíä :
1 · H(ρk) 1 · H(ρk+1)
...
1 · H(ρl)
and
−1 · H(ρk)
−1 · H(ρk+1) ...
−1 · H(ρl)
for J = 2 and (50)
M V h¥_äíÉ[BbZªJ°)FJóú@
ív¦−0§à@²¾. 7¥<ví²¾, Bb¹ªJ*h = √
M V híÉ[V° )äí
¦−,¿¡b. ~R<, J,í}&ubÊç|HJ(ρk)|1/J, ..., |HJ(ρl)|1/J¥<M·ï×ív`l
|VíMnÄü [2]. 7Ê¥øˇó¹©/í;|í8”5-, ¥<Fl|VíJ_hîª JdÑ
£üí¦−,¿.
cqBb.Éøˇó¹©/í;|µóBbEͪJ‚à°ší–1V,¿¦−. 5?cà B bsˇó¹©/í;|, /¥<;|îOï×íÓïà@ : k, ..., l ¸m, ..., n.
ª?í¦−,¿h, w2íguH[O;|ˇíbñ. Ñ7bÊ¥<ª?í,¿ç2vƒ£üí,¿M, Bb´ u‚à7ä (47) íj¶Vl. BbêÛ, Å—ä (47) í¦−hEÍJª?M. Ä
¤BbZÓ<íÊ¥Jª?4-²¦ø_,¿, Í(y‚àä (13) Vl|óú@íä í,
¿h. ʤ´ubR<øõ, ¥š|VíMEÍOø_c ñíóP.üìÄä, 7¥_Ääí
+É?âtð;|V®A.
BbªJ*,Þí}&êÛ, CSC ¥_j¶TX7óçÀ/0§íƶV°),¿M, 1 / .}d MMD íj¶øš, OøO¦−¼bLÓ‹, l¾ÿ}O0§Ó‹íÔ4, Uí CSCí j¶0§/Z. l¾¥øjÞ, ÄÑ MMD ÛbJL+1íª?4í«¾, 7 CSC É ÛbJgí
«¾, â¤ZªJnj«¾íÏæ. Í7, c CSC O.˜íiõ, …´u<&Z¾5T.
ÄÑBbêÛ, ÊÉøˇó¹©/í;|v, Ñ7ı?°)œ Äüí,¿M, Ê5?M = 64v [8], ¦Bb×Ûb 40 _;|n?®ƒ,¿Mh Äüíñí. 7ç;|ˇíbñÖv, ;|íb
ñ6}.iÓ‹, ĤӋ7ä³í&( Z}Ó‹óú@í«¾.
Ê-Þíı³, BbZVnFT|íj¶, V«n¤j¶íŸÜ£Ô4. BbFT|íj¶Ê –1,wFsj¶éN, Ou?Dº¯ø<ƶí^ZVy‹Ë±Q CSCí«¾.
4.5 Jª0 (Ratio) íj¶d¦−,¿
4.5.1 FIR Í$íä0à@
−1 −0.5 0 0.5 1
−1
−0.8
−0.6
−0.4
−0.2 0 0.2 0.4 0.6 0.8 1
4
Real Part
Imaginary Part
θ1 k’
d4
d3
d2 d1
θ4
θ3 θ2
θo 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0
0 0 . 2 0 . 4 0 . 6 0 . 8 1 1 . 2 1 . 4
0 1 0 2 0 3 0 4 0 5 0 6 0 7 0
- 5 0 0 - 4 0 0 - 3 0 0 - 2 0 0 - 1 0 0 0
Ç 2: ø_FIR Í$í”ÉõDä0à@Ç. M =64.
ÊÇáÜBbíj¶5‡, BblV+3ø- FIR Í$í×ü£²Pà@íÔ4. íl¡5Ç 2, ÇÑø FIR Í$í z Þ”ÉõÇD×ü£óPà@Ç. ·<úF¼b ×kÉí FIR Í$, w”õ.ìÕ2ÊŸõ. µó;WÇ2, BbªJ)ƒ-Þí!‹:
!‹ 1 : *Ç2, úk/_;|k0 7k, H(ej2πk0M ) = H(ρk0) í×üíà@[ýÑ|H(ρk0)| = Q4
i=1di, 7wóPà@[ýÑ ]H(ρk0) = P4
j=1θj− 4 · θo. w2θouH[”õíóPi. µóBb
ÿªJ*¥<}&)ƒ FIR Í$í×ü£óPà@à- :
|H(ρk0)| = YL i=1
di (55)
]H(ρk0) = XL
i=1
θi− L · θo (56)
w2θou”õíóPi, 7Lu FIR ¦−í¼b. diu;|k0DÉõí×, 7θiuw óú@íÉõ óPi.
!‹ 2 : *Ç2BbªJêÛ, çFIR Í$í×üà@×ív`, wFú@íóPà@íó P‰
“ªœîM, Í7Ju×üà@ªœüív`, wFú@íóPà@ÿª?}ø_éNó P.©/, CóP” &” íÔ4. ĤBbÑ7fǤóP.©/íÔ4, BbZz·<‰Õ 2ƒ×íÓï Pàí¶M. ;W¥<O×íÓïà@í;|, 1‚àwó¹íóPà@íóPî ‰“, Bbı
?‚à¥_ÔõV,wFíóPà@M, JZªJøFíM´Ÿ, )ƒ|(í, ¿. ĤBbZ
7ú_!‹.
!‹ 3 : Bb²Ïµ<OòÓïà@í;|Vdl, ¹×í|HJ(ρk)|1/J, ¥uÄÑ…bO îMíóP‰“. ‚àó¹s_;|5ÈóPîM‰íÔ4VøFíóPøø´Ÿ.
4.5.2 ª0 (Ratio) j¶}&
Q-VBbVnàS‚àóP5ÈíÉ[Vd¦−,¿. BbT|-Þíj¶. Bbì2ª0∆Hk , H(ρk+1)
H(ρk) , w2k ∈ [0, M − 2]. µó¹ªJ)ƒ-Þíä :
∆HkJ = |∆HkJ| · ej(]∆HkJ) = |∆HkJ| · ej(J· ]∆Hk) (57)
w2]∆Hk= ]H(ρk+1) − ]H(ρk) .7∆HkíóPOJª?4, ?¹Ñ-Þíä :
]∆Hk+2mπ
J m ∈ [0, J − 1] (58)
¥³Bbc5?óPí3M, ¹[−π, π]íM. µóBbÿªJâu´∆Hk íóPi?DÅ—-Þ íbçVv|¥J_óPMç2¨_nu£üí :
−π
J < ]∆Hk+2mπ J < π
J (59)
w2J =2 C 4 . ¥_Ÿ†u;Wó¹ís_;|íóPOîM퉓ícqFRû|Ví, 7 JóP‰¬×†.?Å—,. 7*,Þ)ní)ø, óP}Ê×Óïà@íË¡OîMí
‰ “. Ĥ²Ïµ<O×Óïà@í;|Vd,Þíln.}|˜. Ĥ, Êâä (59) ° ) H(ρk+1)DH(ρk)5È£üíóPÏM5(, J]H(ρk)íM#ì , Bb¹ªâ-ÞíäV°
)H(ρk+1) :
]H(ρk+1) = ]∆Hk + ]H(ρk) (60)
w2]∆HkuH[H(ρk+1)DH(ρk)5È, Ê Jª?4ç2£üíóPÏM. ~·<, ÖÍ]H(ρk)M ucq#ì˛ø, Ouõ Ò,BbÉ?ø−]H(ρk)MíJª?4ç2íw2ø_, ÄÑ* HJ(ρk)M bR H(ρk)MŸ…ÿOø_xJª?4íóP.üìÄä [1]. 7/y½bíu, Ê¥<J
ª?4ç2,]∆HkMîu ì .‰í. ĤBbZªJâä (60) V°)]H(ρk+1), 7¤°)í MD ]H(ρk)Oó°íóPÔ4. YÎ¥j¶, BbªJøøíø ]H(ρk+2) ]H(ρk+3)... ¥
<M#l|V, 1/·]H(ρk)íMó°íóPÔ4. âkú©_;|kVz, ¦−í× üà@
ªJ'üìÌOËâ-äl|V :
|H(ρk)| = |HJ(ρk)|1/J (61)
BbZªJø¥<ÓïD,ÞFlíóP¯9, AÑø_êcíà@¡b, 1ø¡b§Aøò²
¾à- :
Ê-Þíqñç2, BbbVÌzpFT|j¶íÆ¥ , J£ø<óÉí½æ.
Step 1. š…Ì
ílBbÛøä (33) íHJ(ρk)Ml|V. bl¥_¡b, BbSàš…Ìíj¶, ä à- :
HˆJ(ρk) = − Q J · αJ{1
I XI−1
i=0
yJ(i, k)} k ∈ [0, M − 1] (65)
'ògí*ä (65) Võ, ÉbBbàÖíf£²¾mUbñI, BbøìªJíƒyÄü í,¿
M ˆHJ(ρk).
Step 2. ²Ï×ÓïM |H(ρk)|
-ø¥BbÛb©v_çí;|Vdl. Í7;|í©vj˛Êl‡dı2í!‹ 3 Fn
, ¹u‘²xœ×Óïà@í;|Vdl :
| ˆH(ρk)| = | ˆHJ(ρk)|1/J (66)
Í(BbÉÛz·<‰[Ê¥<;|,ÞÿW7. yVZªW-Þíl.
Step 3. øˇó¹©;|íÌóP.üì4
cqBbøˇó¹©/í;|, k0, ..., k0+m, 1/¥<;|Oï×íÓïà@. íl, Bbl l] ˆH(ρk0). ~·<, BbÉÛbÓZ²Ïw2íø _.üìÄ乪, Í(‚àä (57) (59) BbªJz]∆ ˆHk0 l|V. QO] ˆH(ρk0+1)ZªJ‚à (60) Vdl. 7¥<l |VíM
·] ˆH(ρk0)øšO°šíóPÔ4. ¥ší¥ BbªJøòªW- , òƒF²í;|·l
êH. püøõVz, JBb²Ï7øˇó¹ ©/í;|, k0, ..., k0 + m, w2mu/_£cb /k0 < k0+ m < M . µóBbøÆ¥ Ì |à- :
1. ll] ˆH(ρk0) = ] ˆHJJ(ρk0) +2πnJ M , 1/ÉÓ<²¦w2íø_n¹ª,n ∈ [0, J − 1].
2. àä (57) (59) Vl]∆ ˆHk0M.
3. ‚àä (60) Vl] ˆH(ρk0+1)M.
4. ½µ2 ƒ3 òƒFí;|íóP·lêH, )ƒ] ˆH(ρk0+2), ..., ] ˆH(ρk0+m).
*2 2BbªJ£üílí]∆ ˆHkíM, w2 k ∈ [k0, k0 + m − 1], ŸÄuÄÑBbʲ;
|ív`, F²Ïí;|x×íÓïà@, Ĥ?‚à ä (59) Vl, ´†ª?}|˜. 7 ] ˆH(ρk0), ..., ] ˆH(ρk0+m) ¥<óú ˆH(ρk0)Fl|VíM·…O°šíóPÔ4, ¹…bcñ 7kÉ ø_óP.üìÄä.
Ê£ülê¥<óPM5(, BbZ‚àä (66) l|ú@ ˆH(ρk0), ..., ˆH(ρk0+m) íÓïà
@,| ˆH(ρk0)|, ..., | ˆH(ρk0+m)|, Í(ø¥<MD˛lßíóP à@¯97)ƒFÛbíä0¡b, à -Fý :
H(ρˆ k) = | ˆH(ρk)| · e] ˆH(ρk) k ∈ [k0, k0+ m] (67)
Step 4. |üj (Least Square) l
*ä (67) )øBbªJUàä (13) Vl|,¿h :
H(ρˆ k0) ... H(ρˆ k0+m)
m+1
= √
M W ˆh (68)
hˆ = 1
√M(WHW )−1WH
H(ρˆ k0) ...
H(ρˆ k0+m)
m+1
(69)
w2 W , F (k0 : k0 + m , 1 : L + 1) u*×àZ s²ä³~’|Víüä³, OF í
k0, ..., k0+ míJ£‡ÞíL + 1_W. ä2éñåu[ý%â|üj l°)íM. ~
·<øõ, Ñ7b?U|üjƶªJÏW, BbÛ b(WHW )¥_ä³uÅ–ä³. ¹uz, W ¥_ä³íbñ.âb×kCk…íW bñ, C[ýÑm ≥ L. µóBbZªJâ-Þí
äV°)h
hˆ =√
M V ˆh (70)
â,°)íˆh´ø_cñíóP.üìÄä& tð;|Vj². '½bíøõ, ÿu CSC íj¶øš, çÊÉøˇó¹©/í;|v, J M = 64†BbÛb×40_;|Vdl, àŸ n?)ƒœÄüí,¿M ˆh.¥_½æv`ª?}ݶ,, à°Ç 3 í FIR ¦ −Fý. Ç2í FIR ¦−âkØÖíÉõÔ¡ÀPÆ, ĤJøˇó¹©/í;|íj¶V²† 40 _;|}
˚Ø.
−2.5 −2 −1.5 −1 −0.5 0 0.5 1
−1.5
−1
−0.5 0 0.5 1 1.5
7
Real Part
Imaginary Part
0 10 20 30 40 50 60 70
0 1 2 3 4 5
0 10 20 30 40 50 60 70
−2000
−1500
−1000
−500 0
Ç 3: ø_FIR Í$í”ÉõDä0à@Ç. Ç2Óïà@Çí0§‰“uâkPkÀPÆË¡ íÉ õ¬ÖF¨A. M =64.
4.5.4 sˇó¹©/í;|CuÖˇí½æ
−1 −0.5 0 0.5 1
−1
−0.8
−0.6
−0.4
−0.2 0 0.2 0.4 0.6 0.8 1
4
Real Part
Imaginary Part
0 1 0 2 0 3 0 4 0 5 0 6 0 7 0
0 0 . 2 0 . 4 0 . 6 0 . 8 1 1 . 2 1 . 4
0 1 0 2 0 3 0 4 0 5 0 6 0 7 0
- 5 0 0 - 4 0 0 - 3 0 0 - 2 0 0 - 1 0 0 0
Ç 4: FIR¦−”ÉõDä0à@Ç, ¤ÇÑø_zpàíWä. L = 4 and M = 64.
cqBbø FIR ¦−àÇ 3, Bb²õ†}˚Ø. Ñ7j²¥<½æ, ílBblV 5?s ˇó¹©/í;| , 8”ÿdÇ4øš. BbFní8”·uM = 64. cqB b;bɲÏøˇ ó¹©/í;|Vdl, µ'".ª?v)ƒ40_;|, JuÉ‚ àÇ2w2íøüˇ;|Vdl
, †âkõb.D, JBkä (68) C (69) íW 䳑K (condition) ‰ü7|í,¿ª?}
Ýí.Ä. J-Bb‚àøj¶øsˇ;|d¯9.
5?àÇ 4í8”, ílBbúøˇí;|dl, lj¶D¥ êrD4.5.3ínøš. Í (yzùˇí;|6d°ší«(, øùˇ (wõLSøˇîª) F|Víä²¾, ^,F
ª?íóP.üìÄä (çJ = 2vÑ{1, −1}, çJ = 4vÑ{1, −1, i, −i}), yVøˇ|
Ví!‹¯9Aø_œÅ, /Jª?4íò²¾, à-ÞäF[ý : CSC Fníj¶Oø<í.°. ¥uâkBbFT|íj¶ÉJg−1 ª?íò²¾Í7 CSC íj¶üJg_, w2gÑˇíbñ. à¤, J¥š¯9sˇ;|íj¶ZªJÓ ‹ä³W í×ü, 6ÿªJÓ‹w‘K. µóâä (68) (70), 1/à¥_%¬^Z¬(íW ä³, W = F ((k0 : k0+ m)&(l0 : l0+ n) , 1 : L + 1), BbZªJl|J_óú@í¦−,¿. ˆh
1, ..., ˆh
J, Í7w2É
ø_u£üí. b*¥J_ç2vƒ£üí,¿, BbUàJ-D [1].°íj¶Vl :
hˆ = arg min
hˆi kˆhJ − ˆhJik (73)
w2
hˆJ ,
HˆJ(ρ0) ... HˆJ(ρM −1)
(74)
u*ä (65) °)/ˆhJi6uâä (74) °šíj¶Vl|V. ¥šâä (73) F°)í£ü ,¿ˆh´uø_|(cñíóP.üì Ää&tð;|Vj². JuXƒÖ_ˇb (úˇJ,) í
½æv, Bb´uYÎJ,íj¶ø;|ˇ¯9, 7)ƒJg−1_ª?íˆh. |(£üí,¿´uâä (73) V²ì , OF)ƒíˆhuJ_, LSø_îªdÑ£üíÔ−,¿.
4.5.5 â²ÏøˇÝó¹©/í;|V“Ál¾
BbwõªJàÝ©/í;|ˇVòü«¾. ŸÄà-, Bbø−ç FIR íÓïà@×í v
`, wóú@íóP‰“}ªœîM. BbêÛ¥Ô4, Ê|×Óïí;|,Þ, w óP퉓yu îM, ĤBb7J-í;¶. Bb²Ï7J-í;| : k0+ p, k0+ 2p, ..., k0+ qp, w2pJ£qu
£cb/k0 < k0+ qp < M . BbJp = 2ÑWVzp. à‹BbF²Ïí¥<;|O|×í Ó ïà@v, BbªJゃ…bFú@íóP‰“}uóçîMí. Ĥª?ó½b_ õ5È;|í óP‰“6uîMí. Ĥ, Êó¹b_õ5È;|íóPà@J‰“6uîMí 8”-, ä (59) ZEÍA . Bb¹ªJ,ÞFníj¶Vl¦−í,¿, 1?)ƒD ä (68) ¸ (69) ó°
í!‹, Éu-ÓíW ä³¢ªŸVú@ä (71) C (72) íüø<. ¥šíßT Êk, JuJ¥
¯ÇíjV²Ï;|, µó;|íbñÉÛŸVr²íøš, OuW ä³í ‘Kº?&MGß, wŸÄuÄÑ×àZ s²ä³F íÔ4UÍ. ¥šÿªJÄüí,¿M, /l¾‰ü. ¥³ íp¡bªJ\Ó‹, Obe¦−íÔ4£ SNR Vd²ì. Ĥ¥;|²¦í–1uªWí.
BbVÔ_Wä, cqBbsˇó¹©/í;|, /¤vp = 2, BbªJYÎ,ÞínV)
ƒ D (71) ¸ (72) óNíbç, |à- :
4.5.6 Ìj¶
BbªJâ^Z4.5.5 Vyªø¥íVòü«¾. 5?Bbsˇó¹©/í ;|, OJ -;|í²¦j¶ : k0, k0+ 2, ..., k0+ m , l0, l0+ 2, ..., l0 + nw2mDncqÑ Xb. BbªJ Uà-Þíj¶V|Ö_¦−,¿1‹JÌ :
;|²¶ 1 : k0, k0+ 2, ..., k0+ m , l0, l0+ 2, ..., l0+ n =⇒ ° ˆh1
;|²¶ 2 : k0, k0+ 2, ..., k0+ m , l0+ 1, l0+ 3, ..., l0+ n + 1 =⇒ ° ˆh2
;|²¶ 3 : k0+ 1, k0+ 3, ..., k0+ m + 1 , l0, l0 + 2, ..., l0+ n =⇒ ° ˆh3
...
Bb?J,F·Hí²Ïj, wõ'péíuâkBbF²ÏUàí;|u” Ýó¹” í, Ä
¤BbªJø;|íP0¯Ç. 7/'ògíªJêÛ, çpbM‰×v, BbªJyÖ í²ÏVd
Ì. Ĥ,Þ¥ší²õ_, Bbz©ø_ú@í²¦_, àl‡4.5.5 FÜíj¶Vv|w ú@í¦−,¿. Í(b·<íu, Fl|VíFú@í¦−,¿ ss5ÈEOø_óP.ü ìíÄä&^£, ĤÊÌ5‡Bb.Ûbdø<óP^£. BbzFí,¿·óúkw2íø _ (LSø_îª) ,¿dóPí^£, é…br¶·ƒø _íóPÕG. Í(Bb¹ªJ‚à-ÞíbçVv|…bíÌMJÓ‹,¿Äü :
hˆ = 1 z
Xz i=1
hˆi (77)
w2ízuH[F¦−,¿íbñ. ~b·<íu, ä (77) FÌ|í¦−,¿ ˆhEÍO ø _cñíóP.üìÄä&tð;|Vj².âä (77) FÌl|Ví¦−,¿íü ?Ë
œÄüí,¿M, ¥_Ô4ªJâÇ5£Ç6Vhô)ø :
5 10 15 20 25 30 35 40 10−3
10−2 10−1 100 101
x : no average o : average (z = 9)
Eb/N0 (dB) NRMSE
BPSK, I = 20, Monte Carlo = 200, M = 64, L = 4
5 10 15 20 25 30
10−5 10−4 10−3 10−2 10−1 100
BER
Eb/N0 (dB) BPSK, I = 20, Monte Carlo = 200, M = 64, L = 4
+ : perfect channel o : average (z = 9)
* : no average
Ç 5: UàÌj¶ø¦−,¿ÏÏ£óú@íBER ±Q. z = 9. |‰j¶Ñ BPSK.
5 10 15 20 25 30 35 40
10−3 10−2 10−1 100 101
QPSK, I = 20, Monte Carlo = 200, M = 64, L = 4
Eb/N0 (dB) NRMSE
+ : no average o : average (z = 9)
5 10 15 20 25 30
10−6 10−5 10−4 10−3 10−2 10−1 100
QPSK, I = 20, Monte Carlo = 200, M = 64, L = 4
BER
Eb/N0 (dB)
+ : perfect channel o : average (z = 9)
* : no average
Ç 6: UàÌj¶ø¦−,¿ÏÏ£óú@íBER ±Q. z = 9. |‰j¶Ñ QPSK.
J,FÜí_Ò!‹ç2, Bb¦−,¿íÏÏĆuà£djÌ;ÏÏ ( NRMSE,Normalized Root Mean Square Error), ¥_ĆBb}Ê_ÒıdÌí Ü. ¤Õ, àí FIR ¦−
Ñ{0.459 + 0.265i, −0.2078 − 0.12i, −0.4677 − 0.27i, 0.0953 + 0.055i, −0.0312 − 0.018i}. ¤ ÕBb´TX7 BPSK D QPSK í¦−,¿ÏÏJ£óú@íPj˜Ï0_Ò!‹. â_ÒÇB bªJêÛ‚àÌíÀ–1íü?Ó‹,¿Ä. Í7…6_'péíÿõ, ÿu‚àÌí –1Vd¦−,¿,4.5.5FÜíl¥³ÿblzŸ, ĤTò7«¾.
5. _ÒDªœ
5.1 ,¿DÍ$^?_Ò
Ê¥_ıBbTX7ø<_Òí!‹. BbUà7ú_.°í FIR ¦−, Üà- :
FIR 1 : 2.3977 − 1.0074i, 2.0871 − 1.0725i, −1.6741 + 2.3361i, −1.0562 − 0.1019i (78)
w2¤ FIR ¦−í¼bÑL = 3(4 taps).
FIR 2[5] : 0.459+0.265i, −0.2078−0.12i, −0.4677−0.27i, 0.0953+0.055i, −0.0312−0.018i (79) w2¤ FIR ¦−í¼bÑL = 4(5 taps).
FIR 3 : −0.9191 + 0.7843i, 1.6084 − 0.3839i, 0.0369 − 0.1681i, −0.7509 + 0.6574i (80)
, 1.4452 + 0.1745i
w2¤ FIR ¦−í¼bÑL = 4(5 taps).
Bbì2FUàí¦−,¿ÏÏĆ : £djÌ;ÏÏ (NRMSE,Normalized Root Mean Sqaure Error)[5] :
NRMSE = 1 khk2
vu ut1
N
N −1X
i=0
kˆh(i) − hk22 (81) w2ˆh(i)H[íuiŸõðF)ƒí,¿M, 7N †uH[P˵˚íŸb. 7,ç2íkhk2u H[ö£¦ −í_b(norm) M.
Bb}TX¥ú_ FIR ¦−í BPSK J£ QPSK í_Ò!‹, w2 PSK ¹âä (27) Fì 2. Bb}‚àJ- ú.°íj¶Vd_Ò, 1/‹Jªœ : MMD-PD, CSC ¸ª0 (Ratio).
¤ÕBb´}dø<ÇD«n.
ílBblVnjø-¥ú_ FIR ¦−ö£íä0à@íÔ4ÑS :
−1.5 −1 −0.5 0 0.5 1
−1 −0.5 0 0.5 1 1.5
−1
−0.8
−0.6
−0.4
−0.2 0 0.2 0.4 0.6 0.8 1
4
Real Part
Imaginary Part
0 10 20 30 40 50 60 70
0 1 2 3 4 5 6
0 10 20 30 40 50 60 70
-400 -300 -200 -100 0 100
Ç 9: FIR 3¦−í”ÉõDä0à@Ç. L = 4, M = 64.
*J,í¦−à@ÇBbªJ)ø, FIR 1 íóPà@‰“î7FIR 3íóP‰“óç0§.
ĤBbªJã‚, FT|íj¶ÊFIR 1ø}.˜í^?, 7ÊFIR 3^@ª?}‰Ï.
QOBbZVú¥ú_ FIR ¦−døÍí_Ò, _ÒÇà- :
5 10 15 20 25 30 35 40
10−4 10−3 10−2 10−1
NRMSE
Eb/N0 (dB)
+ : MMD−PD o : CSC(36)
* : Ratio(20) FIR 1, L = 3, BPSK, I = 20, Monte Carlo N = 100
4 6 8 10 12 14 16 18
10−4 10−3 10−2 10−1
MMD−PD CSC(36) Ratio(20) perfect channel
Eb/N0 (dB) BER
FIR 1, L = 3, BPSK, I = 20, Monte Carlo N = 100
Ç 10: FIR 1í NRMSE Dóú@í BER ^?_ÒÇ. L = 3, M = 64, BPSK.
5 10 15 20 25 30 35 40 10−4
10−3 10−2 10−1 100
FIR 1, L = 3, QPSK, I = 20, Monte Carlo N = 100
NRMSE
Eb/N0 (dB)
+ : MMD−PD o : CSC(36)
* : Ratio(20)
4 6 8 10 12 14 16 18
10−4 10−3 10−2 10−1
+ : MMD−PD CSC(36)
* : Ratio(20) perfec channel FIR 1, L = 3, QPSK, I = 20, Monte Carlo N = 100
BER
Eb/N0 (dB)
Ç 11: FIR 1í NRMSE Dóú@í BER ^?_ÒÇ. L = 3, M = 64, QPSK.
5 10 15 20 25 30 35 40
10−4 10−3 10−2 10−1 100
FIR 2, L = 4, BPSK, I = 20, Monte Carlo N = 100
NRMSE
Eb/N0 (dB)
+ : MMD−PD o : CSC(40)
* : Ratio(26)
4 6 8 10 12 14 16 18 20 22
10−4 10−3 10−2 10−1 100
+ : MMD−PD o : CSC(40)
* : Ratio(26) x : perfect channel FIR 2, L = 4, BPSK, I = 20, Monte Carlo N = 100
BER
Eb/N0 (dB)
Ç 12: FIR 2í NRMSE Dóú@í BER ^?_ÒÇ. L = 4, M = 64, BPSK.
5 10 15 20 25 30 35 40 10−4
10−3 10−2 10−1 100 101
Eb/N0 (dB) NRMSE
FIR 2, L = 4, QPSK, I = 20, Monte Carlo N = 100
+ : MMD−PD o : CSC(40)
* : Ratio(26)
5 10 15 20 25
10−4 10−3 10−2 10−1 100
FIR 2, L = 4, QPSK, I = 20, Monte Carlo N = 100
BER
Eb/N0 (dB)
+ : MMD−PD o : CSC(40)
* : Ratio(26) x : perfect channel
Ç 13: FIR 2í NRMSE Dóú@í BER ^?_ÒÇ. L = 4, M = 64, QPSK.
5 10 15 20 25 30 35 40
10-4 10-3 10-2 10-1 100
+ : MMD-PD o : CSC(33)
* : Ratio (17)
Eb/N0(dB) NRMSE
FIR 3, L = 4, BPSK, I = 20, Monte Carlo N = 100
5 10 15 20 25 30
10-4 10-3 10-2 10-1 100
+ : MMD-PD o : CSC(33)
* : Ratio(17) x : perfect channel FIR 3, L = 4, BPSK, I = 20, Monte Carlo N = 100
Eb/N0(dB) BER
Ç 14: FIR 3í NRMSE Dóú@í BER ^?_ÒÇ. L = 4, M = 64, BPSK.
5 10 15 20 25 30 35 40 10-4
10-3 10-2 10-1 100 101
+ : MMD-PD o : CSC(33)
* : Ratio(17) FIR 3, L = 4, QPSK, I = 20, Monte Carlo N = 100
Eb/N0(dB) NRMSE
5 10 15 20 25 30
10-4 10-3 10-2 10-1 100
+ : MMD-PD o : CSC(33)
* : Ratio(17) x : perfect channel FIR 3, L = 4, QPSK, I = 20, Monte Carlo N = 100
BER
Eb/N 0(dB)
Ç 15: FIR 3í NRMSE Dóú@í BER ^?_ÒÇ. L = 4, M = 64, QPSK.
*J,í_ÒÇç2, BbªJêÛø_í½æ. ÿuÍ$íÏÏ}ÓOEb/N0í Ó‹7Á ý. ¥_ÛïN˛'¯¯òg. OuJƒ5‡Fní!‹Võ, ; Wä (32) C (33) Bbª JêÛ¦−,¿í½æuDÆmÌÉí. ÄѹUÊä (30) ç2 Æmn(k)æÊ, …í^@YÍ }ÄÑc (circular) ícqÔ47¾Ü. Ñ7j„¥_Ûï, ~Ô<íu, BbFàíÆm_Ò õÒ,ÉuUàøOíÌMÑÉíµbòg Æm, 1.uÅ—cògÔ4íògÆm. âkp mUx(k)u (œ}ÌË) *ä (27) Fì2í PSK rÙÇç2²¦|Ví, ĤFímUí Š0.ì·u 1. µó'péíVõ, càBbøEb/N0Ó‹íu, óú@íÆmŠ0Z}ªmUŠ0 ü, 7/uük1. FJà‹BbSàä (30) í¦−f_íu, çEb/N0Ó‹v, âkÆ mí Š0ük 1, 7ük1íbíò¼Ÿj.ìyü, FJä (32) íò¼ÆmáZ}Ó OEb/N0Ó×7 0§‰ü. FJBbJ,íÍ$^?_ÒÇ·uÓOEb/N0Ó×7×Û|ÏÏ ‰üíÛï, ¹uâk
¤ŸÄF_, /¥Ûï6óçí¯¯òg.
BbÛÊVÌËj„J,í_ÒÇ. ÊÇ 10 £ 11 2, ¥<uÊFIR 1 ¦−Fdí_Ò. CSC (ÞFŸíbåuH[ÊM = 64í8”-FUàí;|íbñ, FJú CSC VzBbà736_;
|Vd l, 7úª0Vz, Bbà7 20 _;| . Ê¥³BbbT|øõíu, Êdı [3]ç2, T
6T| ø_h1, ¹Ê©øˇó¹©/í;|7k, FUàí;|íbñÖ, †,¿MZ}Ä. â ¥_hõ, BbkuÊà CSC íj¶ç2, à7r¶ªJàíõVTl. ~·<íu, ÊÇ 10
£ 112BbuUà7sˇó¹©/í;|VT36õí CSC(36) í,¿j¶, /ú©ø ˇ;|Vz, Bbu®à7 18õ. Bkú Ratio(20) íj¶Vz, BbuÊ©_;|ˇ 2®Uà710õÝó¹©
/íõVl, w2õDõí×Ñp = 2.
*Ç 10 £ 11 BbªJêÛú BPSK J£ QPSK 7k, cBbFT|íj¶Ê NRMSE í
^?,ª MMD-PDC CSC bVíšÏø<, OuÊPj˜Ï0í^?Vz, ¥ú_j¶í!‹
˛ªJ zuÏ.Ö, ÝBÊPj˜Ï0í^?,ªJàÇFéý, ?V¡ö£í¦−¡b^?. ¤ Õ ´øõbzpíu, BbÊ MMD í¬˙2Éà7L + 1_õbVdl, ¥u;W [1]FT|
íj¶. .ÍJàyÖíõVl, ÊJ = 4ív(«¾}óçí˚A.
5?Ç 12£13, ¥uÊ FIR 2 í¦−Fdí_Ò, ¥³Bb´uUàsˇVd}&. ú CSC(40) Vz, Bbu®à7 20 õVl, 7ú Ratio(26) Vz , Bb†u® Uà7.©/í 13 õVl, /w2íȽÑp = 2. 7úk MMD íl, Bb´u ÉUà7L + 1_õV}&. *¥"ÇVõ, BbªJ'péí)ƒéNÇ 10£11FË íÔ4, ¹s6í!uó°í.
ÊÇ 14£15Bb†uú FIR 3 ¦ƒd_Ò. ú CSC(33) Vz , øˇuà16õ, Çøˇ†uà 17 õ. ú Ratio(17) Vz, øˇàíuøˇ 8 _.©/íõ, øˇ†u 9 _.©/íõ, FàíȽ6 up = 2. 7 MMD Bb´uEÍuàL + 1_õdl. Ou*¥s"ÇVõ, w!‹N˛DFIR 1 D 2 í!‹.Øøš. ~·<, *Ç 9 Võ, wõBbÊFIR 3 ,uUàÆ˛Tsˇ ó¹©/í;
|Vdl, Ouw!‹éýÊ NRMSE ^?jÞ MMD-PD íj¶ªwìís6bß'Ö. wŸ ĹuÊkFIR 3 …™óP‰¬k0§F_. ĤBb6ªJêÛ CSC £ª0sj¶úk¦−
œ Ü>, 7 MMD-PD íj¶Oœòí#U (robustness).
Q-VBbTX7yÖí_ÒÇ, 1âJ-íÇVdø<}& :
2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 0 1 0 0
1 0- 3 1 0- 2 1 0- 1
N R M S E
F I R 1 , L = 3 , B P S K , M o n t e C a r l o N = 1 0 0
I ( b l o c k s )
+ : M M D - P D o : C S C ( 3 6 )
* : R a t i o ( 2 0 )
20 30 40 50 60 70 80 90 100
10-3 10-2
FIR 1, L = 3, BPSK, Monte Carlo N = 100
BER
I (blocks) Eb/No = 10 (dB)
Note : BER for all the methods including perfect channel are all zero under 20 dB.
Ç 16: FIR 1í NRMSE Dóú@í BER ^?_ÒÇ, ú@.°íI. L = 3, M = 64, BPSK.
2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 0 1 0 0
1 0- 3 1 0- 2 1 0- 1
+ : M M D - P D o : C S C ( 3 6 )
* : R a t i o ( 2 0 ) F I R 1 , L = 3 , Q P S K , M o n t e C a r l o N = 1 0 0
N R M S E
I ( b l o c k s )
20 30 40 50 60 70 80 90 100
10-3 10-2
FIR 1, L = 3, QPSK, Monte Carlo N = 100
BER
I (blocks) Eb/No = 10 (dB)
Note : BER for all the methods including perfect channel are all zero under 20 dB.
Ç 17: FIR 1í NRMSE Dóú@í BER ^?_ÒÇ, ú@.°íI. L = 3, M = 64, QPSK.
2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 0 1 0 0 1 0- 3
1 0- 2 1 0- 1
F I R 2 , L = 4 , B P S K , M o n t e C a r l o N = 1 0 0
N R M S E
I ( b l o c k s )
+ : M M D - P D o : C S C ( 4 0 )
* : R a t i o ( 2 6 )
20 30 40 50 60 70 80 90 100
10-4 10-3 10-2 10-1
FIR 2, L = 4, BPSK, Monte Carlo N = 100
BER
I (blocks) Eb/No = 10 (dB)
Eb/No = 20 (dB)
Ç 18: FIR 2í NRMSE Dóú@í BER ^?_ÒÇ, ú@.°íI. L = 4, M = 64, BPSK.
2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 0 1 0 0
1 0- 3 1 0- 2 1 0- 1
F I R 2 , L = 4 , Q P S K , M o n t e C a r l o N = 1 0 0
N R M S E
I ( b l o c k s )
+ : M M D - P D o : C S C ( 4 0 )
* : R a t i o ( 2 6 )
20 30 40 50 60 70 80 90 100
10-4 10-3 10-2 10-1
FIR 2, L = 4, QPSK, Monte Carlo N = 100
BER
I (blocks) Eb/No = 10 (dB)
Eb/No = 20 (dB)
Ç 19: FIR 2í NRMSE Dóú@í BER ^?_ÒÇ, ú@.°íI. L = 4, M = 64, QPSK.
20 30 40 50 60 70 80 90 100 10-3
10-2 10-1 100
+ : MMD-PD o : CSC(331)
* : Ratio(17)
NRMSE
FIR 3, L = 4, BPSK, Monte Carlo = N = 100
I (blocks) Eb/No = 10 (dB)
Eb/No = 10 (dB) Eb/No = 20 (dB)
Eb/No = 20 (dB)
20 30 40 50 60 70 80 90 100
10-3 10-2 10-1
FIR 3, L = 4, BPSK, Monte Carlo N =100
BER
I (blocks) Eb/No = 10 (dB)
Eb/No = 20 (dB)
Ç 20: FIR 3í NRMSE Dóú@í BER ^?_ÒÇ, ú@.°íI. L = 4, M = 64, BPSK.
20 30 40 50 60 70 80 90 100
10-3 10-2 10-1 100
I (blocks)
FIR 3, L = 4, QPSK, Monte Carlo N = 100
NRMSE
+ : MMD-PD o : CSC(33)
* : Ratio(17) Eb/No = 10 (dB)
Eb/No = 20 (dB)
20 30 40 50 60 70 80 90 100
10-3 10-2 10-1 100
FIR 3, L = 4, QPSK, Monte Carlo N = 100
I (blocks) BER
Eb/N0 = 10 (dB)
Eb/N0 = 20 (dB)
Ç 21: FIR 3í NRMSE Dóú@í BER ^?_ÒÇ, ú@.°íI. L = 4, M = 64, QPSK.
BbVÌíjz,Þí_ÒÇ. 5?Ç16£17, BbÊFIR 1í¦−TX7úú@íj¶V T_Ò, 1/BbTX7}Ê BPSK D QPSK í|‰xÍ,óú@í NRMSE J£Pj˜Ï0 íÍ$^ ?_Ò, 7/Bb}ÊEb/N0k 10 D 20(dB) }d7°ší_Ò}&. 7b·<í uÊ20 dB 5-íPj˜Ï0 rÑÉ. Ê¥<_ÒÇ2, Bb b·<íu, Í$í^?uÓO²¾m UbñI퉓7‰“, .yu5‡íEb/N0 ¥_¡b. Ĥ*Ç2BbªJêÛ, Í$í^?1.
}ÓOIíbñÓ‹7éOíÓ ‹, ¥7ÓOEb/N0íÓ‹7/qíø^?Tô. 7Bb´ªJR
<ƒøõ, µÿuFú@í Pj˜Ï0_ÒÇ, úú.°íj¶Vz6u˛ó¡, .u BPSK C QPSK. úkÇ18£19Bb6óN í!‹. OuÊÇ20£212, BbªJ êÛwÊFIR 3í NRMSE ^??D‡s6ø<.°. MMD-PD Fú@í NRMSE ^?ª CSC £ª0 bß. w ŸÄD5‡Fní!‹øš.
*J,í}&Võ, BbFT|íj¶ÖÍÄѦ−óPí0§‰“7Ê NRMSE í^?, ª MMD-P C CSC bVíÏø<, OuwPj˜Ï0í^?ªJzuóçQ¡, ÝB?V¡ö£í¦
−¡b. âk¦mí3bñíuxQí˜Ï0, ĤFT|íj¶EÍuªWí. Í7, BbFT|
íj¶´øá*J,VÖí_ÒÇFõ.Ø|Víiõ, ?¹ul ‡o˛Tƒí«¾í½æ. B b-Þ¹V«nú.°íj¶í«¾ªœ.
5.2 l¾ªœ
Ê¥øüç2BbVúú.°íj¶í«¾Vdø<Ìí}&. OuÊ¥5‡, Bbl Vdø<ãeT. ílBb;W [6]íj¶, øø_«¾ (flop) ì2ÑÀøµbíó‹ÁC Î.
Í(Bb;W [7]íj¶, øø_n níªLj£ä³, wL²FÛbí«¾ì2Ñn3. µó
;WJ,í}&, Bb.Øø¥ú_j ¶í«¾äJø<Í$_Ò¡bV[ý. Í7BbÊ
¥³.TX¥<ä. ÄÑ¥<ä ¬kõÆ/yÅ, *¥<äBb̶)ƒàím7. BbÊ
¤Z²Çøì¾íj¶V} &«¾. à-ÞTXí[Fý. à[2, cqBbI MMD-PD ¥ _j¶FÛbí«¾J ø_ì}õíl¾jVõ, J MMD-PD Ûbí«¾Ûb100%íu, wÊ BPSK Fó ú@í CSC(36) ÉÛb…í76.08%, 7FT|í Ratio(20) j¶yuÉÛbw r¶«¾í 54.5%. ¤Õ, úk QPSK íÍ$_Ò, Bb6TX7¥ú.°íj¶í«¾ª œ, îJì}õÑl¾. BbĤªJ'péíêÛ, CSC ¥j¶ª MMD-PD FÛbí«¾ bVíýrÖ, Í7Bb FT|íj¶, Oyüí«¾, /˛u CSC íøš. 7*FTXíÇ Õs"[Võ, °ší!‹ªJ'péí\êÛ, FT|íj¶.uÊ¥ú_.°í FIR ¦−C u.°|‰ íxÍ, w«¾îu|üíø_. ŸÄwõ'À, âk MMD-PD Ûbí«¾îâ lJL+1 Fú@íFª?í,¿F3û, Í7úk CSC Vz, wl¾ÉâJgíÄäF3û, F JCSC 'péí6üí«¾, /.§¦−¼bLí à. 7úª0Vz, w3bí«¾, % ¬ ø<ƶí^Z, ÉÛbJg−1óú@íl¾, 1/º¯O²ÏÝó¹©/;|íxÍ, y ªJø
«¾±Q. ¥ÛïªJ*[2)øÊJ = 4ív`«¾íÏOÝ×í–.
[ 2. ú.°íj¶ÊFIR 1¦−,l¾íªœ M = 64, I = 20, L = 3 MMD-PD CSC(36) Ratio(20)
BPSK(J = 2) 100% 76.08% 54.5%
QPSK(J = 4) 100% 14.79% 8.67%
[ 3. ú.°íj¶ÊFIR 2¦−,l¾íªœ M = 64, I = 20, L = 4 MMD-PD CSC(40) Ratio(26)
BPSK(J = 2) 100% 67.27% 48.61%
QPSK(J = 4) 100% 12.81% 7.74%
[ 4. ú.°íj¶ÊFIR 3¦−,l¾íªœ M = 64, I = 20, L = 4 MMD-PD CSC(33) Ratio(17)
BPSK(J = 2) 100% 61.41% 45.52%
QPSK(J = 4) 100% 11.62% 7.43%
6. !
Ê…¹dç2, øJÌåjÑ!í OFDM ¦−,¿j¶ \T|. 1/Bbø¤j¶D wF˛\T|ísj¶døPÍ$í}&D_Òªœ. FT| íj¶ÖÍÊ NRMSE íÍ$^
?jÞâk¦−óP×Ù퉓7ªÇÕsj¶V)Ïø<, Ow Pj˜Ï0í^?îDÇs6 Ï.Ö, ÝBö£í¦−¡bQ¡. ¤Õ, FT|íj¶âø<ƶí ^£, ª7UFÛbí
«¾‰ý, 7¥6u…¹dí½-. Ê¥ú.°í,¿j¶ç2, F;Wí·uJ°ší–1 Vd|ê, ?¹F‚íÌåjíÔ4, 7F,¿|Ví¦ −, îÛâtð;|Vd|(íóP^£.
ĤFT|íj¶cñ7kuªWí, 1/ªJñqË@àÊ œÑÀí¦−,, /ODwFj¶
Ï.ÖíPj˜Ï01/l¾´?y‹íÁý.
Í7FT|íj¶EÍOrÖ½æbj². Ê…¹d2, Bb·cq¦−¼bL˛ø, Ou Êöõí½æ2, ¦−¼b6u_„øí¡b. Jʦ−¼bL.ø−í8”-, BbZÛ l dLí,¿, yd¦−í,¿. OuúkLí,¿Vz, ò,CQ,·}¨Aø<çÕí½æ [1]. yV uFIR 3í½æ. Bb*,ÞrÖí_ÒÇ2ªJ)ø, J¦−óP‰“¬k —Ë,
Í$^?Z}-±rÖ. |(¹uÊ5.6ç2FUàí¡bpí½æ, …}D¦−…™í Ô4£ Tí SNR É. B bíñ™ub²Ï_çípM1/?°vÅ—-Þú_‘K :
1. âk«¾íí], F²í;|býß.
2. âkä³W í‘Kíí], Fqìípb×ß.
3. Í$í^?b|‹“.
Bbú_Û°, ŸÄuÄÑJ²ÏíõbD×J._ç, Í$í^?}'ýí- Ë. Ĥ
FT|íj¶EÍOrÖª&Z¾£n5T.
References
[1] S. Zhou and G. B. Giannakis, “Finite Alphabet Property Based Channel Estimation for OFDM and Related Multicarrier Systems,” Proc. 34th Conf. Information Sciences and Systems(CISS’00), Princeton, NJ, March, 2000.
[2] S. Zhou, G. B. iannakis, and A. Scaglione, “Long Codes for Generalized FH-OFDMA Through Unknown Multipath Channels,” IEEE Trans. Commun., vol. 49, pp. 721-733, April, 2001.
[3] T. Petermann, S. Vogeler, K.-D. Kammeyer, D. Boss, “Blind Turbo Channel Estima-tion in OFDM Receivers,” Signals, Systems and Computers, 2001. Conference Record of the Thirty-Fifth Asilomar Conference, Volume: 2, Pages:1489 - 1493, November, 2001.
[4] Leonard J. Cimini, “Analysis and Simulation of a Digital Mobile Channel Using Or-thogonal Frequency Division Multiplexing,” IEEE Trans. Commun., Vol. Com-33, No.
7, July, 1985.
[5] A. Chevreuil, P. Loubaton and G. B. Giannakis, “Blind Channel Identification and Equalization using Periodic Modulation Precoders : Performance Analysis,” IEEE Trans. Signal Processing., vol. 48, pp. 1570-1586, June, 2000.
[6] T. P. Krauss and M. D. Zoltowski, “Bilinear Approach to multiuser Second-Order Statistics-based Blind Channel Estimation,” IEEE Trans. Signal Processing., vol. 48, pp. 2473-2486, September, 2000.
[7] G. Strang, Linear Algebra and Its Applications, THOMSON BROOKS/COLE, 1988.
[8] “IEEE 802.11a” , 1999.
[9] John G. Proakis, Digital Communications, Fourth Edition, New York:McGraw-Hill, 2000.