eXR bbmKTiBQMb

eXRXR am#@+``B2` HHQ+iBQM

*QMiB;mQmb M/ `M/QKHv /Bbi`B#mi2/ bm#@+``B2` T2`KmiiBQM HHQ+iBQMb `2 irQ KBM +i2;Q`B2b Q7 bm#+?MM2H HHQ+iBQM b+?2K2 BM P6.J bvbi2KbX h?2 +QM@

iB;mQmb bm#@+``B2` T2`KmiiBQM Bb H`2/v /Bb+mbb2/ BM *?Ti2` 8X h?2`27Q`2- BM i?Bb +?Ti2`- r2 7Q+mb QM i?2 `M/QKHv /Bbi`B#mi2/ T2`KmiiBQMbX h?2 #2M2}i Q7 /Bbi`B#mi2/ T2`KmiiBQMb Bb iQ +?B2p2 7`2[m2M+v /Bp2`bBiv M/ BMi2`@+2HH BMi2`72`2M+2

p2`;BM;X AM i?2 +?Ti2`- r2 /Bb+mbb i?2 Qmi;2 T`Q##BHBiv 7Q` 72KiQ+2HH Q7 P6.J

bvbi2Kb rBi? KmHiB+``B2` +b2X

**eXRXk _/BQ *?MM2H**

q2 +QMbB/2` i?2 `/BQ +?MM2H 2z2+ib Q7 Ti? HQbb- T2M2i`iBQM HQbb- M/ b?/@

QrBM;- r?B+? `2 /Bb+mbb2/ BM a2+iBQM 8XRXkX

JmHiBTi? 6/BM; QM am#@+``B2`

_vH2B;? 7/BM; Bb mb2/ BM i?2 Qmi;2 T`Q##BHBiv MHvbBb Q7 72KiQ+2HH rBi? irQ@

iB2` BMi2`72`2M+2X _vH2B;? 7/BM; +?`+i2`Bx2b i?2 BKT+i Q7 KmHiBTi? T`QT;iBQM /Bbi`B#miBQMX h?2 T`Q##BHBiv Q7 /2MbBiv 7mM+iBQM 7Q` _vH2B;? /Bbi`B#mi2/ `M/QK p`B#H2 h b

fh(h) = 2he^−h². UeXRV

G2i Y = h²X h?2M i?2 +mKmHiBp2 /2MbBiv 7mM+iBQM Q7 Y +M #2 r`Bii2M b

FY(y) = 1 − e^−y. UeXkV

eXRXj aB;MH iQ AMi2`72`2M+2 M/ LQBb2 _iBQ

q2 +QMbB/2` i?2 irQ@iB2` BMi2`72`2M+2X G2i Pk,j,m #2 i?2 i`MbKBbbBQM TQr2`

Q7 i?2 k@i? #b2 biiBQM QM m@i? bm#@+``B2` Q7 j@i? bm#+?MM2HX a?/QrBM; +M #2 +?`+i2`Bx2/ #v HQ;@MQ`KH `M/QK p`B#H210^ξk,j¹⁰ - r?2`2 ξk,j Bb :mbbBM `M/QK p`B#H2 Q7 j@i? bm#+?MM2H BM i?2 k@i? 72KiQ+2HHX h?2 bm#@+``B2` ;BM #2ir22M i?2 k@i? #b2 biiBQM M/ i?2 +QMbB/2`2/ mb2` Bb yk,j,mX h?2`2 `2 M bm#@+``B2`b BM

 bm#+?MM2HX h?2`27Q`2- i?2 `2+2Bp2/ bB;MH TQr2` i i?2 m@i? bm#@+``B2` BM i?2 72KiQ+2HH KQ#BH2 i2`KBMH +M #2 r`Bii2M b

Pr_k,j,m = Pk,j,m10^ξ^k,j^/10yk,j,m/L(rk), UeXjV

M/ i?2 iQiH TQr2` Q7 bm#+?MM2H BM i?2 72KiQ+2HH KQ#BH2 i2`KBMH Bb T`Q##BHBiv /2MbBiv 7mM+iBQM 7Q` i?2 HBMF ;BM Q7 bm#+?MM2H yk,j Bb

fy(y) = e^−y y^M⁻¹

(M − 1)!, UeXdV

M/ i?2 +mKmHiBp2 /2MbBiv 7mM+iBQM Q7 yk,j +M #2 r`Bii2M b

FY(y) = 1 −

 K+`Q+2HH BM i?2 bvbi2K- H#2H2/ 7`QK k iQ KX qBi?Qmi i?2 HQbb Q7 ;2M2`HBiv- H2i i?2 /2bB`2/ mb2` #2 BM/2t2/ rBi? RX h?2M i?2 iQiH BMi2`72`2M+2 PI_j `2+2Bp2/ 7`QK i?2 Qi?2` (K − 1) 72KiQ+2HH Q7 i?2 j@i? bm#+?MM2H +M #2 2tT`2bb2/ b

PI_j =

K k=2

εk,jPk,j10^ξ^/10yk,j/L(rk), UeXNV

r?2`2 ε^j Bb i?2 miBHBiv 7mM+iBQMX A7 i?2 bm#+?MM2H j Bb b2H2+i2/ iQ i`MbKBi /i-εj = 1c Qi?2`rBb2- εj = 0X

eXk Pmi;2 S`Q##BHBiv Q7 aBM;H2 62KiQ+2HH

6B`bi- r2 +QMbB/2` b+2M`BQ i?i QMHv 72KiQ+2HH R BM i?Bb `2- MQ Qi?2`

K+`Q+2HH Q` 72KiQ+2HHbX "v b2iiBM; i?2 `2[mB`2/ `2+2Bp2/ i?`2b?QH/ γth- i?2 Qmi;2 T`Q##BHBiv rBi? QM2 72KiQ+2HH +M #2 2tT`2bb2/ b

Poutage

**eXj Pmi;2 S`Q##BHBiv Q7 _M/QK *?MM2H a2H2+@**

iBQM S`BM+BTH2 7Q` 62KiQ+2HH rBi? hrQ@iB2` AM@

i2`72`2M+2

**eXjXR aBM;H2 AMi2`72`2M+2 b2 7Q` _M/QK ?MM2H a2H2+iBQM S`BM+BTH2**

6B`bi- r2 +QMbB/2` QM2 BMi2`72`2M+2 QMHv 7`QK i?2 #b2 biiBQM kX bbmK2 i?2 MQBb2 +M #2 M2;H2+i2/ UBX2X N0 = 0V BM i?Bb +b2X h?mb- i?2 Qmi;2 T`Q##BHBiv Q7

`M/QK b2H2+iBQM T`BM+BTH2 7Q` 72KiQ+2HH rBi? irQ@iB2` BMi2`72`2M+2 +M #2 r`Bii2M b Poutage,random

= S`[SIR1,j < γth]

= S`[ P1,j,m10^ξ^i,j^/10yi,j/L(ri)

εk,jPk,j,m10^ξ^k,j^/10yk,j/L(rk) < γth]

= S`[P1,j,m10^ξ^i,j^/10yi,j

L(ri) < γthεk,jPk,j,m10^ξ^k,j^/10yk,j

L(rk) ]

= S`[yi,j < γthεk,jPk,j,m

P1,j,m 10^{ξk,j−ξ1,j}¹⁰ L(r1) L(rk)yk,j]

= S`[yi,j < Ikyk,j], UeXRkV

r?2`2 I^k = γth

ε_k,jP_k,j,m

P_1,j,m 10^{ξk,j−ξ1,j}¹⁰ ^L_L^(r_(r_k¹⁾₎X

h?2 Qmi;2 T`Q##BHBiv Q7 `M/QK b2H2+iBQM T`BM+BTH2 7Q` 72KiQ+2HH mb2` R +M

#2 r`Bii2M b

Poutage,random,2fBSs

**eXjXk JmHiB@BMi2`72`2M+2 b2 7Q` _M/QK ?MM2H a2H2+iBQM S`BM+BTH2**

q2 +QMbB/2` i?2 irQ@iB2` BMi2`72`2M+2- i?2 BMi2`72`2M+2 7`QK iQiH K − 1 #b2 biiBQMb k iQ KX h?Bb K2Mb i?i i?2 72KiQ+2HH ?b iQ 7+2 i?2 irQ@iB2` BMi2`72`2M+2X AM i?b +b2- i?2 MQBb2 2z2+ib Kv #2 M2;H2+i2/X h?mb- i?2 Qmi;2 T`Q##BHBiv Q7 `M/QK b2H2+iBQM T`BM+BTH2 7Q` 72KiQ+2HH rBi? irQ@iB2` BMi2`72`2M+2 +M #2 r`Bii2M b

Poutage,random

= S`[P1,j,m10^ξ^i,j^/10yi,j

`M/QK b2H2+iBQM T`BM+BTH2 7Q` 72KiQ+2HH mb2` R +M #2 r`Bii2M b Poutage,random(r1, ξ1|r, ξ)

= 1 −

**eX9 Pmi;2 S`Q##BHBiv Q7 :BM@P`B2Mi2/ *?MM2H a2H2+iBQM S`BM+BTH2 7Q` 62KiQ+2HH rBi? hrQ@iB2`**

AMi2`72`2M+2

**eX9XR Pmi;2 S`Q##BHBiv Q7 JtBKH GBMF :BM *?MM2H 7Q`**

62KiQ+2HH rBi? hrQ@iB2` AMi2`72`2M+2

AM a2+iBQMX 9Xk- r2 /2p2HQT2/ i?2 ;BM@Q`B2Mi2/ b2H2+iBQM T`BM+BTH2 7Q` i?2 72K@

iQ+2HH bvbi2KbX h?2 ;BM@Q`B2Mi2/ b2H2+iBQM b+?2K2 BKb iQ mb2 i?2 bm#+?MM2Hb rBi?

?B;?2` HBMF ;BM 7Q` +QKKmMB+iBQMX h?2 ;BM@Q`B2Mi2/ b2H2+iBQM b+?2K2 QT2`i2b BM

/Bbi`B#mi2/ M/ miQMQKQmb KMM2`X 1+? 72KiQ+2HH +M b2H2+i i?2 bm#+?MM2Hb 7Q` i`MbKBbbBQM #v Bib2H7X q2 /2iBH i?2 ;BM@Q`B2Mi2/ b2H2+iBQM b+?2K2b BM a2+iBQMbX 9XkXR M/ 9XkXkX

aBM;H2 AMi2`72`2M+2 *b2 7Q` JtBKH GBMF :BM *?MM2H a2H2+iBQM

AM a2+iBQMX eXRXj- r2 FMQr i?2 T`Q##BHBiv /2MbBiv 7mM+iBQM 7Q` i?2 HBMF ;BM Q7

bm#+?MM2H Bb

fZ(z) = e^−z z^M⁻¹

(M − 1)!, UeXRdV

M/ i?2 +mKmHiBp2 /2MbBiv 7mM+iBQM Q7 bm#+?MM2H +M #2 r`Bii2M b

FZ(z) = 1 −

M−1 t=0

e^−zz^t

t! . UeXR3V

*QMbB/2` i?i i?2`2 `2 iQiH N bm#+?MM2HbX A7 r2 mb2 QMHv QM2 b2#+?MM2H 7Q`

i`MbKBbbBQM- r2 +?QQb2 i?2 ?B;?2bi HBMF ;BM +?MM2H #v i?2 ;BM@Q`B2Mi2/ b2H2+iBQM b+?2K2X AM i?Bb +b2- H2i Y = max(z1, z2, ..., zN) M/ z1, z2, ..., zN `2 BM/2T2M/2Mi

M/ B/2MiB+HHv /Bbi`B#mi2/ UBXBX/XVX h?2M i?2 +mKmHiBp2 /2MbBiv 7mM+iBQM Q7 Y +M #2 r`Bii2M b

FY(y) = P {z1 ≤ y, z2 ≤ y, ..., zN ≤ y}

= Fx₁,z₂,...,z_N(y, y, ..., y)

= N i=1

Fz_i(y)

= (1 −

M−1 t=0

e^−yy^t

t! )^N. UeXRNV

6B`bi- r2 +QMbB/2` BMi2`72`2M+2 QMHv 7`QK i?2 #b2 biiBQM k- M/ bbmK2 i?2 2z2+i Q7 MQBb2 +M #2 M2;H2+i2/X h?2 Qmi;2 T`Q##BHBiv Q7 KtBKH HBMF ;BM b2H2+iBQM T`BM+BTH2 7Q` 72KiQ+2HH rBi? irQ@iB2` BMi2`72`2M+2 +M #2 r`Bii2M b

Poutage,(1−st)

= S`[SIR_1,j < γth]

= S`[ P_1,j,m10^ξ^i,j^/10yi,j/L(ri)

εk,jPk,j,m10^ξ^k,j^/10yk,j/L(rk) < γth]

= S`[P1,j,m10^ξ^i,j^/10yi,j

L(ri) < γthεk,jPk,j,m10^ξ^k,j^/10yk,j

L(rk) ]

= S`[yi,j < γthεk,jPk,j,m KtBKH HBMF ;BM b2H2+iBQM T`BM+BTH2 7Q` 72KiQ+2HH R +M #2 r`Bii2M b

Poutage,(1−st)(r1, ξ1|r, ξ)

JmHiB@BMi2`72`2M+2 *b2 7Q` JtBKH GBMF :BM *?MM2H a2H2+iBQM

q?2M r2 +QMbB/2` i?2 BMi2`72`2M+2 7`QK Qi?2` K − 1 #b2 biiBQMb k iQ K-i?2 MQBb2 2z2+ib Kv #2 M2;H2+i2/ BM K-i?2 BMi2`72`2M+2 HBKBi2/ bvbi2KX h?mb- K-i?2 Qmi;2 T`Q##BHBiv Q7 KtBKH HBMF ;BM b2H2+iBQM T`BM+BTH2 7Q` 72KiQ+2HH rBi? irQ@iB2`

BMi2`72`2M+2 +M #2 r`Bii2M b Poutage,(1−st) KtBKH HBMF ;BM b2H2+iBQM T`BM+BTH2 7Q` 72KiQ+2HH mb2` R +M #2 r`Bii2M b

Poutage,(1−st)(r1, ξ1|r, ξ)

**eX9Xk Pmi;2 S`Q##BHBiv Q7 n@i? >B;?2bi GBMF :BM *?MM2H 7Q` 62KiQ+2HH rBi? hrQ@iB2` AMi2`72`2M+2**

6Q` 72KiQ+2HH bvbi2Kb- i?2 72KiQ+2HHb mb2 KmHiBTH2 bm#+?MM2Hb 7Q` b2`pBM; i?2B`

mb2`bX "v ;BM@Q`B2Mi2/ T`BM+BTH2- 72KiQ+2HHb +?QQb2 i?2 bm#+?MM2Hb rBi? ?B;?2` HBMF

;BM 7Q` +QKKmMB+iBQMX h?2`2 `2 iQiH N bm#+?MM2Hb BM 72KiQ+2HH bvbi2KX A7 r2 mb2 n bm#+?MM2Hb 7Q` i`MbKBbbBQM- r2 rBHH +?QQb2 i?2 ?B;?2bi n HBMF ;BM +?MM2H

#v i?2 ;BM@Q`B2Mi2/ b2H2+iBQM b+?2K2X AM i?Bb +b2- H2i Y = {y1, y₂, ..., yN} #2 i?2 Q`/2` biiBbiB+b Q7 BM/2T2M/2Mi M/ B/2MiB+HHv /Bbi`B#mi2/ UBXBX/XV `M/QK p`B#H2 7`QK (z1, z2, ..., zN) r?2`2 y1 ≤ y2 ≤ ... ≤ yN- i?M i?2 +mKmHiBp2 /2MbBiv 7mM+iBQM

M/ T`Q##BHBiv /2MbBiv 7mM+iBQM Q7 Yⁿ +M #2 r`Bii2M b

FY_n(y) =

N i=n

⎛

⎝ N i

⎞

⎠[FZ(y)]ⁱ[1 − FZ(y)]^N⁻ⁱ UeXk9V

fY_n(y) = N!

(N − n)!(n − 1)!fZ(y)[FZ(y)]^N⁻ⁿ[1 − FZ(y)]ⁿ⁻¹. UeXk8V aBM;H2 AMi2`72`2M+2 *b2 7Q` n@i? >B;?2bi GBMF :BM *?MM2H a2H2+iBQM

hrQ 72KiQ+2HH #b2 biiBQMb R M/ k `2 +QMbB/2`2/ BM i?Bb b+2M`BQ- M/ i?2 BMi2`72`2M+2 Bb QMHv +QK2 7`QK i?2 72KiQ+2HH kX h?2`2 `2 N bm#+?MM2Hb BM 72KiQ+2HH bvbi2K- M/ r2 +QMbB/2` 2+? bm#+?MM2H BM/BpB/mHHvX h?2 Qmi;2 T`Q##BHBiv Q7 i?2 n@i? ?B;?2bi HBMF ;BM bm#+?MM2H 7Q` 72KiQ+2HHb rBi? irQ@iB2` BMi2`72`2M+2 +M #2 r`Bii2M b

Poutage,(n−th)

= S`[SNR1,j < γth]

= S`[ P1,j,m10^ξ^i,j^/10yi,j/L(ri)

εk,jPk,j,m10^ξ^k,j^/10yk,j/L(rk) < γth]

= S`[P1,j,m10^ξ^i,j^/10yi,j

L(ri) < γthεk,jPk,j,m10^ξ^k,j^/10yk,j

L(rk) ]

= S`[yi,j < γthεk,jPk,j,m

P_1,j,m 10^{ξk,j−ξ1,j}¹⁰ L(r1) L(rk)yk,j]

= S`[yi,j < yk,jIk], UeXkeV

r?2`2 I^k = γth

ε_k,jP_k,j,m

P_1,j,m 10^{ξk,j−ξ1,j}¹⁰ ^L_L^(r_(r_k¹⁾₎X

G2i r = (r2, r₃, ..., rK) M/ ξ = (ξ₂, ξ₃, ..., ξK)X h?2M i?2 Qmi;2 T`Q##BHBiv Q7 n@i? ?B;?2bi HBMF ;BM b2H2+iBQM T`BM+BTH2 7Q` 72KiQ+2HH mb2` R +M #2 r`Bii2M b Poutage,(n−th)(r1, ξ1|r, ξ)

JmHiB@BMi2`72`2M+2 *b2 7Q` n@i? >B;?2bi GBMF :BM *?MM2H a2H2+iBQM h?2`2 `2 iQiH K #b2 biiBQMb BM i?Bb b+2M`BQ- M/ i?2 72KiQ+2HH R ?b iQ 7+2 i?2 BMi2`72`2M+2 7`QK K+`Q+2HH M/ 72KiQ+2HH k iQ KX h?2`2 `2 N bm#+?MM2Hb BM  72KiQ+2HH bvbi2KX q2 +QMbB/2` 2+? bm#+?MM2H BM/BpB/mHHvX h?2 Qmi;2 T`Q##BHBiv Q7 n@i? ?B;?2bi HBMF ;BM bm#+?MM2H 7Q` 72KiQ+2HH rBi? irQ@iB2` BMi2`72`2M+2 +M #2 r`Bii2M b n@i? ?B;?2bi HBMF ;BM b2H2+iBQM T`BM+BTH2 7Q` 72KiQ+2HH mb2` R +M #2 r`Bii2M b

Poutage,(n−th)(r1, ξ1|r, ξ)

q2 MHvx2 i?2 /QrMHBMF Qmi;2 T`Q##BHBiv Q7 i?2 P6.J@#b2/ 72KiQ+2HHb BM i?Bb +?Ti2`X q2 +QMbB/2` i?2 2t+HmbBp2 bT2+i`mK HHQ+iBQM M/ i?2 b?`2/ bT2+@

i`mK HHQ+iBQM b+?2K2b 7Q` i?2 72KiQ+2HHb M/ K+`Q+2HHX h?2 ;BM@Q`B2Mi2/ /Bb@

i`B#mi2/ +?MM2H b2H2+iBQM b+?2K2 M/ `M/QK b2H2+iBQM b+?2K2 `2 +QMbB/2`2/X q2

bbmK2 i?2 72KiQ+2HH HvQmi b b?QrM BM 6B;X jXRX h?2`2 `2 k9 72KiQ+2HHb `QmM/

i?2 +QMbB/2`2/ 72KiQ+2HH- M/ i?2 ;`QmT Q7 k8 72KiQ+2HHb Bb mMB7Q`KHv /Bbi`B#mi2/ BM K+`Q+2HH rBi? i?2 +Qp2`;2 Q7 8yy K2i2`bX h?2 b2T`iBQM /BbiM+2b #2ir22M 72KiQ@

+2HHb `2 d^sf = 20 K2i2`bX h?2 HBMF `2HB#BHBiv `2[mB`2K2Mi Bb H`;2` i?M NyWX h?2 MQKBMH bvbi2K T`K2i2`b `2 HBbi2/ BM h#H2 9XRX

eX8XR Pmi;2 S`Q##BHBiv BM 1t+HmbBp2 aT2+i`mK HHQ+iBQM

6m;m`2 eXR b?Qrb i?2 Qmi;2 T`Q##BHBiv Q7 /Bz2`2Mi +?MM2Hb rBi? /Bz2`2Mi

?B;?2bi HBMF ;BM ;BMbi i?2 72KiQ+2HH bm#@+?MM2H mb;2 `iBQ ρ rBi? i?2 2t+HmbBp2 bT2+i`mK HHQ+iBQM- r?2`2 dsf = 20 K2i2`bX h?Bb };m`2 b?Qrb i?2 Qmi;2 Q7 bm#+?M@

M2Hb rBi? /Bz2`2Mi ?B;?2bi HBMF ;BM BM i?2 72KiQ+2HH bvbi2KX AM i?2 2t+HmbBp2 bT2+i`mK

HHQ+iBQM b+?2K2- QMHv i?2 72KiQ+2HH@iQ@72KiQ+2HH BMi2`72`2M+2 2z2+i QM Qmi;2 T`Q#@

#BHBivX h?2 Qmi;2 T`Q##BHBiv BM+`2b2b r?2M i?2 bm#@+?MM2H mb;2 `iBQ BM+`2b2b

M/ BMi2`72`2 iQ Qi?2` 72KiQ+2HHb rBi? ?B;?2` T`Q##BHBivX AM i?Bb };m`2- i?2 bm#+?M@

M2H rBi? ?B;?2` i?2 HBMF ;BM +M 2Mbm`2 i?2 Qmi;2 T`Q##BHBivX A7 i?2 bm#+?MM2H rBi? i?2 HBMF ;BM Bb ?B;?2` i?M i?2 R8@i? ?B;?2` bm#+?MM2H- i?Qb2 bm#+?MM2Hb +M

在文檔中正交分頻多工毫微微細胞系統子載波分配與功率控制之研究 (頁 89-105)

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eXRXR am#@+``B2` HHQ+iBQM

eXRXk _/BQ *?MM2H

eXRXj aB;MH iQ AMi2`72`2M+2 M/ LQBb2 _iBQ

eXk Pmi;2 S`Q##BHBiv Q7 aBM;H2 62KiQ+2HH

eXj Pmi;2 S`Q##BHBiv Q7 _M/QK *?MM2H a2H2+@

iBQM S`BM+BTH2 7Q` 62KiQ+2HH rBi? hrQ@iB2` AM@

i2`72`2M+2

eXjXR aBM;H2 AMi2`72`2M+2 *b2 7Q` _M/QK *?MM2H a2H2+iBQM S`BM+BTH2

eXjXk JmHiB@BMi2`72`2M+2 *b2 7Q` _M/QK *?MM2H a2H2+iBQM S`BM+BTH2

eX9 Pmi;2 S`Q##BHBiv Q7 :BM@P`B2Mi2/ *?MM2H a2H2+iBQM S`BM+BTH2 7Q` 62KiQ+2HH rBi? hrQ@iB2`

AMi2`72`2M+2

eX9XR Pmi;2 S`Q##BHBiv Q7 JtBKH GBMF :BM *?MM2H 7Q`

62KiQ+2HH rBi? hrQ@iB2` AMi2`72`2M+2

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eX8XR Pmi;2 S`Q##BHBiv BM 1t+HmbBp2 aT2+i`mK HHQ+iBQM

eXRXR am#@+``B2` HHQ+iBQM

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